arXiv research

Efficient algorithm for sparse PCA reduces data complexity.

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and functional (smooth) aspects and may benefit from a regularization scheme that can captur…

SDSPCA improves PCA for disease diagnosis using sparse components and discriminative information.

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm scalability and model interpretability are difficult to achieve, not to mention the preval…

Solution to sparse PCA tuning problem using Empirical Bayes.

Unified framework for structured principal subspace estimation with bounds and rates.

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…

The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.

Paper proposes tensor sparse PCA for improved face recognition accuracy.

New combinatorial method for sparse PCA works beyond spiked identity model.

Efficiently approximates Sparse PCA with significant speedups and minor error.

New method relaxes PCA orthogonality constraints using explained variance of correlated components.

Sparse PCA selects variables with FDR control for improved performance.

We give a reduction from {\sc clique} to establish that sparse PCA is NP-hard. The reduction has a gap which we use to exclude an FPTAS for sparse PCA (unless P=NP). Under weaker complexity assumptions, we also exclude polynomial constant-factor approximation algorithms.

New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.

Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties o…

A new method for sparse PCA using orthogonal rotations and soft-thresholding.

The paper provides entrywise bounds for Sparse PCA, improving upon previous results.

msPCA solves sparse PCA for multiple components efficiently.

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to be similar to many sparse PCA methods. However, CUR takes a randomized algorithm…

New method solves sparse PCA and CCA with guaranteed convergence.

New PCA method handles multiple datasets and detects sparse patterns robustly.

Algorithm recovers sparse PCA support from incomplete data.

New method solves sparse PCA for multiple components efficiently.

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact tha…

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 solution. By recursively solving these sub-problems in an analytical way, an ef…

Sparse PCA algorithm improves upon existing methods with better guarantees.

The paper analyzes sparse PCA for incomplete data and proves support recovery conditions.

New algorithms recover sparse tensor principal components efficiently.

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components are computed, the interpretation of the selected variables is difficult since ea…

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical cor…

Paper proposes estimators for sparse PCA with oracle property.

A new PCR method using SVD with sparse regularization.

The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the r…

We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between maximizing the variance explained by the components and promoting sparsity of the loading…

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1) a simple and efficient algorithm that achieves an $n^{-1/3}$-approximation; 2) NP-hardness of approximatio…

Reduces average-case complexity of sparse PCA from weak PC conjectures.

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components (PCs) are usually linear combinations of all the original variables, and it is thus…

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical r…

Improved estimation of multiple principal components using manifold optimization and iterative deflation techniques.

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 interpretability of the features. We study the problem of constructing optimal sparse linear a…

Sparse APCA identifies sparse factors in financial returns over time.

We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method. We also discuss the dependent case where the covariance matrix $Σ$ is not necessarily diagonal.

A new method detects sparse changes in high-dimensional data streams using tailored PCA projections.

sPCA models may not have orthogonal scores and loadings, complicating interpretation.

AdvPCA uses robust optimization to achieve sparse PCA without tuning.

PCA minor projection is most sensitive to distributional changes in bivariate data.

Unified analysis for robust PCA decomposition with sparse components in known dictionaries.