arXiv research

Paper proposes tensor sparse PCA for improved face recognition accuracy.

New method uses sparse kernel PCA for better outlier detection.

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

Derives kernel PCA with Nyström method for scalability.

Explains various PCA and SPCA methods with theory and applications.

Solution to sparse PCA tuning problem using Empirical Bayes.

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

Generative Kernel PCA explores latent spaces for data interpretation and novelty detection.

Efficiently approximates Sparse PCA with significant speedups and minor error.

One-shot algorithm for feature-distributed kernel PCA reduces communication costs.

Sparse PCA selects variables with FDR control for improved performance.

Simplifies fair PCA with fast, efficient solution.

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.

Efficient algorithm for sparse PCA reduces data complexity.

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

msPCA solves sparse PCA for multiple components efficiently.

A new method generalizing subspace learning for improved classification.

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…

Efficiently performs PCA on large datasets using Nyström sampling.

Kernel method is a very powerful tool in machine learning. The trick of kernel has been effectively and extensively applied in many areas of machine learning, such as support vector machine (SVM) and kernel principal component analysis (kernel PCA). Kernel trick is to define a kernel function which relies on the inner-…

New method solves sparse PCA and CCA with guaranteed convergence.

Kernel PCA helps analyze multivariate extremes and clusters them effectively.

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

Algorithm recovers sparse PCA support from incomplete data.

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…

Paper proposes estimators for sparse PCA with oracle property.

We describe how cross-kernel matrices, that is, kernel matrices between the data and a custom chosen set of `feature spanning points' can be used for learning. The main potential of cross-kernels lies in the fact that (a) only one side of the matrix scales with the number of data points, and (b) cross-kernels, as oppos…

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…

New bounds on KPCA efficiency reveal conditions for fast convergence.

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…

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.

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…

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…

New algorithm reduces kernel PCA to $O(\sqrt{n})$ features for streaming data.

A fast randomized PCA for sparse data, up to 9.1X faster.

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…

New PCA method detects faults using occupation kernels.

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…

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