Conference/Journal | Paper | Author | Keywords | Year | ICML 2011 | GoDec: Randomized Low-rank & Sparse Matrix Decomposition in Noisy Case | PDF BIBTEX DISCUSS TALK VEDIO CODE Tianyi Zhou, Dacheng Tao | Low-rank, sparse, structured learning, bilateral random projection, matrix decomposition, visual analysis, matrix completion | 2011 | ## Abstract:Low-rank and sparse structures have been profoundly studied in matrix completion and compressed sensing. In this paper, we develop ``Go Decomposition'' (GoDec) to efficiently and robustly estimate the low-rank part $L$ and the sparse part $S$ of a matrix $X=L+S+G$ with noise $G$. GoDec alternatively assigns the low-rank approximation of $X-S$ to $L$ and the sparse approximation of $X-L$ to $S$. The algorithm can be significantly accelerated by bilateral random projections (BRP). We also propose GoDec for matrix completion as an important variant. We prove that the objective value $\|X-L-S\|_F^2$ converges to a local minimum, while $L$ and $S$ linearly converge to local optimums. Theoretically, we analyze the influence of $L$, $S$ and $G$ to the asymptotic/convergence speeds in order to discover the robustness of GoDec. Empirical studies suggest the efficiency, robustness and effectiveness of GoDec comparing with representative matrix decomposition and completion tools, e.g., Robust PCA and OptSpace.## Problem solved:Low-rank and sparse matrix decomposition in noisy case.## Applications:1. Visual analysis, such as background modeling and light/shadow removal2. Matrix Completion
Consider the noisy model $X=L+S+G$, can handle approximated decomposition even when the exact and unique decomposition does not exist;2. Decomposition robustness to the noise part $G$; |

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