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Sparse Principal Component Analysis
Arrays Gene expression Lasso/elastic net Multivariate analysis Singular value decomposition Thresholding
2015/8/21
Principal component analysis (PCA) is widely used in data processing and dimensionality reduction. However,PCA suffers from the fact that each principal component is a linear combination of all the or...
Robust Principal Component Analysis?
Principal components robustness vis-a-vis outliers nuclear-norm minimization `1-norm minimization duality low-rank matrices sparsity video surveillance
2015/6/17
This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove...
Independent component analysis via nonparametric maximum likelihood estimation
Blind source separation density estimation independent component analysis log-concave projection
2012/6/19
Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector $X = AS$, where $A$ is a non-singular matrix and $S$ has in...
Approximation Bounds for Sparse Principal Component Analysis
Sparse PCA convex relaxation semidefinite programming approximation bounds detection
2012/5/9
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testi...