In recent times there has been an increase in data availability in continuous data streams and clustering of this data has many advantages in data analysis. It is often the case that these data streams are not stationary, but evolve over time, and also that the clusters are not regular shapes but form arbitrary shapes in the data space. Previous techniques for clustering such data streams are either hybrid online / offline methods, windowed offline methods, or find only hyper-elliptical clusters. In this paper we present a fully online technique for clustering evolving data streams into arbitrary shaped clusters. It is a two stage technique that is accurate, robust to noise, computationally and memory efficient, with a low time penalty as the number of data dimensions increases. The first stage of the technique produces micro-clusters and the second stage combines these micro-clusters into macro-clusters. Dimensional stability and high speed is achieved through keeping the calculations both simple and minimal using hyper-spherical micro-clusters. By maintaining a graph structure, where the micro-clusters are the nodes and the edges are its pairs with intersecting micro-clusters, we minimise the calculations required for macro-cluster maintenance. The micro-clusters themselves are described in such a way that there is no calculation required for the core and shell regions and no separate definition of outer micro-clusters necessary. We demonstrate the ability of the proposed technique to join and separate macro-clusters as they evolve in a fully online manner. There are no other fully online techniques that the authors are aware of and so we compare the technique with popular online / offline hybrid alternatives for accuracy, purity and speed. The technique is then applied to real atmospheric science data streams and used to discover short term, long term and seasonal drift and their effects on anomaly detection. As well as having favourable computational characteristics, the technique can add analytic value over hyper-elliptical methods by characterising the cluster hyper-shape using Euclidean or fractal shape factors. Because the technique records macro-clusters as graphs, further analytic value accrues from characterising the order, degree, and completeness of the cluster-graphs as they evolve over time.
- Arbitrary shape
ASJC Scopus subject areas
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications
- Information Systems and Management
- Artificial Intelligence