Related papers: Structured Sparse Principal Component Analysis
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
Sparsity driven signal processing has gained tremendous popularity in the last decade. At its core, the assumption is that the signal of interest is sparse with respect to either a fixed transformation or a signal dependent dictionary. To…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing method. We consider two sparsity structures for the sparse…
Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…
We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a…
We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…
Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class…
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…
This paper proposes a novel sparse principal component analysis algorithm with self-learning ability for successive modes, where synaptic intelligence is employed to measure the importance of variables and a regularization term is added to…
In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
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…
This paper presents a new supervised representation learning framework, namely structured probabilistic coding (SPC), to learn compact and informative representations from input related to the target task. SPC is an encoder-only…
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…