DIC: A Novel Discrete Incremental Clustering Technique for the Derivation of Fuzzy Membership Functions

Abstract

Generally, clustering techniques may be classified into hierarchical-based and partition-based techniques. Hierarchical-based clustering techniques included single link [1], complete link [2] and [3][4]. The main drawback of hierarchical clustering is that it is static, and points committed to a given cluster in the early stages cannot be moved to a different cluster. Prototype-based partition clustering techniques, on the other hand, are dynamic and the data points can move from one cluster to another under varying conditions. However, partition-based clustering techniques require prior knowledge such as the number of classes, C, in the set of training data. Such information may be unknown and is difficult to estimate in data sets such as traffic flow data [5]. For tasks such as the 2-Spiral problem [6], computing a predefined number of clusters, C, may not be good enough to satisfactorily solve the tasks. Moreover, partition-based clustering techniques suffer from the stability-plasticity dilemma [7] where new information cannot be learned without running the risk of eroding old (previously learned) but valid knowledge. Therefore, in the context of neural fuzzy systems [8] such as POPFNN [9], hierarchical clustering violates the networks’ ability to self-organize and self-adapt with changing environments while current partition-based clustering techniques have some significant shortcomings. These deficiencies serve as the main motivations behind the development of the Discrete Incremental Clustering (DIC) technique. The DIC technique is not limited by the need to have prior knowledge of the number of clusters C and it preserves the dynamism of partition-based clustering techniques. The proposed DIC technique is implemented in a new neural fuzzy network named Gen-SoFNN [10] to demonstrate its performance.