PTS: Projected Topological Stream clustering algorithm

Abstract

High-dimensional data streams clustering is an attractive research topic, as there are several applications that generate a high number of attributes, bringing new challenges in terms of partitioning due to the curse of dimensionality. In addition, those applications produce unbounded sequences of data which cannot be stored for later analysis. Although the importance of this scenario, there are still very few algorithms available in the literature to meet this task. Despite the theoretical foundation of mathematical topology for dealing with high-dimensional spaces, none of those approaches have investigated the problem of finding topologically similar projected clusters in high-dimensional data streams. Among the advantages of topology is the possibility to analyze data in a coordinate-free and noise-robust manner. In a previous research, we have shown that topologically similar clusters can be meaningful considering real-world data sets. In this paper, we extend those ideas and propose PTS, an algorithm for finding topologically similar clusters in high-dimensional data streams. The algorithm is capable of finding traditional projected clusters and then merging them according to topological features computed using persistent homology. Experiments with synthetic data streams of dimensions d=8,16,32,64 and 128 confirm the ability of PTS to find topologically similar projected clusters.