Unsupervised Fuzzy ARTMAP Classification of Hyperspectral Hyperion Data for Savanna and Agriculture Discrimination in the Brazilian Cerrado Anthony M. Filippi,1 Christian Brannstrom, Iliyana Dobreva, David M. Cairns, and Daehyun Kim Department of Geography, Texas A&M University, College Station, Texas 77843-3147
Abstract: The Brazilian Cerrado is threatened by agricultural land use conversion. Accurate quantification of overall and subtype Cerrado distributions is essential for regional monitoring. In this research, unsupervised fuzzy ARTMAP was compared against conventional k-means classification of Cerrado and agriculture, based on Hyperion satellite data. We systematically tested a range of fuzzy ARTMAP parameters, determining the best parameter combinations. The effect of an additional surface liquid-water input vector was also tested. Similar results were obtained when only Hyperion apparent surface reflectance data were used; fuzzy ARTMAP, however, was generally markedly more accurate than k-means when the additional surface liquid-water input was included.
INTRODUCTION The Brazilian Cerrado, a savanna ecoregion that includes grassland and woodland subtypes, is the Earth’s largest neotropical savanna. The Cerrado extends over ~one quarter of Brazil (~1.8 million km2), and it is a global biodiversity “hotspot” as a consequence of its high species richness and endeminism that are under imminent threat from conversion to crops and pasture (Ratter et al., 1997; Oliveira and Marquis, 2002). Roughly 22,000 to 30,000 km2 of Cerrado are cleared annually, and ~2.2% of the Cerrado’s extent is under a strict protection regime, while another 1.9% is under a sustainable use regime (Klink and Machado, 2005). Overall, between 40 and 55% of the ecoregion has been cleared for pasture and crops (Machado et al., 2004; Sano et al., 2008), although considerable intra-regional variation in the spatial pattern of clearing and Cerrado remnants has been noted (Brannstrom et al., 2008). Accurate quantification of the extent and condition of Cerrado subtypes is critical for regional monitoring and other applications. The large expanse of the Brazilian Cerrado necessitates quantitative assessment via remote sensing. Remote monitoring of the Brazilian Cerrado has been limited to date (e.g., Ferreira and Huete, 2004; Ferreira et al., 2007; Brannstrom and Filippi, 2008), and 1Email:
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1 GIScience & Remote Sensing, 2009, 46, No. 1, p. 1–23. DOI: 10.2747/1548-1603.46.1.1 Copyright © 2009 by Bellwether Publishing, Ltd. All rights reserved.
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hyperspectral remote sensing studies of the Cerrado, in particular, have been uncommon (Ferreira et al., 2004; Filippi et al., 2007). Hyperspectral remote sensing may yield accurate discrimination of vegetation types/species (Jensen, 2005), and accurate classifications can provide useful information for multi-temporal change-detection of Cerrado-agricultural dynamics. Specifically, high-dimensional remote monitoring can enable detailed vegetation classification (Filippi and Jensen, 2006), such that Cerrado subtypes may be distinguished. In the Brazilian Cerrado, an effective classifier should be able to discriminate between agricultural land covers and different Cerrado physiognomies, as these landscapes are fragmented in unequal ways across the ecoregion (Brannstrom et al., 2008). Although ecological studies of the Cerrado have consistently indicated the importance of discriminating subtypes, for biodiversity considerations and other reasons (Ribeiro and Walter 1998), ecoregion-wide assessments have used only one Cerrado class (Mantovani and Pereira, 1998; Machado et al., 2004; Sano et al., 2008). Similarly, most studies focusing on specific regions of the Cerrado have used one Cerrado class (Jepson, 2005; Brannstrom et al., 2008) or two Cerrado classes (Filippi et al., 2007; Brannstrom and Filippi, 2008). Recently, Miura et al. (2003) and Ferreira et al. (2007) have used the same four categories as we use in this paper, although their study region, a protected area, does not include agricultural fields. In addition, our study uses a fuzzy artificial neural network (ANN) instead of the endmember-based spectral linear mixing models used by Ferreira et al. (2007); our approaches also differ in that Ferreira’s group used a vegetation map as reference data for accuracy assessment, while we used plot data obtained along transects for validation, discussed below. In the present research, part of our contribution involves also considering the complexity of soil cover, burned area, and other variables of Cerrado physiognomy. Standard hyperspectral processing methods often rely on the extraction of image endmembers (Jensen, 2005); however, endmember identification (e.g., Ferreira et al., 2007) can be quite difficult, especially for complex vegetation assemblages (Ramsey et al., 2005; Filippi and Jensen, 2006), and relevant in situ or laboratory vegetation spectral libraries are often unavailable. Employment of training data obviates the need for endmember extraction, but traditional statistical classifiers that may utilize training data are typically problematic when operating upon hyperspectral data. Multivariate Gaussian statistical classification requires nonsingular, class-specific covariance matrices, but singular matrices can exist when only limited training samples are derived from high-dimensional data (Roger, 1996). ANNs have thus been deployed for remote sensing classification to avoid such problems; their application to hyperspectral images has been limited, relative to multispectral imaging, but is growing. The ANN most commonly utilized for remote sensing classification has been the multi-layer perceptron (MLP). However, the MLP, often trained with backpropagation, can be disadvantageous in that the ideal number of hidden layers and nodes is difficult to determine, and training can be slow, among other issues (Filippi and Jensen, 2006). Thus, more research involving less conventional ANNs is needed. The fuzzy ARTMAP ANN (Carpenter et al., 1992) represents a viable alternative and has been shown to be effective (e.g., Mannan et al., 1998), but has only been used for remote sensing classification in general on a limited basis relative to other ANNs (Li, 2008). Other previous fuzzy ARTMAP–based remote sensing studies include Carpenter et al. (1997), Abuelgasim et al. (1999), Borak and Strahler (1999), Dutra and
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Huber (1999), Gopal et al. (1999), Baraldi et al. (2001), Muchoney and Williamson (2001), Pax-Lenny et al. (2001), Dell’Acqua and Gamba (2003), Gamba and Dell’Acqua (2003), Amici et al. (2004), Chiarella et al. (2004), Corne et al. (2004), Liu et al. (2004b), Liu and Wu (2005), Stathakis and Vasilakos (2006), Lippitt et al. (2008), and Rogan et al. (2008). Fuzzy ARTMAP classification studies specifically dealing with hyperspectral data have been rare (e.g., Dell’Acqua et al., 2004; Li, 2008). Also, to our knowledge, no fuzzy ARTMAP classification focused upon the Brazilian Cerrado—hyperspectral or otherwise—has previously been conducted. Fuzzy ARTMAP is an ANN based on Adaptive Resonance Theory (ART) and fuzzy logic. The network is trained iteratively by extracting knowledge from input patterns. Initially, adaptive weights are set to 1, and its hidden nodes or categories are uncommitted. When a new pattern is learned, a category is committed, and the adaptive weights adapt to represent the new pattern. But if an input pattern is similar to an existing category, the network modifies the weights of the category to incorporate the new knowledge (Carpenter et al., 1997). Category choice and match functions determine whether a new category should be created, or which of the existing categories should be modified to accommodate the new information. Category choice is an initial selection of a similar category; the match function further compares the input pattern and the selected category. Resonance occurs if the match function finds the input pattern and selected category to be similar. Similarity between new pattern and existing category is determined according to a user-defined vigilance parameter ranging from 0 to 1. If the vigilance criterion is not met, a reset occurs and another category is chosen. The order in which categories are chosen is determined by the choice parameter, which is a user-defined positive constant. The search ends when either a resonance occurs or the category choice function returns an uncommitted node. During learning, a user-defined learning parameter, ranging from 0 to 1, determines how quickly the adaptive weights are modified. Fuzzy ARTMAP can operate in supervised and unsupervised modes (Carpenter et al., 1992). Unsupervised fuzzy ARTMAP operates with one learning module generating categories based on input spectral patterns from the image that is classified. Supervised fuzzy ARTMAP operates with two learning modules, connected through a map field, creating categories from both spectral patterns and the respective classification labels. The two modules are connected through a map field. In the present research, we investigated unsupervised fuzzy ARTMAP because an unsupervised approach was considered to be potentially advantageous for this Cerrado region. Ample training data for supervised analyses were difficult to acquire due to the restricted access to land, as all property with Cerrado present in the study region is privately owned, and researchers must negotiate with farm administrators and owners to obtain entrance. Many landowners are also wary of researchers because they mistrust their motives or believe that researchers will report environmental irregularities to authorities. However, we were able to obtain the necessary validation data for our unsupervised analysis. The aim of this research was to determine whether accurate Cerrado classification products could be generated at a high degree of specificity using hyperspectral satellite remote sensing. The primary objective was to evaluate classification performance of unsupervised fuzzy ARTMAP relative to a conventional unsupervised classifier for the purpose of discriminating among Cerrado physiognomy and agricultural
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Fig. 1. A. Hyperion subscene analyzed (band 55, 905.05 nm). B. Hyperion footprint and surrounding land cover, based on an ISODATA classification of an August 1, 2005 Landsat 5 image. C. Location of study area.
classes based on spaceborne hyperspectral image data. Specifically, we determined the unsupervised fuzzy ARTMAP parameters that generated the most accurate image classifications among those tested, and the results are reported in detail. We also established the effect of employing an image-derived surface liquid-water image as an additional input vector in the context of fuzzy ARTMAP classification. METHODS Study Area and Datasets The study area is located in the Cerrado region of western Bahia, Brazil (Fig. 1), A hyperspectral Hyperion image (Fig. 1) was acquired on December 23, 2005 at 12:56:30 UTC (path/row = 220/68; sun azimuth = 114.81°; sun elevation = 57.850°), with channels covering the 355.59–2577.1 nm wavelength range. The Hyperion pushbroom sensor acquires continuous spectral data in 242 channels using two imaging spectrometers that span the visible/near-infrared (VNIR) and the short-wave infrared (SWIR), and the ground sample distance (GSD) is 30 m. The swath is ~7.7 km on the ground in the across-track dimension (U.S. Geological Survey, 2007).
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Field validation data were collected in December 2005 and January 2006. Randomly generated points constituted starting points for transects in Cerrado and agricultural areas. Transects were laid out in the direction where physiognomic diversity was greatest, with vegetation characteristics, bare soil, and litter described for 4 m2 plots established with dGPS every 15 m for Cerrado sites and every 30 m for agricultural sites. Cerrado field measurements included the number of stems for shrubs, palms, trees 1.3 m. For all trees with woody stems present at ≥1.3 m, diameter at breast height (DBH), canopy area, and canopy height were measured, and basal area was calculated. Where multiple stems existed at 1.3 m, the stems were measured and summed. Also, relative cover of live plants, litter, soil, and burned material were estimated for each plot. Relative burn measures were estimated on a 0– 10 scale, where 0 = no charred surfaces; 5 = charred tree trunks with green foliage; and 10 = completely burned. Descriptive statistics for the raw, unclassified Cerrado field data are shown in Table 1. Agricultural measurements included crop type, tillage type, stand height, number of plants, in addition to estimating relative area of live crops, litter, weeds, soil, and burned surfaces. Fields planted with the major crops of the region were sampled, which included soy, cotton, and maize. Descriptive statistics for the raw, unclassified Agriculture field data are given in Table 2 (Filippi et al., 2007). Field Data Processing Exploratory analysis of both the Cerrado and Agriculture field data revealed that most of the variables possess strong positive skewness (Tables 1 and 2). When a variable exhibited a non-normal distribution, it was transformed to a near-normal distribution, minimizing skewness. However, in the case of the Cerrado data, % Live Cover and “Burn” (Table 1) were not transformed. In the case of the Agriculture data, all non-categorical variables were transformed except for % Soil Cover (Table 2), with dummy variables employed for the categorical variables (crop type, tillage type) (Filippi et al., 2007). Cerrado and Agriculture field datasets were analyzed using hierarchical cluster analysis and nonmetric multidimensional scaling (NMDS) (Clarke, 1993; McCune and Grace, 2002). Hierarchical cluster analysis revealed four groups that represented the entire Cerrado field dataset well: Campo Limpo, or Open Cerrado Grassland (Class A); Campo Sujo, or Shrub Cerrado (Class B); Cerrado Típico, or Wooded Cerrado (Class C); and Cerrado Denso, or Cerrado Woodland (Class D). A descriptive statistics–based summary of these four Cerrado classes determined via this field data processing is given in Table 3. Classes A and B represent sample units chiefly composed of grass or small shrubs, as the low basal area and DBH values indicate. With Class D, relatively large tree species are dominant at these sites along the Cerrado spatial gradient. Class C may be interpreted as consisting of samples intermediate between Classes A/B and Class D. Thus, in summary (Table 3): Class A sites have the highest mean burn score, lowest basal area, lowest canopy cover, and highest soil percent cover of the four classes. Class B has a mean tree canopy cover of 3.25%, indicating increased presence of arboreal vegetation, whereas mean soil cover was 17.5%, and a low mean burn score was posted. For sites in Class C, arboreal plants had a much greater presence compared with Classes A and B because mean basal
9.57
6.18
27
0
0.82
Max
Min
Skewness
Shrub
S.D.
Statistic
n = 119 Mean
Sample size
3.13
0
20
3.45
1.9
Palm
2.28
0
45
8.63
6.61
Tree 1.3 m
2.09
0
0.6
0.12
0.09
DBH (m)
4.01
0
57.67
7.72
3.78
Area (m2)
1.1
0
10.5
1.93
1.83
4.23
0
706.86
108.89
42.83
0.66
0
85
29.47
27.23
Height Basal area (m) (m2/ha) Canopy
Trees > 1.3 m
Table 1. Descriptive Statistics for Selected Variables, Raw Cerrado Field Data
–0.37
5
100
27.21
55.67
Live
1.29
0
65
15.08
16.55
Litter
% plot cover
0.75
0
90
32.61
27.77
Soil
0.04
0
7
2.17
2.35
Burn (0–10)
6 FILIPPI ET AL.
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Fig. 2. Conceptual model of the Cerrado system.
Table 2. Descriptive Statistics for Selected Variables, Raw Agriculture Field Data Cropland Sample Size Statistic
Height (cm)
n = 102 Mean
20.53 20.6
S.D.
Number of Plants
Cover (%) Crop
Soil
Litter
Weeds
Burn (0–10)
86
16.4
57.45
20.22
5.93
0.46
56.96
13.99
26.77
25.49
21.21
0.94
95
85
90
4
5
0
0
0
1.09
3.76
1.86
Max
120
250
55
Min
4
0
0
Skewness
3.68
0.22
0.91
–0.27
area = 17.6 m2/ha, mean tree height = 2.5 m, and mean canopy cover = 37.9%. Class D has mean tree height = 4.85 m, basal area = 223.61 m2/ha, canopy cover = 70.3%, and litter cover = 34.2%. Relative to Class C, these values are much higher, whereas mean soil cover (2.1%) is far lower (Filippi et al., 2007). Based on the analysis of these field data, we devised a conceptual model of the Cerrado system, presented in Figure 2. Note that this model is very much in line with Coutinho’s “classic” Cerrado scheme (Coutinho, 1978). NMDS ordination was also performed on the Cerrado field dataset to determine possible environmental gradients and is well suited for non-normal ecological data; it does not assume linear relationships (Clarke, 1993; McCune and Grace, 2002). The procedure seeks to minimize stress, or the discrepancy, between ecological dissimilarities among samples calculated from a given dataset and those computed based on new data generated by ordination. A state of lowest stress is determined via an iterative-trial process. Then in ordination space, NMDS finds the new configuration of sample units. The distance between samples indicates the degree of dissimilarity between them; samples situated closer together in ordination space exhibit similar physiognomic traits. We utilized PC-ORD Version 4.14 (MjM Software Design, Gleneden Beach, Oregon) for execution of statistical analyses. We observed four classes along two axes, with the axes representing complex environmental gradients that likely refer to fire and moisture abundance (Filippi et al., 2007). Figure 3 illustrates how ordination (NMDS) and classification (cluster analysis) of the Cerrado field data can complement each other and enhance the interpretation of their results.
8.55 6.48 6.50
10.92 6.34 9.00
7.63 5.36 6.00
B Mean (n = 20) S.D. Median
C Mean (n = 48) S.D. Median
D Mean (n = 18) S.D. Median
Shrub
9.34 6.03 10.00
Statistic
A Mean (n = 32) S.D. Median
Class
0.68 1.20 0.00
1.27 2.57 0.00
2.40 2.30 2.00
3.25 5.25 1.00
Palm
4.21 3.15 3.00
6.29 7.49 3.00
10.70 13.61 3.50
5.94 8.00 2.50
Tree 1.3 m
16.61 12.42 14.54
2.79 2.69 1.54
0.09 0.04 0.08 0.32 0.12 0.27
0.01 0.04 0.00
0.00 0.00 0.00
0.00 0.01 0.00
0.00 0.00 0.00
DBH (m)
4.85 1.70 4.80
2.53 0.68 2.45
0.10 0.42 0.00
0.05 0.30 0.00
223.61 188.39 143.14
17.61 17.06 12.57
0.09 0.40 0.00
0.02 0.11 0.00
70.26 15.32 75.00
37.92 21.16 35.00
3.25 10.29 0.00
0.63 3.54 0.00
Trees > 1.3 m Area Height Basal area (m2) (m) (m2/ha) Canopy
Table 3. Descriptive Statistics for Selected Variables, Classified Cerrado Field Data
63.68 17.94 65.00
70.94 20.94 80.00
67.50 16.02 70.00
20.63 8.87 20.00
Live
34.21 17.50 35.00
18.54 11.89 15.00
15.00 12.98 10.00
4.06 3.22 5.00
Litter
% plot cover
2.11 7.13 0.00
10.52 19.95 0.00
17.50 11.06 17.50
75.31 8.61 75.00
Soil
2.16 2.17 3.00
1.81 2.08 0.00
0.75 1.62 0.00
4.28 1.02 4.00
Burn (0–10)
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Fig. 3. Group membership of each Cerrado field sample unit superimposed upon the NMDS diagram. Legend: Class A (“Campo Limpo” or Open Cerrado Grassland) = diamonds; Class B (“Campo Sujo” or Shrub Cerrado) = triangles; Class C (“Cerrado Típico” or Wooded Cerrado) = circles; Class D (“Cerrado Denso” or Cerrado Woodland) = squares.
The classified group membership (Classes A, B, C, and D) of each sample unit was superimposed upon the NMDS diagram (Fig. 3). Although there is some class mixing, samples of each group are generally scattered within their own domains, providing consistency of results between the two techniques. Samples of Class A and Class B are mostly located in the upper-left portion of the plot, whereas those of Class D tend to reside in the lower-right corner. Class C has its samples in the middle of the two extremes. This pattern is a very good fit with our interpretation of the cluster analysis and resultant conceptual model (Fig. 2). Thus, axis 1 and axis 2 represent the spatial gradient of the Cerrado system relatively well. The four Cerrado physiognomy classes identified here based on our field data analysis correspond well (in terms of canopy cover, tree height, basal area, and DBH) to biogeographical (Ribeiro and Walter, 1998) and remote sensing Cerrado literatures (Ferreira et al., 2003, 2004; Ferreira and Heute, 2004) and foundational studies (Goodland, 1971). However, not all Cerrado classes described in the literature were observed in our study area. The same hierarchical cluster analysis and NMDS procedures applied to Cerrado field data were also applied to the Agriculture field dataset, which resulted in the identification of four Agriculture classes: soy under no-tillage cultivation (Class A); soy under conventional tillage (Class B); cotton in the V2 stage (two nodes on main stem with fully developed leaves) (Class C); and maize planted in conventional tillage (Class D) (Filippi et al., 2007). A descriptive statistics–based summary of these Agriculture classes determined via field data processing is given in Table 4. However, these classes were aggregated into one Agriculture class for the validation stage.
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Table 4. Descriptive Statistics for Selected Variables, Classified Agriculture Field Data Class
Cropland Height Number Statistic (cm) of plants
Cover (%) Crop
Soil
Litter
Weeds
Burn (0–10)
A Mean (n = 32) S.D. Median
12.84 5.21 12
101.78 19.63 100
14.25 11.95 10
34.69 15.55 35
51.06 19.02 47.5
0 0 0
0 0 0
B Mean (n = 31) S.D. Median
29.94 34.18 18
49.29 46.64 31
16.03 15.5 10
81.45 15.23 90
2.52 4.02 0
0 0 0
0 0 0
C Mean (n = 22) S.D. Median
18.23 8.15 16
145.95 48.71 149.5
22.73 13.95 20
65.91 15.4 72.5
11.36 16.7 5
0 0 0
2.14 0.71 2
D Mean (n = 17) S.D. Median
20.82 7.06 20
45.65 52.53 21
12.94 13.24 10
45.59 30.15 50
5.88 12.9 0
35.59 41.45 5
0 0 0
Image Preprocessing The Hyperion image was spatially subset to the area of interest (Fig. 1), consisting of 256 samples × 743 lines. The ACORN™ atmospheric correction code, vers. 5.1 (ImSpec LLC, 2004), which is based on the MODTRAN4 radiative transfer model (Berk et al., 1998), was used to model atmospheric characteristics and invert Hyperion radiance values to apparent surface reflectance. ACORN mode 1.5pb was utilized to account for the cross-track spectral variation of this pushbroom sensor, and the average surface elevation within the scene extent (821.23 m), an input to the model, was computed from Shuttle Radar Topography Mission (SRTM) elevation data. In addition to apparent surface reflectance, ACORN generated a surface liquidwater image, in units of expressed path absorption in µm. Surface liquid water can vary as a function of water status, vegetation species, and phenological stage; asphalt and concrete surfaces and dry soil and grass yield low or zero surface liquid-water values (ImSpec LLC, 2004). Beginning with the original 242 Hyperion channels, uncalibrated and spectral overlap bands were discarded, yielding 196 unique bands (U.S. Geological Survey, 2007). High-noise bands 8–9, 77–82, 97–100, 118–133, 165–181, and 220–224 were also removed, resulting in 146 channels that were propagated to further stages of analysis. Geometric rectification was performed using 20 ground control points (GCPs), nearest-neighbor resampling, and a second-degree polynomial warping (RMSE = 0.19504 m).
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Classification Algorithms Unsupervised fuzzy ARTMAP was applied to the Hyperion data, as was a conventional unsupervised k-means classifier (Tou and Gonzalez, 1974) for a baseline comparison. Following initial experimentation, the k-means parameters used to generate the baseline classification were: number of classes = 50; change threshold percentage = 5%; and maximum iterations = 150 (Filippi et al., 2007). Parameter values tested in the fuzzy ARTMAP trials are given in the next subsection. Fuzzy ARTMAP Experiments In the first set of trials, 146 Hyperion apparent reflectance bands were used as input vectors. To help establish optimal parameter settings, we systematically varied the unsupervised fuzzy ARTMAP vigilance parameter and learning rate. Vigilance parameter was tested from 0.6 to 1 in increments of 0.05. Values lower than 0.6 were not considered because they created an insufficient number of categories. An additional value of 0.98 was also tested. Six different learning rates were used: 0.001, 0.01, 0.1, 0.2, 0.6, and 1. This range encompasses the very small value of 0.001 and the maximum value possible for the parameter. Intermediate values were set with an emphasis on higher learning rates because many ART-based ANNs are trained with fast learning, which corresponds to setting the learning rate parameter to 1 (Carpenter et al., 1997). The third fuzzy ARTMAP parameter—the choice parameter—was held constant. Even though the order in which input patterns are presented during choice selection has been shown to influence the results (Georgiopoulos et al., 1996), a single value for the choice parameter was used to facilitate the comparison between varying the vigilance parameter and learning rate.2 A choice parameter value of 0.01 was selected as being within range of the parameter’s conservative limit, which facilitates conserving learned weights as much as possible (Carpenter et al., 1997). The utility of the parameter combinations was evaluated by the classification accuracies accrued (see Results and Discussion section). In a second set of trials, parameters from the most accurate fuzzy ARTMAP classification in the first set of trials were held constant, except that the ACORN-derived surface liquid-water image was utilized as an additional ANN input, resulting in a total of 147 input vectors. K-means was also applied to this 147-input vector dataset, using the same parameters as in the first set of trials. Two additional fuzzy ARTMAP surface liquid-water trials (see Results and Discussion section) were also performed. These trials were conducted to determine whether surface liquid-water data could increase classification accuracy. Accuracy Assessment For all unsupervised fuzzy ARTMAP and k-means classifications, initially identified clusters/classes were merged to yield the final class structure, and the field validation data (see Study Area and Datasets subsection) were used to conduct hard, or 2 Also, the vigilance parameter has previously empirically been found to have a marked effect upon accuracy, relative to other parameters such as the choice parameter (Stathakis and Vasilakos, 2006).
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crisp, accuracy assessments (Jensen, 2005; Filippi and Jensen, 2006). For these field transect–based accuracy assessments (Rogan and Yool, 1996; Muller et al., 1998), the validation stations per class were distributed as follows: Cerrado Class A (n = 20); Cerrado Class B (n = 16); Cerrado Class C (n = 38); Cerrado Class D (n = 17); and Agriculture (n = 99). These sampling stations used in the assessments were a subset of the total number of stations visited, due to the field-sampling density relative to the Hyperion GSD. The number of samples for some Cerrado classes may be less than ideal; however, these samples represent the best practical balance between statistical validity and logistical constraints (Jensen, 2005), consistent with other transect-based assessments (Muller et al., 1998). We subjected the most accurate (four Cerradoclass) fuzzy ARTMAP and k-means classifications to class merging, thus increasing the number of validation samples per Cerrado class, and thus enabling assessments of classifications based on two Cerrado classes, in addition to those involving four Cerrado classes. The NMDS/hierarchical cluster analysis determined that Cerrado Classes A and B were from the same branch, whereas Classes C and D were from another branch. Thus, to form classified images involving two Cerrado classes, Classes A and B were merged to form one class, “Campo”, and Classes C and D were merged into a “Cerrado SS (Strict Sense)” class (Filippi et al., 2007). RESULTS AND DISCUSSION Fuzzy ARTMAP achieved the highest overall accuracy (OA) (76.84%) with learning rate = 0.01 and vigilance = 0.98. Decreasing the vigilance to 0.95 while keeping the learning rate at 0.01 produced the second-highest OA (75.26%). The same OA was achieved with the same fuzzy ARTMAP parameters but with the ACORN-derived surface liquid-water image as an extra input and with the k-means classifier.3 OA, Kappa coefficient, and producer’s and user’s accuracies (Jensen, 2005) for all trials with >60% OA and four Cerrado classes are summarized in Table 5. Table 6 contains the same types of results, but for all four-Cerrado-class trials with ≤60% OA. Results were comparable when only apparent surface reflectance input data were used; however, fuzzy ARTMAP accuracies were generally markedly higher than those of k-means when ancillary surface liquid-water input data were employed. The fuzzy ARTMAP classification with the highest OA (reflectance input data only, four Cerrado classes) compared against the corresponding k-means result was not significantly different at the 95% confidence interval (Z statistic = 0.3139). However, the algorithms did produce significantly different results with the addition of surface liquid-water input data (Z statistic = 3.754). Figure 4 summarizes the relationships among the vigilance parameter, learning rate, and overall classification accuracy for the four-Cerrado-class fuzzy ARTMAP trials. For the higher learning rates (i.e., 0.6 and 1), OA increases markedly as the vigilance increases from 0.6 to 0.65; however, at the upper end of the vigilance range (i.e., >0.9) for these trials, OA steeply 3The learning rate and vigilance used in the initial fuzzy ARTMAP surface liquid-water trial were identical to those from the best fuzzy ARTMAP reflectance-only trial. Two additional fuzzy ARTMAP surface liquid-water trials were performed with learning rate = 0.01/vigilance = 0.95 and learning rate = 0.01/vigilance = 0.90, respectively.
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13
Fig. 4. Overall classification accuracy for the four-Cerrado-class fuzzy ARTMAP classifications as a function of vigilance parameter value. Plots for the various learning-rate trials are shown. Data are derived from Tables 5 and 6.
decreases as vigilance increases. The 0.1 and 0.2 learning-rate trails also exhibit decreased OA for vigilance >0.9, although the decline is not as pronounced. For the lowest learning rates (i.e., 0.001 and 0.01), OA generally increased with increasing vigilance, with only modest OA declines at the highest vigilance values for the 0.01learning-rate reflectance-only and surface liquid-water trials. For visual inspection purposes, Figure 5 gives the classified images for the highest-OA k-means and fuzzy ARTMAP four-Cerrado-class trials. Both classification maps produced results within 4% for the area of the Agriculture class, but wide variation was observed in the Cerrado classes. The areas of the Shrub Cerrado (B) and Cerrado Woodland (D) classes varied in the fuzzy ARTMAP and k-means results by ~60%. Fuzzy ARTMAP classified 59.41% less area (6.429 km2) as Cerrado B than k-means, whereas 66.03% less area (4.744 km2) was classified as Cerrado D by fuzzy ARTMAP. The areas of Cerrado Grassland (A) and Wooded Cerrado (C) were markedly larger in the fuzzy ARTMAP result than in the k-means map (Fig. 5); fuzzy ARTMAP classified 17.91% more area (0.639 km2) as Cerrado A than k-means, and 34.40% more area (14.61 km2) was classified as Cerrado C by fuzzy ARTMAP. Our qualitative assessment of the most accurate fuzzy ARTMAP trial, compared with the k-means result, is that the fuzzy ARTMAP trial produced a more robust distinction between agricultural fields and Cerrado sites with few trees and shrubs. Tables 5 and 6 also show the number of categories generated by unsupervised fuzzy ARTMAP. Large vigilance parameter and learning rate can lead to a proliferation
0.5498
0.2291
0.4880
0.5097
70.00
68.84
67.89
67.37
0.5550
71.58
0.5293
0.5726
72.11
70.00
0.5683
72.11
0.5780
0.5492
72.11
0.5442
0.5882
72.63
70.53
0.5843
72.63
71.58
0.6210
0.6243
75.26
0.6157
75.26
75.26
0.6422
Kappa coefficient
76.84
Overall accuracy, pct.
240/226
0.01/0.98b
1/0.65
0.1/0.85
0.6/0.65
1/0.7
0.2/0.8
0.1/1
0.2/0.9
0.01/0.9
0.6/0.9
0.1/0.9
0.6/0.8
56/56
17/16
36/35
33/32
6773/167
248/247
29/28
529/255
143/141
62/61
24/23
839/187
n/a
0.01/1
99/97
n/ac
99/94
235/228
Categories/ real classes
0.01/0.95
0.01/0.95
b
0.01/0.98
Learning rate/ vigilance
40/72.73
25/83.33
5.26/33.33
75/65.22
60/75
60/66.67
70/70
60/75
60/70.59
65/61.9
25/83.33
70/73.68
65/72.22
70/73.68
70/63.64
70/73.68
70/73.68
Cerrado A PA/UA
12.5/10.53
0/0
0/0
0/0
0/0
0/0
43.75/53.85
0/0
12.5/22.22
0/0
0/0
6.25/25
18.75/50
31.25/50
31.25/50
6.25/33.33
31.25/55.56
Cerrado B PA/UA
28.95/42.31
89.47/49.28
40/22.22
26.32/38.46
39.47/44.12
55.26/42.86
7.89/42.86
76.32/49.15
52.63/46.51
76.32/47.54
92.11/46.67
76.32/56.86
31.58/41.38
39.47/51.72
71.05/54
71.05/50.00
68.42/54.17
Cerrado C PA/UA
58.82/30.3
0/0
0/0
70.59/29.27
47.06/30.77
17.65/15.79
82.35/29.17
0/0
29.41/26.32
0/0
0/0
11.76/15.38
64.71/32.35
58.82/34.48
5.88/12.5
11.76/18.18
11.76/18.18
Cerrado D PA/UA
97.98/96.04
90.91/84.11
90.91/80.36
96.97/96
98.99/88.29
98.99/95.15
98.99/96.08
95.96/91.35
98.99/96.08
95.96/95
97.98/88.99
92.93/95.83
100/96.12
100/96.12
96.97/96
100/96.12
100/96.12
Agriculture PA/UA
Table 5. Fuzzy ARTMAP and k-Means Classification Results, Ordered by Overall Accuracy, with Greater than 60% Overall Accuracy, Where Four Cerrado Classes Were Useda
14 FILIPPI ET AL.
0.4064
0.3799
0.3884
0.3911
63.16
61.58
61.58
61.58
90/89
0.1/0.8
n/a
d
0.2/1
1/0.75
0.6/0.7
32/31
n/a
13896/205
46/45
27/26
35/30
30/26
0.001/0.98
235/20
0.001/1
183/180
677/254
97/96
22/21
712/255
16/15
183/167
0.01/0.9b
0.6/0.85
1/0.9
1/0.8
0.1/0.75
0.1/0.95
0.01/0.85
1/0.85
0.2/0.85
50/62.5
0/0
0/0
60/70.59
0/0
0/0
35/53.85
15/100
60/70.59
35/77.78
65/72.22
10/100
0/0
65/72.22
60/70.59
45/64.29
bFuzzy
= producer’s accuracy (%); UA = user’s accuracy (%). ARTMAP classification result with surface liquid water ancillary input. ck-means classification result. dk-means classification result with surface liquid water ancillary input.
aPA
0.3932
0.4698
65.26
64.00
0.4695
65.26
0.4735
0.4472
65.26
64.74
0.4414
65.26
0.4892
0.4846
65.79
0.4505
0.4912
66.32
65.26
0.4866
66.32
65.26
0.4885
66.84
0/0
0/0
12.5/50
0/0
0/0
0/0
6.25/7.69
25/50
0/0
0/0
6.25/0
0/0
31.25/38.46
0/0
12.5/20
6.25/14.29
68.42/41.94
5.26/25
65.79/48.08
47.37/36.73
84.21/47.06
85.71/43.64
23.68/34.62
10.53/40
10.53/26.67
23.68/32.14
21.05/29.63
42.11/44.44
84.21/50.79
55.26/41.18
73.68/45.16
55.26/39.62
5.88/9.09
94.12/26.23
17.65/13.64
0/0
5.88/14.29
0/0
64.71/28.21
10.53/40
88.24/25.42
64.71/25.58
52.94/23.08
41.18/22.58
0/0
23.53/20
5.88/12.5
17.65/16.67
100/81.82
87.88/78.38
87.88/75.65
87.88/79.09
88.89/81.48
95.96/95.96
100/82.50
93.94/95.88
97.98/92.38
93.94/88.57
100/86.09
87.88/78.38
87.88/91.58
83.84/89.25
92.93/93.88
90.91/90.91
UNSUPERVISED FUZZY ARTMAP CLASSIFICATION
15
-0.0936
0.1124
0.042
27.42
25.79
23.16
1.00/0.60
0.60/0.60
1.00/0.98
0.001/0.90
0.20/0.98
0.60/0.95
0.60/0.98
1.00/0.95
0.60/1.00
0.20/0.70
0.01/0.80
0.10/0.70
0.20/0.95
0.10/0.98
0.001/0.95
0.20/0.75
0.60/0.75
Learning rate/ vigilance
16/15
13/12
30425/255
11./9
3920/255
3464/255
12567/255
5764/255
50323/255
13/11
11./10
12./11
1287/255
2022/255
20/18
27/26
35/34
Categories/ real classes
= producer’s accuracy (%); UA = user’s accuracy (%).
0.2392
aPA
0.0912
43.16
48.95
45.26
0.1862
51.58
0.17
0.1835
53.68
0.1213
0.312
54.74
46.56
0.3855
55
47.89
0.2721
0.3438
55.26
0.3346
0.2924
55.26
0.3275
56.84
0.3392
58.42
Kappa coefficient
60
Overall accuracy, pct.
0/0
20/19.05
0/0
0/0
0/0
5./25
0/0
5/33.33
5./50
5/4.35
75/55.56
68.42/44.83
10./40
35/58.33
10./20
0/0
0/0
Cerrado A PA/UA
0/0
0/0
6.67/8.33
0/0
0/0
0/0
6.25/14.29
18.75/17.65
0/0
0/0
0/0
0/0
6.25/16.67
0/0
0/0
0/0
0/0
Cerrado B PA/UA
100/23.31
94.74/38.71
28.57/12.5
15.79/21.43
34.21/26.53
21.05/22.86
60.53/31.51
31.58/28.57
36.84/33.33
89.47/44.16
2.63/33.33
0/0
57.89/36.67
47.37/32.14
7.89/37.5
18.42/26.92
63.16/40
Cerrado C PA/UA
0/0
0/0
0/0
88.24/22.73
11.76/15.38
29.41/27.78
0/0
29.41/35.71
23.53/33.33
0/0
94.12/22.22
91.67/29.73
0/0
17.65/33.33
76.47/26
64.71/26.19
5.88/9.09
Cerrado D PA/UA
Table 6. Fuzzy ARTMAP Classification Results, Ordered by Overall Accuracy, with 60% Overall Accuracy or Less, Where Four Cerrado Classes Were Useda
6.06/100
9.09/100
40.4/46.51
61.62/95.31
71.72/57.72
75.51/59.68
67.68/63.21
72.73/63.16
79.8/61.24
67.68/79.76
72.73/96
64.65/91.43
80.81/69.57
77.78/71.3
90.91/79.65
93.94/76.23
89.9/74.79
Agriculture PA/UA
16 FILIPPI ET AL.
UNSUPERVISED FUZZY ARTMAP CLASSIFICATION
17
Fig. 5. Comparison of hard/crisp classification maps for the highest overall accuracy (OA) k-means and fuzzy ARTMAP trials, where four Cerrado classes were used (Tables 5 and 6). A. Highest OA-k-means four-Cerrado-class trial result, with OA = 75.26%; number of classes = 50; change threshold percentage = 5%; and maximum iterations = 150. B. Highest OA-fuzzy ARTMAP four-Cerrado-class trial result, with OA = 76.84%; learning rate = 0.01; and vigilance = 0.98.
of categories (Carpenter et al., 1997). After fuzzy ARTMAP was trained to distinguish the different categories, however, it did not always classify pixels into all classes. Thus, there were often fewer real, or populated, classes than the total number of categories generated. Note that the trial with vigilance parameter = 1.0 and learning rate = 1.0 did not yield a result due to computer communication problems; an evaluation of this trial could thus not be performed. Accuracy assessments based on the two-Cerrado-class classifications (i.e., where Cerrado classes A/B [Campo] and C/D [Cerrado SS] were generated) and apparent reflectance input data only are given in Table 7. Fuzzy ARTMAP and k-means accuracies increased, as expected, and were comparable. Kappa analysis for the pairwise comparison of these error matrices yielded a non-significant difference at the 95% confidence interval (Z statistic = –0.1691). A closer evaluation of producer’s accuracy (PA) results from the four-Cerradoclass trials indicates several issues (Tables 5 and 6). First, PA was very high (~97%) for the Agriculture class, but uneven across Cerrado classes in the top OA trials. Highest PA was obtained for Cerrado A and Cerrado C. Cerrado A was mostly confused
18
FILIPPI ET AL.
Table 7. Fuzzy ARTMAP and k-Means Classification Results, Where Two Cerrado Classes Were Used Classification method
Overall accuracy, pct.
Kappa coefficient
Cerrado A/B Cerrado C/D PA/UA PA/UA
Agriculture PA/UA
Fuzzy ARTMAP
86.89
0.778
55.56/71.43
83.33/76.92
100/96.12
K-means
87.43
0.7874
58.33/72.41
83.33/78.43
100/96.12
with Agriculture, and, to lesser degree, with Cerrado B. Further confusion between Cerrado A and Agriculture resulted from the fact that trials often generated classes that included areas known to be Cerrado and Agriculture, and these classes could not be disaggregated further. We have indicated the confusion with respect to grass-dominated Cerrado and agricultural fields in the dry season (Brannstrom and Filippi, 2008); in the wet season, when these data were obtained, confusion is likely due to similar amounts of bare soil. Cerrado C also returned strong PA results, with no confusion with the mapped Agriculture class; but, errors resulted from confusion with Cerrado A and D classes. Subtle differences between Cerrado classes, probably at the subpixel level, may be responsible for this confusion. It is possible that the ecological variables that placed a particular 4 m2 plot into a subtype category were noise at the scale of the 30 m pixel. Cerrado B and D showed the poorest PA results. Cerrado B was confused mainly with Cerrado C, even though the analysis of the field data indicated that Cerrado A was more closely related. Cerrado D was primarily confused with Cerrado C. These errors may have originated in the post-classification combining of classes, or in the classes generated by fuzzy ARTMAP. But in neither case were Cerrado B and D confused with the Agriculture map class. Overall, the PA results indicate that plot-level data for Cerrado physiognomies do not “scale-up” evenly across Cerrado physiognomies to the 30-m pixel size common in remotely-sensed data. Ferreira et al. (2004, p. 445) indicated the “rather narrow distinction” in the radiometric response of Cerrado subtypes because of “unique understory and overstory associations.” However, four-class Cerrado maps may prove very useful in numerous applications, such as biodiversity management/habitat conservation planning and studies of carbon fluxes. Further experiments are required to improve the discrimination among the Cerrado subtypes apparent in field settings so that land cover maps may provide more precise information for various applications. Maintaining high accuracy may require a trade-off, where fewer subtypes are mapped at higher levels of accuracy, unless advances in image quality and processing methods will permit the mapping of Cerrado subtypes from satellite image data with the same precision as those of ecological studies. The present research does demonstrate, however, that relatively accurate, detailed classifications can be accrued via hyperspectral image processing by both fuzzy neural and conventional algorithms.
UNSUPERVISED FUZZY ARTMAP CLASSIFICATION
19
CONCLUSION The objective of this research was satisfied in that we were able to accurately map Cerrado physiognomic subclasses using hyperspectral satellite data. Unsupervised fuzzy ARTMAP performed comparably or favorably relative to k-means in classifying hyperspectral satellite image data acquired over a Cerrado-and agriculture-dominated area. The highest producer’s accuracies were obtained for the Cerrado A (Campo Limpo, or Open Cerrado Grassland) and Cerrado C (Cerrado Típico, or Wooded Cerrado) classes. Attempting classification of Cerrado subtypes in the presence of Agriculture land cover presented challenges; for example, Cerrado A was confused with the Agriculture class. Classification confusion existed among the Cerrado subclasses as well. We identified the unsupervised fuzzy ARTMAP parameter combinations—over a wide range of parameter values tested—that yield the highest classification accuracies based on input reflectance data. However, note that we do not claim to have determined universally optimal fuzzy ARTMAP parameters for the entire Brazilian Cerrado. Instead, the parameter combinations identified in this research as leading to higher classification accuracies may serve as a useful baseline, or starting point, for other unsupervised fuzzy ARTMAP classification investigations over broader areas of the Cerrado. Use of more remotely sensed images acquired over other areas will facilitate ANN parameterization for more universal Cerrado application, although this was outside the scope of the current study. In addition, further experimentation will be useful in assessing the maximal classification accuracies and comparative advantage that fuzzy ARTMAP can accrue with an additional surface liquid-water input. Additional research may involve subpixel fuzzy ARTMAP analysis (Carpenter et al., 1999; Liu et al., 2004a), which may address the problem of subpixel differences among Cerrado classes noted above, as well as the effect of feature selection/dimensionality reduction as a preprocessing step (Filippi and Jensen, 2006). A comparison of unsupervised fuzzy ARTMAP with other unsupervised and supervised algorithms, including supervised fuzzy ARTMAP (and related variants) and the MLP, will be undertaken in a future investigation. ACKNOWLEDGMENTS This work was supported in part by a National Geographic Society Committee for Research and Exploration grant, which provided for the field work and image acquisition. Data processing was supported in part by Stanford Caribbean Investments LLC. The authors thank Fazenda Alvorada, Fazenda Santo Antônio, Fazenda Vila Verde, and Associação de Irrigantes e Agricultores da Bahia (AIBA) for logistical support. We are grateful for the useful comments of the anonymous reviewers, which improved the quality of this paper. REFERENCES Abuelgasim, A., Ross, W., Gopal, S., and C. Woodcock, 1999, “Change Detection Using Adaptive Fuzzy Neural Networks: Environmental Damage Assessment After the Gulf War,” Remote Sensing of Environment, 70(2):208–223.
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