Dynamic Sparse Subspace Clustering for Evolving High-Dimensional Data Streams

In an era of ubiquitous large-scale evolving data streams, data stream clustering (DSC) has received lots of attention because the scale of the data streams far exceeds the ability of expert human analysts. It has been observed that high-dimensional data are usually distributed in a union of low-dimensional subspaces. In this article, we propose a novel sparse representation-based DSC algorithm, called evolutionary dynamic sparse subspace clustering (EDSSC). It can cope with the time-varying nature of subspaces underlying the evolving data streams, such as subspace emergence, disappearance, and recurrence. The proposed EDSSC consists of two phases: 1) static learning and 2) online clustering. During the first phase, a data structure for storing the statistic summary of data streams, called EDSSC summary, is proposed which can better address the dilemma between the two conflicting goals: 1) saving more points for accuracy of subspace clustering (SC) and 2) discarding more points for the efficiency of DSC. By further proposing an algorithm to estimate the subspace number, the proposed EDSSC does not need to know the number of subspaces. In the second phase, a more suitable index, called the average sparsity concentration index (ASCI), is proposed, which dramatically promotes the clustering accuracy compared to the conventionally utilized SCI index. In addition, the subspace evolution detection model based on the Page-Hinkley test is proposed where the appearing, disappearing, and recurring subspaces can be detected and adapted. Extinct experiments on real-world data streams show that the EDSSC outperforms the state-of-the-art online SC approaches.