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Online robust pca via stochastic optimization

by Jiashi Feng, Huan Xu, Shuicheng Yan - in Adv. Neural Info. Proc. Sys. (NIPS , 2013
"... Robust PCA methods are typically based on batch optimization and have to load all the samples into memory during optimization. This prevents them from ef-ficiently processing big data. In this paper, we develop an Online Robust PCA (OR-PCA) that processes one sample per time instance and hence its m ..."
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Robust PCA methods are typically based on batch optimization and have to load all the samples into memory during optimization. This prevents them from ef-ficiently processing big data. In this paper, we develop an Online Robust PCA (OR-PCA) that processes one sample per time instance and hence its memory cost is independent of the number of samples, significantly enhancing the computation and storage efficiency. The proposed OR-PCA is based on stochastic optimization of an equivalent reformulation of the batch RPCA. Indeed, we show that OR-PCA provides a sequence of subspace estimations converging to the optimum of its batch counterpart and hence is provably robust to sparse corruption. Moreover, OR-PCA can naturally be applied for tracking dynamic subspace. Comprehensive simulations on subspace recovering and tracking demonstrate the robustness and efficiency advantages of the OR-PCA over online PCA and batch RPCA methods. 1
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Rank regularization and bayesian inference for tensor completion and extrapolation. arXiv preprint arXiv:1301.7619

by Juan Andrés Bazerque, Gonzalo Mateos, Georgios B. Giannakis , 2013
"... factors capturing the tensor’s rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabil ..."
Abstract - Cited by 6 (4 self) - Add to MetaCart
factors capturing the tensor’s rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and prediction capabilities. This probabilistic approach can naturally accommodate general models for the data distribu-tion, lending itself to various fitting criteria that yield optimum estimates in the maximum-a-posteriori sense. In particular, two algorithms are devised for Gaussian- and Poisson-distributed data, that minimize the rank-regularized least-squares error and Kullback-Leibler divergence, respectively. The proposed technique is able to recover the “ground-truth ” tensor rank when tested on synthetic data, and to complete brain imaging and yeast gene expression datasets with 50 % and 15 % of missing entries respectively, resulting in recovery errors at and. Index Terms—Bayesian inference, low-rank, missing data, Poisson process, tensor. I.
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Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System

by Zhaoyi Kang, Costas J. Spanos
"... Abstract—Sequential or online dimensional reduction is of interests due to the explosion of streaming data based appli-cations and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the cla ..."
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Abstract—Sequential or online dimensional reduction is of interests due to the explosion of streaming data based appli-cations and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional reduction. However, traditional Singular Value Decomposition (SVD) based PCA fails to model data which largely deviates from Gaussian distribution. The Bregman Divergence was recently introduced to achieve a generalized PCA framework. If the random variable under dimensional reduction follows Bernoulli distribution, which occurs in many emerging fields, the generalized PCA is called Logistic PCA (LPCA) [1]. In this paper, we extend the batch LPCA to a sequential version (i.e. SLPCA), based on the sequential convex optimization theory. The convergence property of this algorithm is discussed compared to the batch version of LPCA (i.e. BLPCA), as well as its performance in reducing the dimension for multivariate binary-state systems. Its application in building energy end-use profile modeling is also investigated. I.
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