Task-Oriented Visualization Approaches for Landscape and ... - MDPI

International Journal of

Geo-Information Article

Task-Oriented Visualization Approaches for Landscape and Urban Change Analysis Jochen Schiewe

ID

Lab for Geoinformatics and Geovisualization (g2lab), HafenCity University Hamburg, Überseeallee 16, 20457 Hamburg, Germany; [email protected]; Tel.: +49-40-42827-5442 Received: 7 May 2018; Accepted: 20 July 2018; Published: 24 July 2018







Abstract: Approaches to landscape and urban change analysis are still far away from being fully automatic or operational. For this reason, the concept of Geovisual Analytics is proposed, combining computational and visual/manual processing steps. This contribution concentrates on the latter part with the overall goal of improving its usability. For this purpose, a classification of tasks is created, which often occur in the context of change analysis. This serves as the basis for the assignment of suitable map types to change processing results. Beyond this, it is pointed out that in many cases an appropriate pre-processing of data is imperative to preserve or enhance certain spatial relationships or characteristics for visualization. This is demonstrated using the example of data classification prior to choropleth mapping. Methods are described which allow the preservation of local extreme values, large value differences between adjacent polygons, clusters, and hot/cold spots. Finally, discussing future research and developments, it will be stressed that the importance of visual methods in the context of big data change analysis will continue to increase, which is due to the particular ability of maps to generalize and reduce complex data to a minimum. Keywords: change analysis; visualization; landscape analysis; geovisual analytics; data classification; choropleth mapping

1. Introduction The increasing volume and variety as well as the improved characteristics of spatio-temporal data allow for an increasingly detailed and complex change analysis in the context of urban and landscape research. In particular, the trend toward higher temporal resolutions and an open data policy like the Copernicus program supports more users with more detailed and informative data. However, approaches to analyzing this data are far away from being fully automatic or operational. For this reason, the concept of Geovisual Analytics is pursued, which follows a close linkage between computational and visual/manual processing steps [1]. Computational methods are able to describe results for various spatial effects such as heterogeneity or hot spots. On the other hand, maps and other visualization formats are still necessary in the analysis process [2]. First, visual representations for exploration and hypothesis building are well accepted in a multi-level approach. Second, in some cases, computational methods only give a global value for the entire scene being examined (such as the standard deviation of all attribute values or the global Moran’s index). Visualizations in turn allow for an impression or interpretation of the actual geographic distribution or arrangement (such as northwest gradients, islands, etc.) and other variations in space [3]. This paper focuses on the visual part of the Geovisual Analytics concept. Within this framework, the main contributions are as follows:

•

A classification of low-level tasks is developed that frequently occur in the course of landscape and urban change analysis. This not only takes into account remotely sensed and other categorical data (such as land use classes), but also quantitative data such as (geo-) statistical numbers.

ISPRS Int. J. Geo-Inf. 2018, 7, 288; doi:10.3390/ijgi7080288

www.mdpi.com/journal/ijgi

ISPRS Int. J. Geo-Inf. 2018, 7, 288

•

•

2 of 16

An assignment of suitable visualization methods or map types to the given change analysis tasks is developed. These comprehensive and generalizable recommendations follow the idea of using maps effectively and efficiently, thus improving the overall visual/manual processing part of the analysis. This aspect, together with the aforementioned task classification, follows the frequently expressed demand for “identifying a ‘right’ visualization type for the data/purpose/audience” [4] (p. 126), [3] (p. 130). It is stressed that not only the pure graphical representation, but also the corresponding pre-processing of the data is of great importance. This aspect is demonstrated by the step of data classification prior visualization by emphasizing the need for and development of an algorithmic solution to the problem of preserving spatial properties such as local extreme values or hot spots, which could be lost in maps with conventional data classification methods.

After briefly presenting related work in which this article is embedded (Section 2), Section 3 deals with the classification of low-level change analysis tasks. Based on this, Section 4 describes the guiding principles for the visualization and provides a detailed correspondence of the map types with the type of change analysis outputs. The solution for the aforementioned problem related to data classification is presented in Section 5. Finally, Section 6 summarizes the work and provides some hints for future research and development, especially taking into account the various aspects of future big data. 2. Previous Work As mentioned above, this paper focuses on the visualization component within a Geovisual Analytics concept. According to Keim et al. [5], Visual Analytics “combines automated analysis techniques with interactive visualizations for an effective understanding, reasoning and decision-making on the basis of very large and complex datasets”. As a subdomain, Geovisual Analytics stresses the use of geographical data and analysis methods in an interdisciplinary context [1]. A more detailed discussion of this domain, including its relation to Geovisualization or Cartography, is given in [6]. There are numerous case studies focusing on the change analysis of urban or landscape elements. Because most of them rely on remotely sensed data, change analysis is often restricted to comparing the respective classes based on the pixel or segment level of two or more scenes. More advanced methods are based on object-oriented data modeling concepts [7,8]. In order to integrate more detailed features such as patterns or auxiliary information (like population numbers), quantitative data should also be taken into account [9]. What is missing is an abstract classification of basic tasks that occur in the process of change analysis and allow a close linkage to the visualization of results. This paper uses existing classifications of general tasks related to geographic data as a basis for deriving the specific tasks that occur in the context of spatial change analysis. Firstly, the concept of the Map Use Cube by MacEachren and Kraak [10] is taken into account, which considers the parameters’ information content, user expertise and interactivity of the map. The approach of Peuquet [11] uses the simple spatio-temporal questions “what”, “when” and “where,” for which normally two aspects are given and the missing third is sought. The task taxonomy proposed by Andrienko and Andrienko [12] describes elementary and synoptic tasks, which also include several comparison tasks, some of which are used and modified for the scope of this contribution. Many case studies have been published regarding the visualization of spatial changes, but a well-accepted and abstract classification scheme that provides recommendations for effective and efficient display is not known [4]. There are some theoretical works that combine visualizations of categorical changes with computational techniques, following the idea of Geovisual Analytics [13,14]. Other authors developed software packages that enable interactive change analysis [15–17]; however, a structured classification of “simple” map types for the various types of change analyses is not given here either.

ISPRS Int. J. Geo-Inf. 2018, 7, 288

3 of 16

  3. ClassificationISPRS Int. J. Geo‐Inf. 2018, 7, x FOR PEER REVIEW  of Change Analysis Tasks

3 of 17 

In order to 3. Classification of Change Analysis Tasks  be able to assign suitable visualization types (Section 4), a well-structured classification of low-level tasks isIn  required, which often the context of change analysis. In 4),  thea following, order  to  be  able  to occurs assign  in suitable  visualization  types  (Section  well‐structured  it is assumed that the change analysis includes at least two data sets consisting of more than one classification of low‐level tasks is required, which often occurs in the context of change analysis. In  reference regionthe following, it is assumed that the change analysis includes at least two data sets consisting of more  (represented by “Canadian provinces” in most of the following examples). Following than one reference region (represented by “Canadian provinces” in most of the following examples).  the general classification of map use tasks [10], the focus here is on presentation tasks, Following the general classification of map use tasks [10], the focus here is on presentation tasks,  i.e., the communication of already interpreted data and information. In contrast, exploration tasks i.e., the communication of already interpreted data and information. In contrast, exploration tasks  want to create or verify hypotheses. A conceptual classification framework is proposed that uses the want to create or verify hypotheses. A conceptual classification framework is proposed that uses the  triad model of spatiotemporal analysis introduced by Peuquet [11] as basis. This model breaks down triad  model  of  spatiotemporal  analysis  introduced  by  Peuquet  [11]  as  basis.  This  model  breaks  down  tasks into their components “What”, “Where” and “When”, two of which are generally specified and tasks into their components “What”, “Where” and “When”, two of which are generally specified and  asked for the third. For each of the combinations (e.g., “What” as output clause), possible changes’ asked for the third. For each of the combinations (e.g., “What” as output clause), possible changes’  features (e.g., existential change) are compiled. For each change feature, possible outcomes (e.g., in the features (e.g., existential change) are compiled. For each change feature, possible outcomes (e.g., in  case of “existential change”: gain, loss or none) and exemplary questions for illustration purposes are the case of “existential change”: gain, loss or none) and exemplary questions for illustration purposes  are listed. This follows the approach of Andrienko and Andrienko [12] who developed a taxonomy  listed. This follows the approach of Andrienko and Andrienko [12] who developed a taxonomy for for elementary and synoptic spatio‐temporal tasks; however, they did not explicitly address change  elementary and synoptic spatio-temporal tasks; however, they did not explicitly address change tasks. tasks.  The most complex component, the “What” clause, describes the thematic component in the The  most  complex  component,  the  “What”  clause,  the the thematic  component  context of change analysis. Table 1 summarizes possible features anddescribes  focuses on “What” clause asin  the  context of change analysis. Table 1 summarizes possible features and focuses on the “What” clause  output components only. In addition, it is of course possible that “What” input clauses also contain as output components only. In addition, it is of course possible that “What” input clauses also contain  non-change features (i.e., existence, class, absolute or relative value). non‐change features (i.e., existence, class, absolute or relative value). 

Table 1. Characteristics of “What” output clauses. Table 1. Characteristics of “What” output clauses. 

Change Feature    Change Feature

Feature Value  Feature Value

1a  1a Existential Existential change  change

gain/loss/none gain/loss/none 

1b 1b  Unspecified class change Unspecified class 

change  1c 1c  Specified class change (from/to) Specified class  change (from/to) 



  yes/no

yes/no 

Example Change Questions: When ⊕ Where  Example Change Questions: When ⊕ What Where ➲ What  What kind of existential change of forest areas  What kind of existential change of forest areas can be observed in Canadian provinces can be observed in Canadian provinces  between 1950 and 2000? between 1950 and 2000?  What class changes can be observed in What class changes can be observed in  Canadian provinces between 1950 and 2000?

Canadian provinces between 1950 and 2000? 

Is there any class change between forest and urban in Canadian provinces between 1950 Is there any class change between forest and  and 2000?

urban in Canadian provinces between 1950 

What is the population change in Canadian and 2000?  provinces between 1950 and 2000? What is the population change in Canadian  What kind of population change can be OR: provinces between 1950 and 2000?  1d observed in Canadian provinces between increase/decrease/constant   Change of absolute value 1950 and 2000? What kind of population change can be  OR: 1d  OR:  What maximum population change in observed in Canadian provinces between 1950  Change of  increase/decrease/constant  Canadian provinces can be observed between and 2000?  1950 and 2000? absolute value    OR:  What maximum population change in  What is the change of population density in   Canadian provinces can be observed between  Canadian provinces between 1950 and 2000? 1950 and 2000?  What kind of change of population density OR: 1e can be observed in Canadian provinces What is the change of population density in  increase/decrease/constant Change of relative value between 1950 and 2000? Canadian provinces between 1950 and 2000?  OR: What maximum change of population density   What kind of change of population density  can be observed in Canadian provinces 1e  OR:  can be observed in Canadian provinces  between 1950 and 2000?

Change of relative  value   

increase/decrease/constant  between 1950 and 2000?  OR:  What maximum change of population density    Cardinal data are divided into absolute and relative values (1d and 1e, resp.), as this affects can be observed in Canadian provinces  follow-up visualization (Chapter 4). In both cases, a changebetween 1950 and 2000?  value may include the actual value

difference, but also just a trend (increase, decrease, constant), local or global extreme values (maximum, minimum), or other statistical parameters such as mean or standard deviation.

ISPRS Int. J. Geo-Inf. 2018, 7, 288

4 of 16

It should be noted that the “What” output clause could also integrate the important aspect of analyzing changes in patterns such as hot or cold spots, clusters, or neighboring gradients. Using hot and cold spots as an example, all types of change features are possible, for example:

•

Existential change: “What kind of existential change of hot spots can be observed in Canadian ISPRS Int. J. Geo‐Inf. 2018, 7, x FOR PEER REVIEW  provinces between 1950 and 2000?”  

3 of 17 

•

Unspecified class changes: “What changes in hot spot classes (such as very significant, significant, 3. Classification of Change Analysis Tasks  etc.) can be observed in Canadian provinces between 1950 and 2000? • Specified change: “Inassign  Canadian provinces between types  1950 and 2000, 4),  is there any change In  order class to  be  able  to  suitable  visualization  (Section  a  well‐structured  between very significant hot spots (Getis Ord Index z-score above 2.0) and very significant cold classification of low‐level tasks is required, which often occurs in the context of change analysis. In  spots (Getis Ord Index z-score below −2.0)?” the following, it is assumed that the change analysis includes at least two data sets consisting of more  • than one reference region (represented by “Canadian provinces” in most of the following examples).  Change in relative value: “What is the change in Getis Ord Index z-core for describing hot spots inFollowing the general classification of map use tasks [10], the focus here is on presentation tasks,  Canadian provinces between 1950 and 2000?” i.e., the communication of already interpreted data and information. In contrast, exploration tasks  All examples given in Table 1 ask for a bi-temporal comparison between two given dates. want to create or verify hypotheses. A conceptual classification framework is proposed that uses the  Of course, it is possible to extend these questions to multi-temporal scenarios, for example: triad  model  of  spatiotemporal  analysis  introduced  by  Peuquet  [11]  as  basis.  This  model  breaks  down  • tasks into their components “What”, “Where” and “When”, two of which are generally specified and  Existential change: “What kind of existential changes in lakes can be observed in Canada in 1950, asked for the third. For each of the combinations (e.g., “What” as output clause), possible changes’  1960, 1970 and 1980?” • features (e.g., existential change) are compiled. For each change feature, possible outcomes (e.g., in  Change in absolute values: What is the average population change in Canadian provinces between the case of “existential change”: gain, loss or none) and exemplary questions for illustration purposes  1950 and 2000 in 10-year-increments? are listed. This follows the approach of Andrienko and Andrienko [12] who developed a taxonomy  The “Where” clause (Table 2) describes the spatial component of the change analysis. It should be for elementary and synoptic spatio‐temporal tasks; however, they did not explicitly address change  noted that “Where” explicitly asks only for a position or a position change. Other geometric attributes tasks.  such as size or shape can component,  be used in addition to theclause,  position, but, in the  these cases, they are normally The  most  complex  the  “What”  describes  thematic  component  in  the  treated as absolute or relative thematic values. The following example, looking for a change in area context of change analysis. Table 1 summarizes possible features and focuses on the “What” clause  size, is illustrating this: “Where in Canada can we observe an increase in forest areas between 1950 as output components only. In addition, it is of course possible that “What” input clauses also contain  and 2000?” Often, the triad model requires “Where” clauses in the input and output (for example: 2c). non‐change features (i.e., existence, class, absolute or relative value).  Table 2. Characteristics of “Where” output clauses. Table 1. Characteristics of “What” output clauses. 

Example Change Questions: When ⊕ Where  Example Change Questions: When ⊕ What ➲ What  Where What kind of existential change of forest areas  1a  2a In which Canadian provinces did the OR gain/loss/none  can be observed in Canadian provinces  Region population change between 1950 and 2000? Existential change  between 1950 and 2000?  1b  2b In which Canadian cities did the population What class changes can be observed in  OR Unspecified class    Location change between 1950 and 2000? Canadian provinces between 1950 and 2000?  change  Which movements of grassland can be 1c  2c Specified class  yes/no  urban in Canadian provinces between 1950  Canadian provinces? change (from/to)  and 2000?  What is the population change in Canadian  The “When” clause (Table 3) describes the temporal component of the change analysis. provinces between 1950 and 2000?    Most output clauses ask for dates or time periods (duration, time interval, and time series) that What kind of population change can be  1d  OR:  relate to specified thematic and/or geometric events or changes. Frequently, “When” clauses appear observed in Canadian provinces between 1950  increase/decrease/constant  in bothChange of  the input and output components of the task (3a to 3d). Questions about actual changes in and 2000?  OR:  3e) can also be described with the next order time type (e.g., time absolute value  features (such a  change in duration; What maximum population change in  a change in date is equal to  a duration or time interval). Canadian provinces can be observed between  1950 and 2000?  What is the change of population density in  Canadian provinces between 1950 and 2000?    What kind of change of population density  1e  OR:  can be observed in Canadian provinces  Change of relative  increase/decrease/constant  between 1950 and 2000?  value    OR:  What maximum change of population density    can be observed in Canadian provinces  Change Feature  Change Feature  

Feature Value  Feature Value

are listed. This follows the approach of Andrienko and Andrienko [12] who developed a taxonomy  3 of 17  for elementary and synoptic spatio‐temporal tasks; however, they did not explicitly address change  tasks.  Tasks  The  most  complex  component,  the  “What”  clause,  describes  the  thematic  component  in  the  suitable  visualization  types context of change analysis. Table 1 summarizes possible features and focuses on the “What” clause  (Section  4),  a  well‐structured  ISPRS Int. J. Geo-Inf. 2018, 7, 288 5 of 16 as output components only. In addition, it is of course possible that “What” input clauses also contain  ired, which often occurs in the context of change analysis. In  non‐change features (i.e., existence, class, absolute or relative value). 

W   

ange analysis includes at least two data sets consisting of more   by “Canadian provinces” in most of the following examples).  Table 3. Possible characteristics of “When” output clauses. Table 1. Characteristics of “What” output clauses.  n of map use tasks [10], the focus here is on presentation tasks,  Example Change Questions: When ⊕ Where  Example Change Questions: Where ⊕ erpreted data and information. In contrast, exploration tasks  Change Feature    Feature Value  Change Feature Feature Value What ➲ What  When conceptual classification framework is proposed that uses the  What kind of existential change of forest areas  In which year between 1940 and 2000 was the 1a  model  breaks  down  3a This  troduced  by  Peuquet  [11]  as  basis.  maximum population number reached in gain/loss/none  can be observed in Canadian provinces  Date Existential change  Where” and “When”, two of which are generally specified and  Canadian provinces? between 1950 and 2000?  mbinations (e.g., “What” as output clause), possible changes’  How long did it take to double the 3b 1b  What class changes can be observed in  Duration population in Canadian provinces since 1900? ompiled. For each change feature, possible outcomes (e.g., in  Unspecified class    Canadian provinces between 1950 and 2000?  In which decade between 1900 and 2000 was oss or none) and exemplary questions for illustration purposes  3c change  the maximum increase in population in 1c  Is there any class change between forest and  Time-interval (bi-temporal) f Andrienko and Andrienko [12] who developed a taxonomy  Canadian provinces? Specified class  yes/no  urban in Canadian provinces between 1950  mporal tasks; however, they did not explicitly address change 

In which successive years can we observe an and 2000?  increase and then a decrease in population What is the population change in Canadian  numbers in Canadian provinces within the provinces between 1950 and 2000?  entire time span between 1900 and 2000? mmarizes possible features and focuses on the “What” clause    What kind of population change can be  What is the time period difference to increase OR:  n, it is of course possible that “What” input clauses also contain  3e 1d  observed in Canadian provinces between 1950  the population about 10% in the neighboring Change in duration Change of  increase/decrease/constant  countries compared to France? ss, absolute or relative value).  and 2000?  absolute value    OR:  What maximum population change in    aracteristics of “What” output clauses.  Canadian provinces can be observed between  Finally, it should be noted that, for all “W” combinations, there are also exceptions from the 1950 and 2000?  Example Change Questions: When ⊕ Where  standard syntax that two given components require. For example, the following task, following the Value  What is the change of population density in  syntax “When ➲ What  What ⊕ Where”, has only one input and two output components: “How has the Canadian provinces between 1950 and 2000?    position and health index of forest areas in Canadian provinces changed between 1950 and 2000?” What kind of existential change of forest areas  What kind of change of population density  1e  OR:  none  can be observed in Canadian provinces  can be observed in Canadian provinces  increase/decrease/constant  4. VisualizingChange of relative  Outputs of Change Analysis between 1950 and 2000?  between 1950 and 2000?  value    OR:  What maximum change of population density  4.1. Guiding Principles   What class changes can be observed in  can be observed in Canadian provinces  name (s)>  Canadian provinces between 1950 and 2000?  between 1950 and 2000?  Apart from the typical quality requirements such as accuracy and legibility, the overall guiding

change (from/to) 

3d Time series he  “What”  clause,  describes  the (multi-temporal) thematic  component  in  the 

principle for the development of visual elements should be usability, i.e., the provision of effective Is there any class change between forest and  and efficient solutions for the analysis of changes. Satisfaction, the third aspect of usability according o  urban in Canadian provinces between 1950  to its definition [18], is neglected in the remainder of this paper. The need for further research and and 2000?  development in this context is expressed, among others, in the research agendas of the International What is the population change in Canadian  Cartographic Association (e.g., [19]). provinces between 1950 and 2000?  nce>  A major goal of maps is a reduction of complexity and a focus on relevant change What kind of population change can be  behavior. Based on common cartographic and cognitive concepts and principles (e.g., [20–22]), observed in Canadian provinces between 1950  se/constant  a couple of detailed recommendations for this specific change analysis case can be derived. and 2000?  These recommendations relate to the actual graphical (and possibly interactive) design, but in some What maximum population change in  ference>  cases also to the data processing stage (see Section 5): Canadian provinces can be observed between 

1950 and 2000?  • A rather fundamental aspect relates to the question of whether spatial context (e.g., spatial What is the change of population density in  distribution of changes in the scene) is relevant for the specific application. This leads either to the Canadian provinces between 1950 and 2000?  need for cartographic visualization (either as a single map or as linked views), or to the explicit ce >  What kind of change of population density  abandonment of a map-like representation. can be observed in Canadian provinces  • The visualization should be tailored to the tasks or questions that relate to the specific application. se/constant  between 1950 and 2000?  This requires a predetermined classification of tasks that often occur in the context of change analysis. What maximum change of population density  This task-oriented approach is becoming increasingly apparent as the complexity of applications ference>  can be observed in Canadian provinces  increases and workflows should be still effective and efficient. between 1950 and 2000?  • In terms of efficiency, explicit visualization of changes should be made where possible. For example, instead of displaying two maps of different points in time side-by-side and asking the users to detect changes themselves, changes should be explicitly displayed in a difference map in order to free human resources for interpretation tasks.

ISPRS Int. J. Geo-Inf. 2018, 7, 288

•

• •

6 of 16

More technically, the visualization should minimize eye-movements. During these movements (called saccades), cognitive reception of information is not possible and, even worse, a typical loss of exact locations can occur as one moves from one map to another. One should also consider an appropriate degree of interaction functionalities—again, to allow efficient use. In this context, the tools should also enable users to save and annotate on findings for further interpretation and comparison [19] (p. 38).

Taking into account the aforementioned principles, the possible output feature values from Table 1 to Table 3 are taken up in the following and assigned to suitable map types—differentiating between bi-temporal and multi-temporal applications (Sections 4.2 and 4.3, resp.). Basically, polygons are assumed as reference geometries. Of course, each of the following elementary maps, which show only the output result, can also be supplemented by input components for a better understanding. 4.2. Recommendations for Representing Bi-Temporal Changes Having two maps of different times side by side, we face the problem of various eye movements and the need for further cognitive work by the user to separate changes from non-changes. Therefore, it is claimed here that the difference map is the preferred type in the case of bi-temporal changes because it allows a fast and explicit view on changes. • More technically, the visualization should minimize eye-movements. During these movements More technically, the visualization should minimize iseye-movements. During movements (called saccades), cognitive reception of information not possible and, eventhese worse, a typical With respect to the “What” output clauses,• maps have to distinguish between at (called saccades), cognitive reception information is not and,data even worse, anominal typical loss of exact locations can occur as oneofmoves from one mappossible to another. loss of exact locations can occur as one moves fromofone map to another. • One should also consider an appropriate degree interaction functionalities—again, to allow (categorical) or metric (cardinal) levels of measurement (Table 4). In the first case (4a to 4c), symbol • One should also consider an appropriate degree of interaction functionalities—again, to allow efficient use. efficient use. the tools should also enable users to save and annotate on findings for further • In this context, maps should generally be used to depict the• differences [20]. Assuming polygons as reference In this context,and thecomparison tools should[19] also interpretation (p.enable 38). users to save and annotate on findings for further interpretation and comparison [19] (p. 38). Taking the into account the aforementioned principles, the possible output featureof values from geometries, areal symbol maps (mosaic maps)Tables are first choice when the number possible Taking theinaforementioned principles, feature values from 1 to 3into areaccount taken up the following and assignedthe to possible suitable output map types—differentiating Tables 1 bi-temporal to 3 are taken in the following and assigned to 4.2 suitable map types—differentiating between and up multi-temporal applications (Sections and 4.3, resp.). Basically, polygons output values is limited and can be represented by a small amount of colors filling the polygons between bi-temporal and multi-temporal applications (Sections 4.2 andelementary 4.3, resp.). Basically, polygons are assumed as reference geometries. Of course, each of the following maps, which show are assumed as reference Of course, each of thecomponents following elementary which show the output result, cangeometries. also be supplemented by input for a bettermaps, understanding. (preferably with associative meanings such asonly green forcanincrease, red forcomponents decrease, and grey for only the output result, also be supplemented by input for a better understanding. Recommendations for Representing Bi-Temporal Changes constant behavior; 4a). On the other hand, if the 4.2. number offoroutput valuesChanges is too large or more than one 4.2. Recommendations Representing Bi-Temporal Having two maps of different times side by side, we face the problem of various eye movements Having two maps ofcognitive differentwork timesby side side, we face the problem of non-changes. various eye movements and or the need for further theby user to separate changes from Therefore, value is required per polygon, point like symbols (micro) diagrams should be used. An example of and need for further cognitive work by is thethe user to separate changes Therefore, it is the claimed here that the difference map preferred type in the from case non-changes. of bi-temporal changes it is claimed herea that the explicit differenceview mapon is changes. the preferred type in the case of bi-temporal changes because it allows fast and this is an unspecified land cover class change (4b), where many combinations of from and to classes because it allows explicit viewclauses, on changes. With respectatofast theand “What” output maps have to distinguish between data at nominal With respect to the “What” output maps have to distinguish between at nominal (categorical) or metric (cardinal) levels ofclauses, measurement (Table 4). In the first case (4adata to 4c), symbol are possible. A specified class change might consist only of a particular tuple of classes (such as change (categorical) metric (cardinal) of measurement (Table 4). Assuming In the first polygons case (4a toas 4c), symbol maps shouldorgenerally be usedlevels to depict the differences [20]. reference maps should generally be used to depict the differences [20]. Assuming polygons as reference geometries, areal symbol maps (mosaic maps) are the first choice when the number of possible output from forest to urban; 4c). A larger number of class combinations canmaps) bearevisualized using apossible linked geometries, arealand symbol (mosaic the first choice whenfilling the number of output view values is limited can maps be represented by a small amount of colors the polygons (preferably values is limitedmeanings and can be represented by increase, a small amount of colors filling thefor polygons (preferably with associative such as green for red for decrease, and grey constant behavior; with a change matrix (Figure 1). with associative meanings such as green for increase, red for decrease, and grey for constant behavior; 4a). On the other hand, if the number of output values is too large or more than one value is required ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW

6 of 17 6 of 17

4a). On the other hand, the number outputdiagrams values is should too largebeorused. more An thanexample one value required per polygon, point likeif symbols or of (micro) ofisthis is an per polygon,land point like class symbols or (micro) diagrams be used.ofAn example this is are an unspecified cover change (4b), where manyshould combinations from and toofclasses unspecified land cover class change (4b), where many combinations ofoffrom and(such to classes are possible. A specified class change might consist only of a particular tuple classes as change possible. A to specified class might consist of a particular of classes (such as change from forest urban; 4c). A change larger number of classonly combinations can betuple visualized using a linked view from aforest to urban; A larger with change matrix4c). (Figure 1). number of class combinations can be visualized using a linked view with a change matrix (Figure 1).

Table 4. Visualization of “What” output clauses (compare classification in Table 1). Visualization

Change Feature

Example Change Question

Table 4. Visualization of “What” output clauses (compare classification in Table 1). Table 4. Visualization of “What” output clauses (compare classification in Table 1).

Change Change Feature Feature

Example Change Map Type Example Change Question Question

Map Type Map Type

4a Existential change

What kind of existential change of 4a forest areas can be observed inExistential 4a Existential Canadian provinces between 1950 change change and 2000?

What kind of existential What kind existential change of of forest areas change of forest areas Mosaic map can be observed in Mosaic map Mosaic map can be observed in Canadian provinces Canadian provinces between 1950 and 2000? between 1950 and 2000?

4b Unspecified class change

4b What class changes can be observed 4b Unspecified Unspecified in Canadian provinces between class change class change 1950 and 2000?

What class changes can Symbol Whatbeclass changes observed in can Symbol map/micro be observed in Symbol map/micro Canadian provinces map/micro diagrams Canadian provinces between 1950 and 2000? diagrams diagrams between 1950 and 2000?

Visualization Example Visualization Example Example

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW

4c Specified class change (from/to)

Is there any class change between 4c Specified forest and urban in Canadianclass change (from/to) provinces between 1950 and 2000?

4d Change of absolute value

4e Change of

7 of 17

(Binary) Is there any class mosaic map (Binary) mosaic change between forest map (possibly and urban in Canadian (possibly linked with linked with provinces between 1950 change matrix) change and 2000? matrix) (1) What is the population change in Canadian provinces between 1950 and 2000?

(Bi-polar) Proportional Symbol map

(2) What kind of population change can be observed in Canadian provinces between 1950 and 2000?

Mosaic map

(1) What is the change of population density in Canadian provinces between 1950 and 2000?

(Bi-polar) Choropleth map

rf. to 4a

What is the population change in Canadian provinces between 1950 and 2000?

4d Change of 2018, 7, 288 ISPRS Int. J. Geo-Inf. absolute value

(Bi-polar) Proportional Symbol map 7 of 16

(2) What kind of Table 4. Cont. Is there any class population change can 4c Is there any class change between forest 4c Mosaic map Specified change between forest and urban in Canadian Specified be observed in class change and urban in Canadian change provinces between 1950 Change Feature Example Change Question class (from/to) provinces between 1950 and 2000? Map Type (from/to) Canadian provinces and 2000? between 1950 and(1)2000? (1) ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW

What is the population change in Canadian provinces between 1950 4d (1) and 2000? 4d of Change

4d What Change of absolute value

4e Change of relative value

7 of 17 7 of 17

(Binary) (Binary) mosaic map mosaic map (possibly (possibly Visualization linked with linked with change change matrix) matrix)

rf. to 4a Example

(1)

(Bi-polar) What is the population (Bi-polar) Proportional (Bi-polar) What is the population Proportional change in Canadian Proportional change in Canadian Symbol map map provinces between 1950 Symbol provinces andbetween 2000? 1950 and 2000?

Change absoluteof (Bi-polar) is the change of (2) absolute value What(2) kind of (2) value What kind of can Choropleth population density in population change What kind of population change can population change can beMosaic observed inmap be observed in be observed in Canadian provincesmap Canadian Canadian provinces provinces Canadian provinces between 1950 and 2000? between 1950 and 2000? between 1950 and 2000? between 1950 and 2000?

Symbol map

Mosaic map Mosaic map

rf. to 4a

rf.rf.to 4a to 4a

(1)

(1)change of (1) (Bi-polar) What is the (Bi-polar) What is the density change in of Choropleth population What is the change of population Choropleth population density in (Bi-polar) map map CanadianChoropleth provinces (2) density in Canadian provinces 4e map Canadian provinces between 1950 and 2000? between 1950 and 2000? 4e of between 1950 and 2000? Change What kind of change of

4e Change of relative value

Change of relative value

(2)

relative value What kind(2) of change of population density (2) can What kind of change of population density can Mosaic map population density be observed in can What kind of change be observed in of population be observed in Canadian provinces density can be observed in Mosaic map Canadian between 1950provinces and 2000? Canadian between 1950 and 2000? Canadianprovinces provinces between 1950 and 2000? between 1950 and 2000?

Mosaic map Mosaic map

rf. to 4a rf. to 4a

rf. to 4a

rf. to 4a

Figure 1. Linked view between change matrix and binary mosaic map for depicting various Figure 1. Linked view between change matrix binary from mosaic depicting various combinations of class changes (related task: “Is thereand any change anymap classfor to class C in Canadian combinations of class changes (related task: “Is there any change from any class to class C in Canadian provinces between 1900 and 2000?”). provinces between 1900 and 2000?”).

In the case of metric data, absolute and relative values must be differentiated for visualization In theresulting case of metric data, absolute and relative values must be differentiated for visualization purposes, in proportional symbol maps (4d) or choropleth maps (4e) [20]. If the value purposes, resulting proportional symbol maps (4d)(increase, or choropleth mapsnone), (4e) [20]. If the value difference as such isinnot wanted, but only the trend decrease, one can refer to difference as such is not wanted, but only the trend (increase, decrease, none), one can refer to

Figure 1. Linked view between change matrix and binary mosaic map for depicting various Figure 1. Linked view between change matrix and binary mosaic map for depicting various combinations of class changes (related task: “Is there any change from any class to class C in Canadian combinations of class changes (related task: “Is there any change from any class to class C in Canadian provinces between 1900 and 2000?”). provinces between 1900 and 2000?”).

In the case of metric data, absolute and relative values must be differentiated for visualization In the case of metric data, absolutesymbol and relative be differentiated visualization purposes, resulting in proportional maps values (4d) ormust choropleth maps (4e)for [20]. If the value purposes, resulting in proportional symbol maps (4d) or choropleth maps (4e) [20]. If the value difference as such is not wanted, but only the trend (increase, decrease, none), one can refer to difference as such is not wanted, but only the trend (increase, decrease, none), one can refer to existential change maps (4a). If also extreme values shall be highlighted, additional symbols (such as flags) can be used. With respect to the “Where” output clauses (Table 5), a typical map based task is to represent regions or locations that meet certain thematic and/or geometric conditions (5a and 5b). In order to depict translations or movements of objects, origin-destination flow maps [23] are an appropriate choice in which vectors represent the distance and orientation of the movement (5c). Depending on the complexity, also the objects under consideration (such as grassland regions in example 5c) can be visualized together with the vectors for clarification purposes. It should be noted that curved arrows, in contrast to the recommendations for origin-destination flow maps [23], do not make sense because an accurate description of the direction of movement is lost.

ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW

8 of 17 8 of 17 8 of 17

existential change maps (4a). If also extreme values shall be highlighted, additional symbols (such as existential change maps (4a). If also extreme values shall be highlighted, additional symbols (such as flags) can be used. maps (4a). If also extreme values shall be highlighted, additional symbols (such as existential change flags) can be used. respect the “Where” output clauses (Table 5), a typical map based task is to represent flags)With can be used.to With respect to the “Where” output clauses (Table 5), a typical map based task is to represent regions or locations meet certain thematic and/or geometric conditions (5a and order to With to that the “Where” output clauses (Table 5), a typical map based task5b). is toIn regions or respect locations that meet certain thematic and/or geometric conditions (5a and 5b). Inrepresent order to depict translations or movements of objects, maps [23] are an regionstranslations or locationsorthat meet certain thematicorigin-destination and/or geometricflow conditions (5a and 5b).appropriate In order to depict movements of objects, origin-destination flow maps [23] are an appropriate choice in which vectors represent the distanceorigin-destination and orientation offlow the movement (5c). Depending on depict translations or movements of objects, maps [23] are an appropriate choice in which vectors represent the distance and orientation of the movement (5c). Depending on the complexity, the objects under (such as grassland regions in (5c). example 5c) can on be choice in whichalso vectors represent the consideration distance and orientation of the movement Depending the complexity, also the objects under consideration (such as grassland regions in example 5c) can be visualized together with the vectors forconsideration clarification purposes. It shouldregions be notedinthat curved arrows, the complexity, also the objects under (such as grassland example 5c) can be visualized together with the vectors for clarification purposes. It should be noted that curved arrows, in contrast to the recommendations for origin-destination flow maps [23], do not make sense because visualized with the vectorsfor fororigin-destination clarification purposes. should bedo noted that curved arrows, in contrast together to the recommendations flow It maps [23], not make sense because an accurate description of the direction of movement is lost. in contrast the recommendations for origin-destination flow maps [23], do not make sense because an accurateto description of the direction of movement is lost. an accurate description of the direction of movement is lost.

ISPRS Int. J. Geo-Inf. 2018, 7, 288

8 of 16

Table 5. Visualization of “Where” output clauses (compare classification in Table 2).

Table 5. Visualization of “Where” output clauses (compare classification in Table 2). Table 5. Visualization of “Where” output clauses (compare classification in Table 2).

Visualization

Change Feature

Example Change Question

5a Region

In which Canadian provinces did the population change between 1950 and 2000?

5. Visualization of “Where” output clauses (compare classification in Table 2). Visualization Change Table Example Change Visualization Change Example Change Map Type Example Feature Question Map Type Example Visualization Change Example Change Feature Question Map Type Example Feature Question Map Type Example

5a 5a Region 5a Region Region

In which Canadian In which Canadian provinces did the

(Binary)

In which Canadian (Binary) provinces did the (Binary) mosaic mapmosaic map population change (Binary) provinces did the population change between 1950 and 2000? population change between 1950 and 2000?

mosaic map mosaic map

In which Canadian cities In which Canadian cities did the population In which Canadian cities did the population

(Binary) (Binary)

between 1950 and 2000?

5b Location

5c Trans-lation

In which Canadian cities did the population change between 1950 and 2000?

5b 5b Location 5b Location Location

Point map change 1950 map and (Binary) did the between population (Binary) Point Point map change between 1950 and 2000? change between 1950 and 2000? 2000?

Point map

Which relocations of Which relocations of Origingrassland can be of 5c Which relocations Origingrassland can be 5c desti-nation observed TransOrigingrasslandbetween can be 1950 5c desti-nation observed between 1950 Transflow maps and 2000 in Canadian lation desti-nation observed between 1950 TransOrigin-desti-nation flow maps flow maps and 2000 in Canadian lation provinces? flow maps and 2000 in Canadian lation provinces? provinces?

Which relocations of grassland can be observed between 1950 and 2000 in Canadian provinces?

With respect to the “When” output clauses (Table 6), maps mainly show dates or time periods With respect to the “When” output clauses (Table 6), maps mainly show dates or time periods (duration, time interval, time series) that are related to defined thematic and/or geometric events or With respect to the “When” output (Table 6), mapsthematic mainly show or time periods (duration, time interval, time series) that clauses are related to defined and/ordates geometric events or changes. or time the presented graphical depictions maythematic be used for thisgeometric purpose (6a to 6d). (duration,Either time labels interval, series) that are related to defined events or changes. Either labels or the presented graphical depictions may be used and/or for this purpose (6a to 6d). It has to be noted that or dates (such as years in 6a) depictions are strictly may speaking absolute values; however, we changes. Either labels the presented graphical be used for this purpose (6a to 6d). It has to be noted that dates (such as years in 6a) are strictly speaking absolute values; however, we prefer choropleth in order to as enhance the6a) more important sequential aspect. It has to be noted maps that dates (such years in are strictly speaking absolute values; however, we prefer choropleth maps in order to enhance the more important sequential aspect. Based on the previous lists for single change features (Tables 4–6), it isaspect. also possible to combine prefer choropleth maps in order to enhance the more important sequential Based on the previous lists for single change features (Tables 4–6), it is also possible to combine graphical for more complex tasks. Considering example Section Basedrecommendations on the previous lists for single change features (Tables the 4–6), it is alsomentioned possible toin graphical recommendations for more complex tasks. Considering the example mentioned incombine Section 3graphical (“How has the position and health index of forest areas in Canadian provinces changedinbetween recommendations forhealth more index complex tasks. areas Considering the example mentioned Section 3 (“How has the position and of forest in Canadian provinces changed between 1950 and has 2000?”), Figure 2and shows thatindex the proposed representations forprovinces translationchanged (flow map) and 3 (“How the position health of forest areas in Canadian between 1950 and 2000?”), Figure 2 shows that the proposed representations for translation (flow map) and absolute value (proportional symbol) can be combined into a compact symbol instead of using 1950 and value 2000?”), Figure 2 shows that the representations for translation (flow map) and absolute (proportional symbol) can proposed be combined into a compact symbol instead of using separate representations. absolute representations. value (proportional symbol) can be combined into a compact symbol instead of using separate separate representations.

With respect to the “When” output clauses (Table 6), maps mainly show dates or time periods (duration, time interval, time series) that are related to defined thematic and/or geometric events or changes. Either labels or the presented graphical depictions may be used for this purpose (6a to 6d). It has to be noted that dates (such as years in 6a) are strictly speaking absolute values; however, we prefer choropleth maps in order to enhance the more important sequential aspect. Based on the previous lists for single change features (Tables 4–6), it is also possible to combine graphical recommendations for more complex tasks. Considering the example mentioned in Section 3 (“How has the position and health index of forest areas in Canadian provinces changed between 1950 and 2000?”), Figure 2 shows that the proposed representations for translation (flow map) and absolute value (proportional symbol) can be combined into a compact symbol instead of using separate representations. Table 6. Visualization of “When” output clauses (compare classification in Table 3). ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEERof REVIEW Table 6. Visualization “When” output clauses (compare classification in Table 3). ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW

Visualization

Change Feature

6a Date

6b Duration

6c Time-interval (bi-temporal)

Example Change Question Change

Table 6. Visualization of “When” output clauses (compare classification in Table 3).

Change Table 6. Example Visualization of “When” output clauses (compareVisualization classification in Table 3). Map Type Example Visualization of clauses (compare classification in Table 6. 6.Example Visualization of “When” “When” output output clauses classification in Table Table 3). 3). Change Table Change Feature Question Map Type(compareVisualization Example Visualization Change Example Change Feature Question Map Type Example Visualization Change Example Change Visualization Change Example Change Feature Question Map Type Example Feature Question Map Example year between Feature Question Map Type Type Example In which year between 1940 and In which In which 1940 and year 2000 between was the Choropleth 6a 2000 was the maximum population In which between 1940 and year 2000 was the In which year between maximum population Choropleth map In which year between Choropleth 6a map 1940 and 2000 was the maximum population number reached in Date 1940 and was the number reached Choropleth 6a 1940 and 2000 2000 wasin the map Date Choropleth 6a maximum population Choropleth 6a number reached in maximum population Canadian provinces? map maximum population Canadian provinces? Date map Date number reached in map Date Canadian provinces? number reached in number reached in Canadian provinces? Canadian Canadian provinces? provinces? 6b the How long did it take to double 6b Duration population in Canadian provinces 6b Duration 6b 6b Duration since 1900? Duration Duration 6c 6c Time6c Time6c interval 6c and In which decade between 1900 Timeinterval Time(biTimeinterval (bi2000 was the maximum increase in interval temporal) interval (bitemporal) (bipopulation in Canadian provinces? (bitemporal) temporal) temporal) 6d

6d Time series (multi-temporal)

6d In which successive yearsTime can we series 6d Time series 6d (multi6d observe an increase andTime then a series (multiTime series temporal) Time series (multidecrease in population numbers in temporal) (multi(multitemporal) Canadian provinces in thetemporal) entire temporal) time span between 1900 and 2000?

6e Change in duration

Change in What is the time period difference 6e Change in 6e duration 6e in to increase the populationChange about duration Change in Change in duration duration 10% in the neighboring countries duration compared to France?

6e 6e

How long did it take to How long did it take to Proportional double the population in How long did it take to Proportional double theprovinces population in Proportional How did to Symbol map Canadian since How long long did itit take take to Proportional double the population in Symbol map Canadian provinces since Proportional double the population in 1900? Symbol Proportional double the population inmap Symbol map Canadian provinces since 1900? Symbol Canadian provinces Symbol map map Canadian1900? provinces since since 1900? 1900? In which decade between In1900 which between Symbol map anddecade 2000 was the In which decade between Symbol map 1900 and 2000 was the In which decade between (micro maximum increase in In1900 which decade between Symbol map and 2000 was the (micro maximum increase in Symbol map 1900 and 2000 was the diagrams) population in Canadian Symbol map (micro Symbol map 1900 and 2000 was the (micro maximum increase in diagrams) population in Canadian (micro maximum increase in provinces? (micro maximum increase in diagrams) diagrams) population in Canadian provinces? diagrams) population in Canadian diagrams) population in Canadian provinces? provinces? In which successive years provinces? In which years can wesuccessive observe an In which successive years can we observe In which successive years increase and thenan a In which successive years Symbol map can we observe an increase and thenana can observe decrease population can we wein observe ana Symbol map (micro increase and then decrease in population increase and then aa numbers inand Canadian Symbol map increase then (micro Symbol map diagrams) decrease population Symbol map numbersin in Canadian Symbol map decrease in population provinces in the entire (micro decrease in population diagrams) (micro numbers in (micro provinces inCanadian the entire numbers in Canadian time span(micro between 1900 diagrams) numbers in Canadian diagrams) diagrams) provinces in the entire diagrams) time span between 1900 provinces in the entire and 2000? provinces in the entire time span andbetween 2000? 1900 time between 1900 time span span andbetween 2000? 1900 What isand the 2000? time period and 2000? What is the period (Bipolar) difference to time increase the What is the time period (Bipolar) difference toabout increase the What time period Choropleth population 10% in What is is the the time period (Bipolar) difference to increase the Choropleth population about 10% in (Bipolar) difference to increase the map the neighboring countries (Bipolar) difference to increase the Choropleth population about 10% in (Bipolar) map the neighboring countries Choropleth population about 10% in compared to France? Choropleth population about 10% in map the neighboring countries compared to France? map the neighboring countries Choropleth map map the neighboring countries compared to France? compared to France? compared to France?

Figure 2. Combined symbol for object translation and change in absolute value. Figure 2. Combined symbol for object translation and change in absolute value. Figure 2. Combined symbol for object translation and change in absolute value. Figure 2. Combined symbol for object translation and change in absolute value.

9 of 17 9 of 17 9 of 17 9 of 17 9 of 17

6e Change in duration

What is the time period difference to increase the population about 10% in the neighboring countries compared to France?

(Bipolar) Choropleth map

ISPRS Int. J. Geo-Inf. 2018, 7, 288

9 of 16

Figure 2. 2. Combined for object object translation translation and and change change in in absolute absolute value. value. Figure Combined symbol symbol for

4.3. Recommendations for Representing Multi-Temporal Changes Animations are often used as a presentation format for multi-temporal scenes. From a cognitive point of view, however, they inherit some limitations [24–27]. For useful animations, the changes should be fairly close together in the users’ field of view and show the same trend over the entire scene (e.g., loss of forest only). Otherwise, too many changes are simply overlooked and too many eye movements (saccades) are needed, which in many cases cannot be handled due to the limited animation frequency. The integration of interactive control elements (such as stop, backward) seems to avoid these problems; however, the use of these elements in turn requires additional eye-movements and leads to a cognitive loss of information. The map series, i.e., a sequence of static single maps, is an alternative to animations [20]. To extend the aforementioned recommendation in the context of bi-temporal changes, difference maps should also be used here: For n scenes with different points of time, this would cause (n − 1) difference maps if only a comparison between directly subsequent dates takes place. If all possible combinations of dates are desired, (n − 1)! difference maps must be generated. Again, a linkage similar to that between the change matrix and the binary mosaic map (Figure 1) may help to select the desired combination in an interactive manner. Of course, the multi-temporal change analysis can also include the search for various specific temporal patterns over two or more selected scenes—like the aforementioned question “In which successive years can we observe an increase and then a decrease in population numbers in Canadian provinces?” In principle, it is possible to reduce each of these temporal patterns to elementary outputs as shown in Section 3. 5. Data Processing Prior Visualization 5.1. Problem Statement The aforementioned choice of map types has the goal of effectively and efficiently supporting change analysis tasks through a graphical display of information. In many applications, it is also necessary to perform an appropriate pre-processing of data before a display can be meaningful at all. This includes, for example:

• • • •

a proper choice of time intervals (e.g., to avoid smoothing effects due to long time lags or a large redundancy due to short time lags), a meaningful aggregation of spatial units, the definition of thresholds (e.g., to separate an actual change from random behavior), or simply, an appropriate cartographical generalization.

Another very relevant problem, which will be elaborated in more detail below, is related to the use of classified choropleth maps, which are necessary for the depiction of relative values (Tables 4e and 6a). In contrast to the unclassified version, the transformation of original values into discrete

ISPRS Int. J. Geo-Inf. 2018, 7, 288

10 of 16

intervals offers the advantage of a better and faster overview due to the reduced number of classes together with sharper color or grey value contrasts. However, conventional classification methods such as equidistant, quantile or natural breaks, together with the number of classes, the consideration of boundary classes or the possible neglect of outliers, are known to have a significant impact on the class memberships—and thus on the visual perception and interpretation of choropleth maps. Moreover, the above-mentioned classification methods, which are typically implemented in GI software packages, do not consider spatial context. This could result to the loss of important spatial relationships or patterns such as extreme values, hot/cold spots, or clusters. The reason for this is that these methods work data driven, i.e., intervals are determined only on the frequency distribution of original values without consideration of topological properties. For example, it may happen that a region having an extreme value is placed into the same class as one or more of its neighboring regions. Thus, the extreme value can no longer be extracted visually. Relatively little has been published on the problem of neglecting the spatial context or a ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 11 of 17 task-oriented approach; an overview is given by [20,28]. Attempts to describe and maintain value differences Often, differences of of spatial spatial neighbors neighbors were were published published several several years years ago, ago, for for example, example, by by [29–31]. [29–31]. Often, however, theaim aimhere here was to simplify the patterns that the map moregrasp quickly however, the was to simplify the patterns so thatsothe map user canuser morecan quickly the grasp the gross trends in the representation without being disturbed by a detailed and “patchy” gross trends in the representation without being disturbed by a detailed and “patchy” impression impression [32–34].this However, this does procedure does not that guarantee that any existing significant spatial [32–34]. However, procedure not guarantee any existing significant spatial variations variations andwill patterns will be maintained. and patterns be maintained. One way to tackle One way to tackle this this problem problem is is to to perform perform aa manual-subjective manual-subjective selection selection from from many many data data classification developed and and applied—Section applied—Section 5.2 classification methods. methods. Instead, Instead, task-oriented task-oriented methods methods should should be be developed 5.2 provides a selection from some of these developments. provides a selection from some of these developments. Finally, it Finally, itit has hasto tobe bepointed pointedout outthat thatthere thereisisno noobjective objectiveororeven evencorrect correctclassification; classification;however, however, is forfor a map to preserve or enhance certain relationships of interest depending on the it necessary is necessary a map to preserve or enhance certain relationships of interest depending ontask the or purpose. task or purpose. 5.2. Task-Oriented Data Classification Methods 5.2. Task-Oriented Data Classification Methods A typical task is to preserve local extreme values, i.e., those polygons that show (significant) A typical task is to preserve local extreme values, i.e., those polygons that show (significant) higher or lower value compared to all of their neighbors. A detailed description of the proposed higher or lower value compared to all of their neighbors. A detailed description of the proposed method is given in [35]; the following is an overview of the principle (see also Figure 3). method is given in [35]; the following is an overview of the principle (see also Figure 3).

Figure 3. Schematic workflow for preserving local extreme value polygons: Determination of intervals Figure 3. Schematic workflow for preserving local extreme value polygons: Determination of intervals and setting of class boundaries. and setting of class boundaries.

The search for extreme value polygons by considering the value differences to all direct neighbors is accelerated by a spatial R-tree index. From all neighbors of a local extreme polygon, the attribute value closest to the extreme value is extracted—setting a class boundary within the interval between this neighboring value and the extreme value ensures the isolation of the extreme value against all neighbors. All of these intervals are sorted by magnitude and plotted on a number line. A plane sweep algorithm is used to identify the optimal class boundaries: to do this, a line is passed

ISPRS Int. J. Geo-Inf. 2018, 7, 288

11 of 16

The search for extreme value polygons by considering the value differences to all direct neighbors is accelerated by a spatial R-tree index. From all neighbors of a local extreme polygon, the attribute value closest to the extreme value is extracted—setting a class boundary within the interval between this neighboring value and the extreme value ensures the isolation of the extreme value against all neighbors. All of these intervals are sorted by magnitude and plotted on a number line. A plane sweep algorithm is used to identify the optimal class boundaries: to do this, a line is passed incrementally over the range of values while counting and storing the number of intersections. Starting from the polygon with the largest interval width, the first class boundary is then set where the maximum number of intersections is found. After excluding all intervals that are hit by this first boundary, the next pass is made over the next largest remaining interval. This step is repeated until either all intervals (i.e., all local extreme values) have been covered or the predetermined number of classes has been reached. In order to not only visually demonstrate the added value of the approach (Figure 4), empirical tests were conducted to investigate the degree of conservation of local extreme value polygons depending on the number of classes and the characteristics of the data set. Table 7 describes three ISPRS Int. J. Geo-Inf. 2018, 7, x FOR PEER REVIEW 12 of 17 selected datasets and Figure 5 shows the respective numerical results. In summary, the empirical tests have demonstrated that the presented approach, in comparison In summary, the empirical tests have demonstrated that the presented approach, in comparison to the known data-driven methods, requires a significantly smaller number of classes in order to to the known data-driven methods, requires a significantly smaller number of classes in order to achieve the desired goal of preserving extreme value polygons. Conversely, the degree of preservation achieve the desired goal of preserving extreme value polygons. Conversely, the degree of for a preservation given number classesnumber is greater for theisproposed Unfortunately, a prediction aof the for of a given of classes greater formethod. the proposed method. Unfortunately, preservation rate based on statistical measures of the input data is difficult. Obviously, number of prediction of the preservation rate based on statistical measures of the input data isthe difficult. necessary classesthe fornumber a 100 preservation rate correlates the absoluterate number of local extreme values Obviously, of necessary classes for a 100topreservation correlates to the absolute number of local extreme that exist, varies from application to application. that exist, which varies fromvalues application to which application. Table Data sets sets for Table 7.7Data for empirical empiricaltests. tests.

Input Data Set Proposed Method: Proposed Method: No. Input Data Setof Local Data Set No. of Classes to Preserve No. Data Set No. of Polygons of Classes to Preserve All Extreme Values Extreme Values Values No. of Polygons No. of Local Extreme All Extreme Values A: Average age 439 159 (36%) 22 A: Average age 439 159 (36%) 22 Social index 847 847 271 (32%) 37 B: SocialB: index 271 (32%) 37 C: Election 103 3030 (29%) 12 C: Election result result 103 (29%) 12 sources: A: Average of Germans, per in county 2011. https://www.destatis.de/DE/ Data Data sources: A: Average age of age Germans, per county 2011. inhttps://www.destatis.de/DE/Methoden/ Methoden/Zensus_/Downloads/2F_BevoelkerungAlterGeschlecht.html. B:Hamburg Social 2016. monitoring Zensus_/Downloads/2F_BevoelkerungAlterGeschlecht.html. B: Social monitoring http://suche. transparenz.hamburg.de/dataset/sozialmonitoring-integrierte-stadtteilentwicklung-bericht-2016-anhang. C: Hamburg 2016. http://suche.transparenz.hamburg.de/dataset/sozialmonitoring-integrierte-stadttei Federal elections 2017, second votes for SPD party inelections Hamburg: https://www.statistik-nord.de/wahlen/wahlenlentwicklung-bericht-2016-anhang. C: Federal 2017, second votes for SPD party in Hamburg: in-hamburg/bundestagswahlen/2017/. https://www.statistik-nord.de/wahlen/wahlen-in-hamburg/bundestagswahlen/2017/.

Figure 4. Depending on the data classification method, local extreme values (outlined in red) can be

Figure 4. Depending on the data classification method, local extreme values (outlined in red) can be partially categorized with neighboring regions into one class (left; using the natural breaks method, partially categorized with neighboring regions into one class (left; using the natural breaks method, the extreme value polygon is in the same class (0.53 .. 2.38) as its left neighbor), or be isolated in one the extreme value polygon is in the same class (0.53 .. 2.38) as its left neighbor), or be isolated in one class as desired (right, using the proposed method); data set B (see Table 4). class as desired (right, using the proposed method); data set B (see Table 4).

Figure 4. Depending on the data classification method, local extreme values (outlined in red) can be partially categorized with neighboring regions into one class (left; using the natural breaks method, polygon is in the same class (0.53 .. 2.38) as its left neighbor), or be isolated in one ISPRSthe Int. extreme J. Geo-Inf.value 2018, 7, 288 12 of 16 class as desired (right, using the proposed method); data set B (see Table 4).

Figure Figure 5. 5. Better Better preservation preservation of of polygons polygons with with local local extreme extreme values values using using the the proposed proposed approach approach (red (red line) compared to conventional methods—the right axis shows number of classes, the axis line) compared to conventional methods—the right axis shows number of classes, the upperupper axis shows preservation (data sources: see4). Table 4). ISPRSshows Int. J. Geo-Inf. 2018,(data 7, rate x FOR PEER REVIEW 13 of 17 preservation rate sources: see Table

Another objective could be to preserve or enhance “large” attribute value differences of Another objective could be to preserve or enhance “large” attribute value differences of adjacent adjacent polygons in choropleth maps. A detailed description of the method outlined below is given polygons in choropleth maps. A detailed description of the method outlined below is given in [36]. in [36]. The algorithm starts with a determination of the value differences of all neighboring polygons. The algorithm starts with a determination of the value differences of all neighboring polygons. Thereafter, a reduction to the “significant” (i.e., the largest differences) takes place. The necessary Thereafter, a reduction to the “significant” (i.e., the largest differences) takes place. The necessary threshold can be derived, for example, from a percentile of the frequency distribution. Then, various threshold can be derived, for example, from a percentile of the frequency distribution. Then, various data classifications are calculated taking into account predefined conditions such as minimum and data classifications are calculated taking into account predefined conditions such as minimum and maximum number of classes. For each classification, a new index, the Edge Preserving Index (EPI), maximum number of classes. For each classification, a new index, the Edge Preserving Index (EPI), is calculated, which compares the original attribute value difference with the respective class value is calculated, which compares the original attribute value difference with the respective class value difference. Based on this index, it is now possible to identify best preservation (EPI against 0) or the difference. Based on this index, it is now possible to identify best preservation (EPI against 0) or the best emphasis (EPI against +1). Not only numerically via the EPI [36], but also visually, it can be best emphasis (EPI against +1). Not only numerically via the EPI [36], but also visually, it can be shown shown that the new approach improves the desired effect of preserving or emphasizing value that the new approach improves the desired effect of preserving or emphasizing value differences differences (Figure 6). (Figure 6).

Figure 6. Comparison of choropleth maps generated with different methods for data classification Figure 6. Comparison of choropleth maps generated with different methods for data classification following the purpose of preserving large value differences of adjacent polygons: Data set shows following the purpose of preserving large value differences of adjacent polygons: Data set shows population density density in in Germany Germany in in 2012 2012 (darker (darker colors colors indicate indicate larger larger values), values), in in each each map map three three population classes are used. Data Source: http://de.statista.com/statistik/daten/studie/1242/umfrage/ classes are used. Data Source: http://de.statista.com/statistik/daten/studie/1242/umfrage/ bevoelkerungsdichte-in-deutschland-nach-bundeslaendern/. bevoelkerungsdichte-in-deutschland-nach-bundeslaendern/.

Another task is to preserve or enhance spatial clusters, i.e., polygons that have similar values in Another task is to preserve or enhance spatial clusters, i.e., polygons that have similar values in a a certain neighborhood. In a first step, the identification of clusters takes place, for example with the certain neighborhood. In a first step, the identification of clusters takes place, for example with the Watershed algorithm [37]. All polygons belonging to a cluster are labeled. The transformation of the Watershed algorithm [37]. All polygons belonging to a cluster are labeled. The transformation of the original polygon values into class values then follows the same principle as described above for the original polygon values into class values then follows the same principle as described above for the adjacent polygons with large value differences. adjacent polygons with large value differences. A special case is the preservation or emphasis of hot or cold spots, i.e., polygons with high (or small) values surrounded by polygons with high (or small) values in a certain neighborhood. These polygons are determined by standard methods such as the Getis Ord index (and derived z scores in conjunction with the application of a threshold value for these; [38]). From this, a binary classification (and labeling) into hot/cold spots and other polygons is possible. The transformation of the original polygon values into class values then follows the idea of preserving local extreme values (see above).

ISPRS Int. J. Geo-Inf. 2018, 7, 288

13 of 16

A special case is the preservation or emphasis of hot or cold spots, i.e., polygons with high (or small) values surrounded by polygons with high (or small) values in a certain neighborhood. These polygons are determined by standard methods such as the Getis Ord index (and derived z scores in conjunction with the application of a threshold value for these; [38]). From this, a binary classification (and labeling) into hot/cold spots and other polygons is possible. The transformation of the original polygon values into class values then follows the idea of preserving local extreme values (see above). The only difference is that now it has to be ensured that all polygons that belong to a spot must be in a different class than any polygon that surrounds this spot. 6. Conclusions 6.1. Summary In the context of change analysis of urban or landscape research, a visual display and interpretation is still needed to reduce the complexity of the inherent information and to reveal the actual, possibly non-homogeneous, geographic distribution of changes. In this paper, two major requirements for the use visual representations (and in particular maps) along with computational methods have been addressed. First, the type of map and its design should consider usability aspects. For this purpose, one contribution of this article has been to develop a detailed classification framework for low-level tasks that frequently occur in the course of landscape and urban change analysis. Tasks are broken down to their “What”, “Where” and “When” components, for which normally two aspects are given and the missing third is sought. For each combination of components, a list has been set up comprising relevant change features (e.g., existential change) and possible feature values (e.g., gain/loss/none). This list can now be used for the categorization of any given change analysis task for any type of data (including remotely sensed and other categorical data, as well as quantitative data). Based on this classification, an assignment of suitable visualization methods or map types to the given change analysis tasks has been developed, meeting the frequently expressed demand for identifying a ‘right’ visualization type, along with the fact that further guidelines have been summarized—which include the demand for explicit display of changes (e.g., by using difference maps) or the minimization of eye movements. The second requirement for the use visual representations relates to appropriate pre-processing of data focusing on the preservation of spatial relationships. As an example, the data classification step prior to choropleth mapping was treated: since conventional methods do not consider the actual spatial context such as neighborhoods, important spatial information or patterns might be lost. The contribution of this paper has not only been to raise awareness of the problem, but also to present the concepts for algorithms that focus on the preservation of extreme values, hot/cold spots, large value differences between adjacent polygons, or clusters. 6.2. Future Directions In the context of map use tasks according to MacEachren and Kraak [10], the focus of this contribution was on the presentation of rather low-level tasks in the context of change analysis. However, it is believed that these representations can provide a valuable foundation for more complex workflows in a Geovisual Analytics environment. Obviously, this requires future work for the integration and implementation of these visual representations into those workflows. With the primary goal of usability in mind, it is obvious that, in the future, a profound empirical usability testing has to be carried out. By testing a particular visual representation of uncertainty information in the context of land cover change analysis, we have had positive experiences with quality-based methods, namely semi-structured interviews with expert groups [39]. In the context of change analysis based on remotely sensed data, it is often noted that this domain has been working for many years with “big data”. This might be the case because of the actual volume

ISPRS Int. J. Geo-Inf. 2018, 7, 288

14 of 16

of data—although there is no strict limit between “small” and “big” data in terms of bytes. However, considering the “4V” definition of big data (volume, velocity, variety, veracity) and focusing on the analysis of change, there are still major research and developments gaps, for example:

•

•

•

Big data is characterized by a complex and less structured appearance. As an example, earlier in this paper, the benefits of difference maps also in the case of multi-temporal scenes that lead to (n − 1)! maps were pointed out. This increases the need for a compact and generalized presentation. In this context, the role of maps and Cartography needs to be emphasized again as maps are well-accepted means of reducing and generalizing data to a usable minimum. On the other hand, methods for visualization, for interacting with them as well as for pre-processing (e.g., data classification or generalization) are not sufficiently integrated in big data platforms yet. This is also due to the fact that many GIS methods are not able to deal with extremely large amounts of data [3,19]. The core goal of inductive big data analytics is to detect and interpret patterns, correlations and other information. For this purpose, an extended task-oriented approach is certainly helpful, especially at early stages in dealing with big data for getting an overview. However, again, existing methods for overview purposes are not suited for big data cases yet [19]. With the increasing volume and variety of data, the consideration of inherent uncertainties (i.e., veracity) becomes more and more important [40]. This is particularly important in change analysis where a distinction must always be made between actual changes and differences due to uncertain input information and modeling operations. In earlier studies, we have already made attempts in this direction by reviewing the various methods for uncertainty visualization [41]; however, more application scenarios are needed along with usability testing.

Funding: Part of the work presented here (in particular, Section 5) has been conducted within the project “Task-oriented data classification and design of choropleth maps (aChor)”, funded by the German Research Foundation (DFG). Conflicts of Interest: The author declares no conflicts of interest.

References 1. 2.

3.

4. 5. 6. 7. 8.

9.

Andrienko, G.; Andrienko, N.; Keim, D.; MacEachren, A.M.; Wrobel, S. Challenging Problems of Geospatial Visual Analytics. J. Vis. Lang. Comput. 2011, 22, 251–256. [CrossRef] Zhang, L.; Stoffel, A.; Behrisch, M.; Mittelstadt, S.; Schreck, T.; Pompl, R. Visual analytics for the big data era—A comparative review of state-of-the-art commercial systems. In Proceedings of the 2012 IEEE Conference on Visual Analytics Science and Technology (VAST), Seattle, WA, USA, 14–19 October 2012; pp. 173–182. Li, S.; Dragicevic, S.; Castro, F.A.; Sester, M.; Winter, S.; Coltekin, A.; Cheng, T. Geospatial big data handling theory and methods: A review and research challenges. ISPRS J. Photogramm. Remote Sens. 2016, 115, 119–133. [CrossRef] Çöltekin, A.; Bleisch, S.; Andrienko, G.; Dykes, J. Persistent challenges in geovisualization—A community perspective. Int. J. Cartogr. 2017, 3, 115–139. [CrossRef] Keim, D.; Kohlhammer, J.; Ellis, G.; Mansmann, F. Mastering the Information Age—Solving Problems with Visual Analytics; Eurographics Association: Goslar, Germany, 2011; ISBN 978-3-905673-77-7. Schiewe, J. Geovisualization and geovisual analytics: The interdisciplinary perspective on cartography. Kartogr. Nachr. 2013, 122–126. Tiede, D. A new geospatial overlay method for the analysis and visualization of spatial change patterns using object-oriented data modeling concepts. Cartogr. Geogr. Inf. Sci. 2014, 41, 227–234. [CrossRef] [PubMed] Ma, L.; Fu, T.; Blaschke, T.; Li, M.; Tiede, D.; Zhou, Z.; Ma, X.; Chen, D. Evaluation of feature selection methods for object-based land cover mapping of unmanned aerial vehicle imagery using random forest and support vector machine classifiers. ISPRS Int. J. Geo Inf. 2017, 6, 51. [CrossRef] Krüger, T.; Meinel, G.; Schumacher, U. Land-use monitoring by topographic data analysis. Cartogr. Geogr. Inf. Sci. 2013, 40, 220–228. [CrossRef]

ISPRS Int. J. Geo-Inf. 2018, 7, 288

10. 11. 12. 13.

14.

15.

16. 17. 18. 19.

20. 21. 22.

23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

15 of 16

MacEachren, A.M.; Kraak, M.-J. Research challenges in geovisualization. Cartogr. Geogr. Inf. Sci. 2001, 28, 3–12. [CrossRef] Peuquet, D.J. It’s about time: A conceptual framework for the representation of temporal dynamics in geographic information systems. Ann. Assoc. Am. Geogr. 1994, 84, 441–461. [CrossRef] Andrienko, N.; Andrienko, G. Exploratory Analysis of Spatial and Temporal Data: A Systematic Approach; Springer: Heidelberg, Germany, 2006; ISBN 978-3-540-31190-4. Andrienko, N.; Andrienko, G.; Gatalsky, P. Impact of data and task characteristics on design of spatio-temporal data visualization tools. In Exploring Geovisualization; Dykes, J., MacEachren, A.M., Kraak, M.-J., Eds.; Elsevier: New York, NY, USA, 2005; pp. 201–222, ISBN 9780080445311. Von Landesberger, T.; Bremm, S.; Andrienko, N.; Andrienko, G.; Tekusova, M. Visual analytics methods for categoric spatio-temporal data. In Proceedings of the IEEE Conference on Visual Analytics Science and Technology (VAST), Seattle, WA, USA, 14–19 October 2012; pp. 183–192. Zurita-Milla, R.; Blok, C.; Retsios, V. Geovisual analytics of satellite image time series. In Proceedings of the 2012 International Congress on Environmental Modelling and Software, Leipzig, Germany, 1–5 July 2011; pp. 1431–1438. Green, K. Change matters. Photogramm. Eng. Remote Sens. 2011, 77, 305–309. Bogucka, E.P.; Jahnke, M. Feasibility of the space-time cube in temporal cultural landscape visualization. ISPRS Int. J. Geo Inf. 2017, 7, 209. [CrossRef] International Organization for Standardization (ISO). 1995. Available online: http://www.cipr.rpi.edu/ research/publications/Woods/MPEGcontrib/S15.doc (accessed on 12 May 2018). Robinson, A.C.; Demsar, U.; Moore, A.B.; Buckley, A.; Jiang, B.; Field, K.; Kraak, M.-J.; Camboin, S.P.; Sluter, C.R. Geospatial big data and cartography: Research challenges and opportunities for making maps that matter. Int. J. Cartogr. 2017, 3, 32–60. [CrossRef] Slocum, T.A.; McMaster, R.B.; Kessler, F.C.; Howard, H.H. Thematic Cartography and Geovisualization; Pearson Prentice Hall: Upper Saddle River, NJ, USA, 2009. Slocum, T.A.; Blok, C.; Jiang, B.; Koussoulakou, A.; Montello, D.; Fuhrmann, S.; Hedley, N. Cognitive and usability issues in geovisualization. Cartogr. Geogr. Inf. Sci. 2001, 28, 61–75. [CrossRef] MacEachren, A.M.; Boscoe, F.P.; Haug, D.; Pickle, L.W. Geographic visualization: Designing manipulable maps for exploring temporally varying georeferenced statistics. In Proceedings of the IEEE Symposium on Information Visualization, Research Triangle, CA, USA, 19–20 October 1998; pp. 87–94. Jenny, B.; Stephen, D.M.; Muehlenhaus, I.; Marston, B.E.; Sharma, R.; Zhang, E.; Jenny, H. Design principles for origin-destination flow maps. Cartogr. Geogr. Inf. Sci. 2016, 62–75. [CrossRef] Opach, T. Semantic and pragmatic aspects of transmitting information by animated maps. In Proceedings of the ICA International Cartographic Conference, A Coruna, Spain, 9–16 July 2005. Harrower, M. Cognitive limits of animated maps. Cartographica 2007, 42, 349–357. [CrossRef] Goldsberry, K.; Battersby, S. Issues of change detection in animated choropleth maps. Cartographica 2009, 44, 201–215. [CrossRef] Fish, C.; Goldsberry, K.P.; Battersby, S. Change blindness in animated choropleth maps: An empirical study. Cartogr. Geogr. Inf. Sci. 2011, 38, 350–362. [CrossRef] Armstrong, M.P.; Xiao, N.; Bennett, D.A. Using genetic algorithms to create multicriteria class intervals for choropleth maps. Ann. Assoc. Am. Geogr. 2003, 91, 595–623. [CrossRef] Smith, R.M. Comparing traditional methods for selecting class intervals on choropleth maps. Prof. Geogr. 1986, 38, 62–67. [CrossRef] Monmonier, M. Contiguity-biased class-interval selection and location allocation models. Geogr. Rev. 1972, 62, 203–228. [CrossRef] Jenks, G.; Caspall, F. Error on choroplethic maps: Definition, measurement, reduction. Ann. Assoc. Am. Geogr. 1971, 61, 217–244. [CrossRef] Andrienko, G.; Andrienko, N.; Savinov, A. Choropleth maps: Classification revisited. In Proceedings of the ICA International Cartographic Conference, Rome, Italy, 2–7 September 2001. Cromley, R.G. A comparison of optimal classification strategies for choroplethic displays of spatially aggregated data. Int. J. Geogr. Inf. Syst. 1996, 10, 405–424. [CrossRef]

ISPRS Int. J. Geo-Inf. 2018, 7, 288

34.

35.

36. 37.

38. 39.

40. 41.

16 of 16

MacEachren, A.M. Some Truth with Maps: A Primer on Symbolization and Design. Available online: http://www.cartographicperspectives.org/index.php/journal/article/view/cp20-patton/936 (accessed on 12 May 2018). Schiewe, J. Data classification for highlighting polygons with local extreme values in choropleth maps. In Advances in Cartography and GIScience; Peterson, M.P., Ed.; Lecture Notes in Geoinformation and Cartography; Springer: Heidelberg, Germany, 2017; pp. 449–459. Schiewe, J. Preserving attribute value differences of neighboring regions in classified choropleth maps. Int. J. Cartogr. 2016, 2, 6–19. [CrossRef] Beucher, S.; Meyer, F. The morphological approach to segmentation: The watershed transformation. In Mathematical Morphology in Image Processing; Dougherty, E., Ed.; Marcel Dekker Inc.: New York, NY, USA, 1993; pp. 433–481, ISBN 08247-87242. Getis, A.; Ord, J.K. The analysis of spatial association by use of distance statistics. Geogr. Anal. 1992, 24, 189–206. [CrossRef] Kinkeldey, C.; Schiewe, J.; Gerstmann, H.; Götze, C.; Kit, O.; Lüdecke, M.; Taubenböck, H.; Wurm, M. Evaluating the use of uncertainty visualization for exploratory analysis of land cover change: A qualitative expert user study. Comput. Geosci. 2015, 84, 46–53. [CrossRef] Shi, W.; Zhang, A.; Zhou, X.; Zhang, M. Challenges and prospects of uncertainties in spatial big data analytics. Ann. Am. Assoc. Geogr. 2018. [CrossRef] Kinkeldey, C.; MacEachren, A.M.; Schiewe, J. How to assess visual communication of uncertainty? A systematic review of geospatial uncertainty visualisation user studies. Cartogr. J. 2015, 51, 372–386. [CrossRef] © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).