Finding Pattern Behavior in Temporal Data Using Fuzzy Clustering

A clustering technique based on a fuzzy equivalence relation is used to characterize temporal data. Data collected during an initial time period are separated into clusters. These clusters are characterized by their centroids. Clusters formed during subsequent time periods are either merged with an existing cluster or added to the cluster list. The resulting list of cluster centroids, called a cluster group, characterizes the behavior of a particular set of temporal data. The degree to which new clusters formed in a subsequent time period are similar to the cluster group is characterized by a similarity measure, q. This technique has been applied to the problem of detecting driver behavior. INTRODUCTION Many different clustering techniques have been used for analyzing multivariate data [1]. These methods have been applied to problems in knowledge discovery and data mining [2]. The standard clustering algorithms assign each data sample to one of many clusters in which all samples in a particular cluster are similar in some sense. Fuzzy clustering algorithms do not insist that each sample must belong to only one cluster, but rather samples can belong to more than one cluster to varying degrees. The most well known fuzzy clustering algorithm is the fuzzy c-means algorithm [3] that requires that the number of cluster centers, c, be given. A different clustering approach that does not require the number of clusters to be known beforehand is based on the use of fuzzy equivalence relations [4, 5]. In this method a fuzzy compatibility relation matrix, Q, is formed in which each entry in the matrix represents the degree to which two different samples are close to each other. A value of 1 (on the main diagonal) represents the degree to which a sample is close to itself, while a value of 0 represents samples separated by the largest possible distance in the data set. The transitive closure of Q will induce crisp partitions of the data (resulting in different numbers of clusters) by choosing different α-cuts of a fuzzy set [5]. Clusters formed in this manner will be used in this paper to characterize pattern behavior in temporal data. This research was motivated by the desire to characterize a driver’s behavior by monitoring signals that are already being measured by the car’s computer