A Distributed and Incremental SVD Algorithm for Agglomerative Data Analysis on Large Networks

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix $A$ is known. Further, the hierarchical algorithm can be used to recover the $d$ largest singular values and left singular vectors with bounded error. We also show that the proposed method is stable with respect to roundoff errors or corruption of the original matrix entries. Numerical experiments validate the proposed algorithms and parallel cost analysis

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Robust recursive eigendecomposition and subspace-based algorithms with application to fault detection in wireless sensor networks

The principal component analysis (PCA) is a valuable tool in multivariate statistics, and it is an effective method for fault detection in wireless sensor networks (WSNs) and other related applications. However, its online implementation requires the computation of eigendecomposition (ED) or singular value decomposition. To reduce the arithmetic complexity, we propose an efficient fault detection approach using the subspace tracking concept. In particular, two new robust subspace tracking algorithms are developed, namely, the robust orthonormal projection approximation subspace tracking (OPAST) with rank-1 modification and the robust OPAST with deflation. Both methods rely on robust M-estimate-based recursive covariance estimate to improve the robustness against the effect of faulty samples, and they offer different tradeoff between fault detection accuracy and arithmetic complexity. Since only the ED in the major subspace is computed, their arithmetic complexities are much lower than those of other conventional PCA-based algorithms. Furthermore, we propose new robust T 2 score and SPE detection criteria with recursive update formulas to improve the robustness over their conventional counterparts and to facilitate online implementation for the proposed robust subspace ED and tracking algorithms. Computer simulation and experimental results on WSN data show that the proposed fault detection approach, which combines the aforementioned robust subspace tracking algorithms with the robust detection criteria, is able to achieve better performance than other conventional approaches. Hence, it serves as an attractive alternative to other conventional approaches to fault detection in WSNs and other related applications because of its low complexity, efficient recursive implementation, and good performance. © 2012 IEEE.published_or_final_versio