Hierarchical Clustering from ICA Mixtures

Abstract

In this chapter, we present a procedure for clustering (unsupervised learning) data from a model based on mixtures of independent component analyzers. Clustering techniques have been extensively studied in many different fields for a long time. They can be organized in different ways according to several theoretical criteria. However, a rough widely accepted classification of these techniques is: hierarchical and partitional clustering; see for instance. Both clustering categories provide a division of the data objects. The hierarchical approach also yields a hierarchical structure from a sequence of partitions performed from singleton clusters to a cluster including all data objects (agglomerative or bottom-up strategy) or vice versa (divisive or top-down strategy). This structure consists of a binary tree (dendrogram) whose leaves are the data objects and whose internal nodes represent nested clusters of various sizes. The whole node of the dendrogram represents the whole data set. The internal nodes describe the extent that the objects are proximal to each other; and the height of the dendrogram usually represents the distance between each pair of objects or clusters, or an object and a cluster.