Related papers: Iterative Block Tensor Singular Value Thresholding…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
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…
The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…
We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…
Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…
Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…
Low-rank tensor recovery problems have been widely studied in many applications of signal processing and machine learning. Tucker decomposition is known as one of the most popular decompositions in the tensor framework. In recent years,…
We introduce a novel visual tokenization framework that embeds a provable PCA-like structure into the latent token space. While existing visual tokenizers primarily optimize for reconstruction fidelity, they often neglect the structural…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
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…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
Early work established convergence of the principal component estimators of the factors and loadings up to a rotation for large dimensional approximate factor models with weak factors in that the factor loading $\Lambda^{(0)}$ scales…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…