Related papers: Optimal Projected Variance Group-Sparse Block PCA
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…
Sparse linear prediction methods suffer from decreased prediction accuracy when the predictor variables have cluster structure (e.g. there are highly correlated groups of variables). To improve prediction accuracy, various methods have been…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
Block Principal Component Analysis (Block PCA) of a data matrix A, where loadings Z are determined by maximization of AZ 2 over unit norm orthogonal loadings, is difficult to use for the design of sparse PCA by 1 regularization, due to the…
Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning. While existing study of PCA focuses on the recovery of principal components and their associated eigenvalues, there are few precise characterizations…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…
When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when…
Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…
We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is…
Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…
We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…