We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a low-rank core and the corresponding sparse residual. Rigorous theoretical analysis of the proposed algorithm results in exact recovery guarantees with low computati...

Complex principal component analysis (CPCA) is a useful linear method for dimensionality reduction of data sets characterized by propagating patterns, where the CPCA modes are linear functions of the complex principal component (CPC), consisting of an amplitude and a phase. The use of non-linear 5 methods, such as the neural-network based circular non-linear principal component analysis (NLPCA....

In this paper, we propose an improved principal component analysis based on maximum entropy (MaxEnt) preservation, called MaxEnt-PCA, which is derived from a Parzen window estimation of Renyi’s quadratic entropy. Instead of minimizing the reconstruction error either based on L2-norm or L1-norm, the MaxEnt-PCA attempts to preserve as much as possible the uncertainty information of the data measu...

Principal Component Analysis (PCA) is one of the most important methods to handle highdimensional data. However, the high computational complexitymakes it hard to apply to the large scale data with high dimensionality, and the used 2-norm makes it sensitive to outliers. A recent work proposed principal component analysis based on 1-normmaximization, which is efficient and robust to outliers. In...

In this paper, we analyze the performance of a semiparametric principal component analysis named Copula Component Analysis (COCA) (Han & Liu, 2012) when the data are dependent. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. We study the scenario where the observations are drawn from non-i.i.d. processes ...