Proximity-Based Clustering: A Search for Structural Consistency in Data With Semantic Blocks of Features

A class of clustering problems that is studied here is concerned with the development of a structure of a global nature given a collection of structures (clusters) constructed locally for data that are represented by several collections (blocks) of features. These blocks of features come with a well-defined semantics. For instance, in spatiotemporal data, a certain block of features concerns a spatial component of the data (say, x-y or x-y-z coordinates), while another one deals with the features that describe time series associated with the corresponding locations. The results of clustering that are being produced locally are reconciled by minimizing a distance between the proximity matrices that are formed at the higher conceptual level and induced by the individual partition matrices. The optimization problem is formulated and presented along with its iterative scheme.