Adaptive Fuzzy Leader Clustering

AFLC is an integrated neural-fuzzy clustering algorithm that can be used to learn cluster structure embedded in complex datasets in a self-organizing manner. The algorithm has a two-layer structure as illustrated in Fig. 6.1. The first layer uses a self-organizing neural network similar to ART1 [26-28] to find hard clusters. Let C be the current number of centroids and v^i = 1,...,C) representing the centroids. When a new sample xk comes in, it is normalized and then initially classified into the cluster on which it has the largest projection (a winner-take-all or MAXNET [29, 30] learning rule):

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where i* is the index of the winning centroid.

Vc Recognition

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Comparison

Xji Xj2 Xjp layer

Xj = {Xji, Xj2,...,Xjp} Figure 6.1: Adaptive fuzzy leader clustering (AFLC) structure.

The second layer serves as a verification process. By verifying the initial sample recognition through a vigilance test, the algorithm is able to dynamically create new clusters according to the data distribution when the verification fails, or optimize and update the system when the initial sample recognition is confirmed. The vigilance test consists of calculating a ratio between the distance of the sample to the winning cluster and the average distance of all the samples in this cluster to the cluster centroid,

When this ratio is higher than a user-defined threshold, the test fails and a new cluster is created, taking the sample as the initial centroid and assigning an initial cluster distance value to this new cluster (which has only one sample coinciding with the centroid; it is necessary to assign an initial distance value so that the vigilance test can be performed when the next sample is presented). Otherwise, the sample is officially classified into this cluster, and then its centroid and the fuzzy membership values are updated with the following optimization parameters:

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