On the clustering of large-scale data: A matrix-based approach

Nowadays, the analysis of large amounts of digital documents become a hot research topic since the libraries and database are converted electronically, such as PUBMED and IEEE publications. The ubiquitous phenomenon of massive data and sparse information imposes considerable challenges in data mining research. In this paper, we propose a theoretical framework, Exemplar-based Low-rank sparse Matrix Decomposition (ELMD), to cluster large-scale datasets. Specifically, given a data matrix, ELMD first computes a representative data subspace and a near-optimal low-rank approximation. Then, the cluster centroids and indicators are obtained through matrix decomposition, in which we require that the cluster centroids lie within the representative data subspace. From a theoretical perspective, we show the correctness and convergence of the ELMD algorithm, and provide detailed analysis on its efficiency. Through extensive experiments performed on both synthetic and real datasets, we demonstrate the superior performance of ELMD for clustering large-scale data.