Related papers: Provable Inductive Robust PCA via Iterative Hard T…

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…

Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

In the field of data mining, how to deal with high-dimensional data is an inevitable problem. Unsupervised feature selection has attracted more and more attention because it does not rely on labels. The performance of spectral-based…

Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…

High-dimensional data often contain low-dimensional signals obscured by structured background noise, which limits the effectiveness of standard PCA. Motivated by contrastive learning, we address the problem of recovering shared signal…

We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…

This work studies the problem of sequentially recovering a sparse vector $x_t$ and a vector from a low-dimensional subspace $l_t$ from knowledge of their sum $m_t = x_t + l_t$. If the primary goal is to recover the low-dimensional subspace…

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

The locally competitive algorithm (LCA) can solve sparse coding problems across a wide range of use cases. Recently, convolution-based LCA approaches have been shown to be highly effective for enhancing robustness for image recognition…

Machine learning models are prone to capturing the spurious correlations between non-causal attributes and classes, with counterfactual data augmentation being a promising direction for breaking these spurious associations. However,…

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or…

We analyze the decomposition of a data matrix, assumed to be a superposition of a low-rank component and a component which is sparse in a known dictionary, using a convex demixing method. We provide a unified analysis, encompassing both…

This paper studies the principal component (PC) method-based estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PC estimators of loadings, which comes from the…

Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…