Obtaining fuzzy sequential patterns for Ambient Intelligence Problem ...

ESTYLF08, Cuencas Mineras (Mieres - Langreo), 17 - 19 de Septiembre de 2008

Obtaining fuzzy sequential patterns for Ambient Intelligence Problem Solving Miguel Delgado1

Mar´ıa Ros2

M. Amparo Vila3

1

2

Department of Computer Science and Artificial Intelligence. University of Granada, [email protected] Department of Computer Science and Artificial Intelligence. University of Granada, [email protected] 3 Department of Computer Science and Artificial Intelligence. University of Granada, [email protected]

Abstract Many traditional environment applications base their operations in using sensors, for this reason sensors are becoming more and more common in daily life. One of that applications is the Tagged World which uses the information from sensors to identify the user behavior and to provide any service. In this paper, we present a method to use the sensor information in order to extract the behavior pattern on time performed by the user. The method uses frequent itemsets to represent the common actions that are realized by user. After, it obtains the sequences patterns which defines the specific behavior from the extracted frequent itemsets. However, the user behavior has random imprecision by definition. Thus, we have designed a method to manage this imprecision from the user behavior, establishing a temporal constraint: a Fuzzy Temporal Window. Keywords: Tagged World, Frequent Itemsets, Sequence Patterns, α-cut.

1

INTRODUCTION

The ubiquitous systems is one of the today’s technology reefs. Sensors are able to collect the human activity. That permits to develop a system which is able to detect the user’s actions from sensor information. Therefore, the goal of such systems is to find a mechanism that would identify the different actions with the specific activity carried out by the user. A Tagged World [8] is defined as a smart area that serves to recognize user’s behavior using information about their daily activity. This information is collected

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by sensors placed (embedded) in the environment. The sensor information is continuous on time, i.e., it could arrive at the system at any time. This information can be processed with different techniques of Data Mining, or Stream Mining specifically, in order to extract some knowledge pattern. When the information is continuos, we need to use some techniques to realize a representative sampling of the data [3]. There exists several techniques to reduce the input data [7]: sampling, sliding window, histogram,sketches, etc. Sensor information should be processed to be used in real applications. In [5] it is proposed a system to identify correct behavior using Data Mining Techniques. The system is divided into two fundamental parts: inductive learning mechanism, whose final output will be a behavior database using Frequent Itemsets; and a system for the recognition of sequences performed by the users by Regular Grammar. The second stage will be built on the behavior database obtained in the previous process. That system uses the Frequent Itemset concept to process the sensor information, without keeping in mind the time when the action happens. That is an important problem because this time determines some system features. There are many proposal about time constraints for sequence mining. In [6] Fiot et al. present a soften temporal constraints used for generalized sequential pattern mining. The temporal constraints are established between the itemset that are in the sequence patterns, pointing out the minimum and maximum distance among them. The result is fuzzy sequences patterns. There exists many papers which propose some algorithm to obtain the sequences patterns. AprioriAll and AprioriSome, which were proposed by Rakesh Agrawal et al. [Rakesh Agrawal et al.1995], are the first method we can find in the bibliography. Henceforth, many variants have been appeared, where we could emphasize the algorithm PrefixSpan [Pei et al. 2001].which explores prefix projection in sequential pattern min-

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ing. PrefixSpan mines the complete set of patterns but greatly reduces the efforts of candidate subsequence generation. The method to obtain the sequence of actions that defines an user behavior. However, these method solves crips problem. But, we have mentioned that the system have to manage random imprecision. There are other methods to work with fuzzy sequences patterns, but the most common approach is to extract the fuzzy sequences patterns to quantitative attributes. For example, [4] propose Fuzzy Grids Based Sequential Pattern Mining Algorithm (FGBSPMA) to generate all fuzzy sequential patterns from relational database, where each quantitative attribute is viewed as a linguistic variable, and can be divided into many candidate I-dim fuzzy grids. Although that, there are not many applications of fuzzy sequential patterns to discrete attributes. There are many kind of sensors, between them we could emphasize the RFID. RFID technology is based on radio-frequency communication and permits the univocal identification of the elements in the system. RFID systems [12] consists of tags (chips that contain identifying and often other data) and reading devices that convey information from the tags to computers. RFID Devices are beginning to replace magnetic-stripe security cards for unlocking doors and granting access to secured areas, especially at facilities with special security needs, such as military installations. Such systems are already in limited use and are being tested widely for applications involving the tracking of inventory from manufacturers to stores. However, nowadays new uses are appearing for RFID systems such that identifying object in a Tagged World [9]. Philipose and et al. [9] propose a system to inferring Activities of Daily Living in Tagged World. They present a new paradigm for ADL inferencing leverages radiofrequency-identification technology, data mining and a probabilistic inference engine to recognize ADLs based on the objects people use. As sensor, they use RFID technology with other sensor streams to fill in the gaps. The system represents activities as linear sequences of activity stages, and annotate each stage with the objects involved and the probability of their involvement. This paper is organized into five main sections. In section 2 we present the formal problem to solve with the designed method. In the next section, the crisp model is presented explaining the method to obtain the knowledge for a specific behavior. In section 4 we present the Fuzzy Temporal Window concept and the method that permits to work with the uncertainty of the problem. As well, we present an illustrative example of operation model. Finally, the conclusions and future works are reported in section 5.

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2

FORMAL PROBLEM

This section defines the formal problem we try to solve: to obtain the pattern sequences that identify the user behavior in a specific domain and context. Thus, we have to define some basic concepts which will be the systems’ aims. When we observe an user, the most essential concept that he could do is the action. Definition 2.1 (Action) An action is defined as the occurrence of a fact over a specific object. However, it results very interested to know when the action happened on time. Definition 2.2 (Action on time) An action is the occurrence of a fact over a specific object in a given time and it denotes as a pattern ij = (hj , lj ), where hj is a fact and lj is a temporal label defines the time of occurrence of the action. These definitions give us the basic element to work, but our aim is to find the different actions make a behavior up. Definition 2.3 (Behavior) Let A = {a1 , ..., an } be the set of possible user’s actions in some situation or domain. A user behavior is a finite set of actions: β = {α1 , α2 , , .......αp(β) } with αj ∈ A∀j , and where αj is performed before αk iif j ≤ k. In this definition, we have not taken in mind the time, although, in general, a behavior happen in a specific moment on time. Definition 2.4 (Behavior on time) Let A = {a1 , ..., an } be the set of possible user’s actions in some situation or domain. Let τ be the temporal line, then A user behavior on time is a finite set of pairs such as: bI = {(α1 , t1 ), ...(αn(b) , tn(b) )} where αj ∈ A∀j, where αj is performed before αk iif j ≤ k, tj ∈ [0, τ ] ∀ti < tj si i ≥ j, con I = [t1 , tn(b) ] The system takes, as its basis, a database about the user action. This database has been obtained from the observation of the user, i.e., from the actions the user has done. In the rest of the document, this database will be named by Observation Data Base (ODB). The selected representation for ODB is a transactional database T, where each fils is a observation over the user, normally his activity all day long; and each column is the possible actions in the A set, A = {a1 , ..., an }.

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3

CRISP MODEL

In this section, we present a solution to the problem has been explained in section 2 but only to the crisp problem. This version of the problem consider each action as an occurrence, without any time. The process followed to obtain the pattern sequences is explained in [5]. That process has two stages: to extract the common actions and to obtain the correct sequences.

3.1

OBTAINING COMMON ACTIONS

Before to explain the method, it is convenient to understand what the common actions are and what they represent on the method. When we talk about common actions, we refer the actions what person performs generally to do a specific behavior. Example 3.1 (Common actions) Let us considerer the to go out home behavior which contains always two actions, to take the keys and to close the door. However, if the user to take a bag or to take a scarf, it will not be a common action in the behavior.

3.2

OBTAINING CORRECT SEQUENCES

When we have obtained the common actions, we have to obtain the possible order of these actions to build the sequence patterns. To obtain them, we will use the permutation of a set to obtain all possible sequences. But, not all permutation will be accepted as a pattern sequence. Only we accept the permutation whose order is in the ODB. Definition 3.1 (Correct sequences) Let T be the transactional database which represents the ODB and let I be an itemset obtained from it for behavior b. Then a correct sequence p is a permutation of I where the order among its elements are defined in the ODB. Example 3.3 (Correct sequences) Let us consider an example of leave home behavior. The ODB is showed in the Table 1. This is represented in the transactional database T. If we apply the Apriori Algorithm over T, with support = 0.9, we obtain the itemset {Keys, ODoor, MobilePhone}. From this itemset, we could obtain the permutations showed in table 2. However, the order of all sequences are not valid in the ODB. For example, the sequences s3 and s4 never could happen. After removing all invalid sequences, we accept as valid sequences s2 and s6 . Table 1: Leave Home ODB

As we have mentioned above in this paper, the system observes the user and collects his activity in the ODB, which could be able to represent as a transactional database T. Thus, the common actions can be identified with the concept of frequent itemset extracted from the transactional database. Thus, the common actions will be defined as the sequence of events that occur more often in the observed knowledge. Each frequent itemset corresponds to a particular common behavior [5]. The extraction of the common actions could make by any algorithm based in Apriori Algorithm [1]. After applying the Apriori Algorithm, itemsets have been obtained. However, a itemset is a set and lacks order among its elements. That results a problem, because a behavior has an order among its actions.

Example 3.2 (Valid order) Let us considerer a to leave home behavior. The itemset defines that behavior will be door key mobile_phone. To this actions, it could think in two possible ordinations: mobile_phone keys door or keys mobile_phone door. Nevertheless, we could not considered any order where the door will be before the mobile phone or the keys.

XIV Congreso Español sobre Tecnologías y Lógica fuzzy

TRANS t1

ELEMENTS Clothes, Shoes, MobilePhone, Bag, Keys, ODoor, Elevator Shoes, Bag, Keys, MobilePhone,ODoor, Keys2, ODoor2, Elevator Tap, Towel, BathroomDoor, BedroomDoor, Clothes,Shoes, Bag, Keys, MobilePhone, ODoor, Keys2,ODoor2, Elevator Shoes, Keys, MobilePhone, Bag, ODoor, Elevator, Keys2, ODoor2 Shoes, Bag, MobilePhone, Keys, ODoor, Keys2, ODoor2, Elevator

t2 t3

t4 t5

Table 2: Possible permutations s1 s2 s3 s4 s5 s6

{Keys, ODoor, MobilePhone} {Keys, MobilePhone, ODoor} {ODoor, Keys, MobilePhone} {ODoor, MobilePhone, Keys} {MobilePhone, ODoor, Keys} {MobilePhone, Keys, ODoor}

So, we use the knowledge of the ODB to determine if a sequence is valid or not. When a sequence is valid,

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we name it as correct pattern. The algorithm 2.1 is designed to detect if we have found a correct pattern or not. Algorithm 3.1 (Valid sequences) For each i ∈ behavior sequence For each t ∈ ODB Check if all elements in the sequence i respect the t elements order Get the position of two t elements Check the positions If this positions are incorrect in the sequence i Get other two t elements If the sequence does not find in neither of ODB, delete the sequence. As we explained in the subsection 1, there exists many algorithm to obtain the sequences patterns. However, we are not looking for this type of sequence patterns but sequence patterns which represent all valid ordinations for elementos of the frequent itemset. In addition, the traditional algorithms do not solve the main problem of the frequent itemset: different order between their elements. The sequences has been obtained by these type of method are statics, i.e., the order is to set up when their build the sequences. These sequences will only be valid if their order is frequent in the data base.

4

INTRODUCTION OF A FUZZY WINDOWS

In the previous section, we have presented a model crisp, but the human behavior is not crisp. The human activity has random imprecise by definition, because the human has free thinking. Then the system has to work with it and to adapt itself to the user habits. 4.1

MOTIVATIONS

In the section 3 we have presented the process to obtain the correct patterns sequences of actions from user behavior. This method extracts from a ODB particular the common action. The ODB contains tuples which are only composed by the action to a specific behavior. However, a general ODB contains actions that have been realized by the user during whole day. For this reason, we do not know where the behavior starts and ends. In [5], the method propose that an expert would indicate when a behavior performs. However, this proposal is not applicable to a real system, where each person has particular activities and habits. Therefore, it has to try to find a mechanism to identify behavior

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patterns from the sequence data collected by the sensors. Traditional Stream Mining techniques focus their activity on the study of a range of information [3]. It defines a Sliding Windows that establishes the range and is moved according to the time increases. Generally, there exists some behavior that are realized by the user at the same time every day. Example 4.1 We want to control the behavior Luis go out home. But, we do not know when the behavior starts or ends, we only know that Luis go out home at 8:30 o’clock. Then, we could use this knowledge to situate an interval on the temporal line. The result will be a subset from the ODB particular to the studied behavior. However nobody does the action at the same moment each day, so he does the action roughly at the same moment. This raises a new problem: how to fix the window’s ranges to detect a particular activity. Ranges should consider the random imprecise of the situations. Example 4.2 As we know Luis go out home at 8:30 o’clock, then we could control the actions happen about 8:30. This interval, which has been defined on the temporal line above a specific time, will be named as Temporal Window. It permits to get a subset from each ODB tuple (See figure 1). In this subset, the actions have not the same degree of importance, since the actions are about the specific time are more important than the actions far from the interval center. So, we could assign a degree of importance at each action, in function of its situation in the interval. Then the interval will be defined as a fuzzy set and name as Fuzzy Temporal Window (See figure 2). 4.2

MODEL FORMULATION

In this section we present a formal representation to the Temporal Window and Fuzzy Temporal Window. Definition 4.1 (Temporal Window) Let τ be a interval from the temporal line τ , ODB the Observation Data Base and t ∈ ODB a tuple from ODB. Let ij be an action ij = (hj , lj ), then a Temporal Window W to a specific behavior, which ocurrs in the interval τ , is defined as a subset of t where ∀ij ∈ W (t) then ij ∈ t and lj ∈ τ The next stage is to include some random imprecision in the specific Temporal Window. Definition 4.2 (Fuzzy Temporal Window) Let τ be a interval from the temporal line τ , ODB the Obser-

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Definition 4.4 (Fuzzy Transactional Data Base) Let T be a Transactional Data Base and W a Fuzzy Temporal Window, it defines T˜ as a Fuzzy Transactional Data Base constructs as W(t) ∀t ∈ T .

Figure 1: Temporal Window over the ODB. vation Data Base and t ∈ ODB a tuple from ODB. Let ij be an action ij = (hj , lj ) and W a Temporal Window to a specific behavior. Let fs be a fuzzy set over τ , then it defines the FW Fuzzy Temporal Window as a Temporal Window where

We represent the Fuzzy Transactional DataBase as a table where for each fils and column we have the membership degree corresponding to the Fuzzy Temporal Window. Once we have the data, we should get the common actions and valid sequences for each behavior. However, we can not apply the method explained in the section 3 directly, because we have to manage the membership degree corresponding to the Fuzzy Temporal Window. The following subsection explains models’ modifications to manage the random imprecision. Therefore, the aim is developed a system that obtains the stimulation from the user who realizes some actions sequentially. So the system has to find the action sequence which corresponds with a specific behavior that is defined by a Fuzzy Temporal Window. 4.3

∀ij ∈ W (t) µF W (ij ) = µf s (lj )

OBTAINING PATTERNS SEQUENCES BY ALPHA-CUTS

Here, we present the techniques used to extract the sequences patterns when we have a specific Fuzzy Tem˜ poral Window W and the Fuzzy ODB ODB, which is represented by the Fuzzy Transactional Database T˜. The ideal situation will be the sequences patterns were fuzzy. However, our method is designed to crisp problem. Thus, we have to work in first time with a crisp problem and, after, transform it to a fuzzy problem again. To do that, we are using the α-cut concept and the Representation Theorem.

4.3.1

Figure 2: Fuzzy Temporal Window over the ODB. Applying a Fuzzy Temporal Window on the ODB, we obtain a image of it where we assign to each item its membership degree. We have represented the ODB as a Transactional Database, thus we should obtain the image of Transactional Database too. Definition 4.3 (Fuzzy ODB applying W) Let ODB be a Observation Data Base and W a Fuzzy ˜ as a Fuzzy ObserTemporal Window, it defines ODB vation Data Base constructs as W(ODB) such as ˜ ∀t ∈ ODB, W (t) ∈ ODB

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Description

The problem consist of extracting the sequences patterns to specific behavior when we have a Fuzzy ODB ˜ ODB, represented as T˜, and a Fuzzy Temporal Window W defined from the user knowledge. In the first stage, we have to transform a fuzzy problem to a crisp problem with the aim of applying the method explained in the section 2. To do that, we could use the α-cut set [10]. Definition 4.5 (α-cut set of A) Aα = x ∈ X|µA (x) ≥ α

(1)

By the α-cut, we would have a new image of T˜, T α , crisp where each value is in {0, 1}. Then, we can apply the classical method to T α , obtaining frequent itemsets and sequences patterns to specific α value (I α and

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P α , respectively). After extracting all sequences patterns, we could create a fuzzy set P by the sequences patterns which have obtained to each α-value applying the Representation Theorem. Theorem 4.1 (Representation Theorem) Let A be a fuzzy set then we can verify [ A= Aα (2) α∈[0,1]

This theorem has an important restriction, the consistent restriction: If α1 > α2 then Aα1 ⊆ Aα2 . As we use the frequent itemset, we need to represent the frequent itemsets extracted as an unique fuzzy set. So we have to ensure the consistent restriction among each α frequent itemset I αi Proposition 4.1 Let T˜ be a fuzzy transactional data base, T α1 and T α2 the result to use the α-cut on T˜ with α = α1 , α2 , α1 , α2 ∈ [0, 1], α1 ≥ α2 . And let I α1 , I α2 be the set of frequent itemsets extracted from T α1 , T α2 respectively. Then, it is declared what I α1 ⊆ I α2 , ie, if I is frequent to level α1 then it is frequent to level α2 . Demonstration We suppose we have T˜ a fuzzy transactional data base, where each t ∈ T˜ represents a fuzzy set of T. If we apply the α-cut on T˜, we obtain T α . Then, if we use the values α1 , α2 ∈ [0, 1] with α1 ≥ α2 we get T α1 , T α2 respectively. So, T α1 ⊆ T α2 , by consistent restriction. Let I α1 , I α2 be the frequent itemsets from T α1 , T α2 respectively. Then ∀i ∈ I α1 , ∃t ∈ T α1 /i ∈ t; with T α1 ⊆ T α2 =⇒ t ∈ T α2 Let I α1 be the frequent itemset to T α1 =⇒ ∀i ∈ I α1 , supp(i) ≥ minsup to T α1 =⇒ supp(i) ≥ minsup to T α2 , ie, i ∈ I α2 =⇒ I α1 ⊆ I α2 In our method, we use the frequent itemset obtained to create the sequences patterns. However, now we have the frequent itemset to specific α value, so we will get sequences patterns to that specific α value. To represent the patterns sequences as a fuzzy set we use the Representation Theorem, for this fact we need to ensure the consistent restriction. αi

αj

Proposition 4.2 Let P , P be sets of sequences patterns where αi ≥ αj then P αi ⊆ P αj . Demonstration Let I αi , I αj be the set of frequent itemset obtained from T αi and T αj , respectively, with αi ≥ αj . Let P αi , P αj be the pattern valid set of I αi and I αj , respectively. We define the function perm(I) such that: perm(I) = {p/p is a I permutation and p ∈ T }

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(3)

where T is a transactional data base and I is a frequent itemset from T. Then, ∀I ∈ I αi perm(I) ∈ P αi . As I αi ⊆ I αj =⇒ I ∈ I αj . αj αi αi So perm(I) ∈ P I =⇒ P I ⊆ P I 4.3.2

An illustrative example

In this example we want to show the operation method. We start from ODB which is collected from the touched object by the user in the daily activity. We do not show the Data Base due to the lack of space. Let W a Fuzzy Temporal Window defines by the following fuzzy set over temporal line τ :   W

=



0,2 0,4 0,6 0,8 1 1 0 8:20 , 8:21 , 8:22 , 8:23 , 8:24 , 8:25 , 8:26 1 1 1 1 1 1 1 1 8:27 , 8:28 , 8:29 , 8:30 , 8:31 , 8:32 , 8:33 , 8:34 0,8 0,6 0,4 0,2 0 1 8:35 , 8:36 , 8:37 , 8:38 , 8:39 , 8:40

  (4) 

Then, we apply the W over the T and obtain a Fuzzy T T˜ where each time of happenes are replaced with the membership degree value of the W. We apply the α-cut for α values α1 = 0.4, α2 = 0.6, α3 = 0.8, α4 = 1.0. We obtain for each α values the T α , the result of apply the α-cut in T˜. After these operations, we have transformed the fuzzy problem to a crisp problem. We can extract frequent itemsets and sequences patterns with the model explained in section 3. We have executed the Apriori Algorithm with two support values: minsup = 0.8 and minsup = 0.9. The results are showed in tables 3 and table 4.

Table 3: Frequent itemset to minsup = 0.8 I α1 I α2 I α3 I α4

{Shoes, Bag, Keys, ODoor, MobilePhone} {Keys, Keys2, ODoor, ODoor2, MobilePhone} {Shoes, Bag, Keys, ODoor, MobilePhone} {Keys, Keys2, ODoor, ODoor2, MobilePhone} {Shoes, Bag, Keys, ODoor, MobilePhone} {Shoes, Bag, Keys, ODoor, MobilePhone}

Table 4: Frequent itemset to minsup = 0.9 I α1 I α2 I α3 I α4

{Keys, ODoor, MobilePhone} {Keys, ODoor, MobilePhone} {Keys, ODoor} {ODoor}

Since we have the common actions to specific behavior, the next stage consists of obtaining the valid sequences patterns and the final representation as a fuzzy set applying the Identity Principle. The valid patterns are

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showed in table 5 and table 6. And the final pattern representation in equation 5 to minsup = 0.8 and equation 6 to minsup = 0.9.

The system result is the fuzzy patterns sequences which define the behavior. To get it, we use the α-cuts and the Representation Theorem to obtain a fuzzy result applying the crisp method. That let us, we could demonstrate that the method obtain a fuzzy pattern Table 5: Valid patterns to minsup = 0.8 sequence set. In future work, we would like to extend the Fuzzy TemP α1 {Shoes, Bag, Keys, MobilePhone, ODoor} p1 poral Window concept, to adjust the interval using the {Shoes, Keys, MobilePhone, Bag, ODoor} p2 knowledge from user we have. This adjustment will be {Shoes, MobilePhone, Bag, Keys, ODoor} p3 made with quantified sentences. With this adjustment {Keys, MobilePhone, ODoor, Keys2, ODoor2} p4 {MobilePhone, Keys, ODoor, Keys2, ODoor2} p5 we will solve the possibility of a person changes his α2 habits. P IDEM α3 P {Shoes, Bag, Keys, MobilePhone, ODoor} p1 As well, we have to present a system which uses the {Shoes, Keys, MobilePhone, Bag, ODoor} p2 knowledge organized in that stage to take decision and {Shoes, MobilePhone, Bag, Keys, ODoor} p3 to send the correct alarms. When we work with sensors we have to control their P α4 IDEM operations. There are many reason to provoke the mistake in the sensor reading: the sensors or the reader could fail, the environment affects to the sensors, the ¾ n ½ o sensor damage, etc. The uncertainty from this situap p p p p p p p p p 2 3 4 5 1 2 3 4 5 1 , , , , = , , , , (5) tion will be studied and controlled in future works too. P˜ = α4 α4 α4 α2 α2 1 0.4 1 1 0.6

References

Table 6: Valid patterns to minsup = 0.9 P α1 P α2 P α3 P α4

½ P˜ =

5

{Keys, MobilePhone, ODoor} {MobilePhone, Keys, ODoor} IDEM {Keys, ODoor} {ODoor}

p1 p2 p3 p4 , , , α2 α2 α3 α4

¾ =

np

p1 p2 p3 p4

p2 p3 p4 o , , 0.6 0.6 0.8 1 1

[1] R. Agrawal; R. Srikan. Fast Algorithms for Mining Association Rules. IBM Research Report RJ9839, Junio 1994.

,

(6)

CONCLUSIONS

In this paper we have proposed a method to detect the user behavior. This problem is random imprecise and uncertain by definition. • random imprecise, because we do not know the interval of the time in which the action happen.

[2] R. Agrawal; R. Srikant. Mining Sequetial Pattern. In 11th International Conference on Data Engineering pages 3-14, Taipei, Taiwan, 1995. IEEE Computer Society Press. [3] Charu C. Aggarwal. Data Streams: Models and Algorithms. Hardcover, Advances in Database Systems Ser. 2003 [4] Ruey-Shun Chen , Gwo-Hshiung Tzengb, C. C. Chen and Yi-Chung Hu. Discovery of fuzzy sequential patterns for fuzzy partitions in quantitative attributes. ACS/IEEE International Conference on Computer Systems and Applications (AICCSA), 2001, pp. 144-150.

• uncertain, because it could exists a mistake in the sensor reading.

[5] Miguel Delgado, Mar´ıa Ros, Amparo Vila. Correct Behavior Identification System in a Tagged World. 1th Jornadas Cientficas sobre RFID, 2007.

We have studied the random imprecision of the problema. This imprecision appears due of a behavior is not static on a context, domain and for an user. Thus, we have designed a method which uses fuzzy logic to limit the events in a specific behavior using the Fuzzy Temporal Window. With the Window, we can assign a membership degree for each event to the studied behavior.

[6] Cline Fiot, Anne Laurent, Maguelonne Teisseire. Extended Time Constraints for Sequence Mining. 14th International Symposium on Temporal Representation and Reasoning TIME’07,2007

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[7] Mohamed Medhat Gaber, Arkady Zaslavsky, Shonali Krishnaswamy.Mining Data Streams: A Review.SIGMOD Record 2005. Vol(34), 2

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[8] Kyohei Koyama, Kouichi Nakagawa, and Hiromitsu Shimakawa, Embedded Action Detector to Enhance Freedom from Care, Proc. of 11th International Conference on Human-Computer Interaction, 8 pages, Las Vegas, Jul., 2005 [9] Matthai Philipose, Kenneth P Fishkin, Mike Perkowitz, Donald J. Patterson, Dieter Fox, Henry Kautz, Dirk Hhnel (2004). Inferring Activities from Interactions with Objects. ContextAware Computing. Pervasive computing 3(50-57) [10] Hung T. Nguyen, Elbert A. Walker, A first Course in Fuzzy Logic, Chapman & Hall/CRC Taoylr & Frances Group. 2006 [11] J. Pei, J. Han, B. Mortazavi-Asl, H. Pinto, Q. Chen, U. Dayal and M-C. Hsu. PrefixSpan: Mining Sequential Patterns Efficiently by PrefixProjected Pattern Growth. In. Proc. 2001 Int. Conf. Data Engineering (ICDE’01), pages 215-224, Heidelberg, Germany, April 2001. http://citeseer.ist.psu.edu/pei01prefixspan.html [12] Want R. RFID: A key to automating everything. Scientific American Magazine, page 10, January 2004.

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