相关论文: Randomized Robust Subspace Recovery for High Dimen…

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show…

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…

This paper addresses how well we can recover a data matrix when only given a few of its elements. We present a randomized algorithm that element-wise sparsifies the data, retaining only a few its elements. Our new algorithm independently…

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…

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…

This work proposes a systematic model reduction approach based on rank adaptive tensor recovery for partial differential equation (PDE) models with high-dimensional random parameters. Since the standard outputs of interest of these models…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…

This paper provides a sparse signal recovery algorithm, DU-PSISTA (Deep Unfolded-Periodic Sketched Iterative Shrinkage-Thresholding Algorithm), which aims to balance computational efficiency and accuracy for recovering high-dimensional…

In large-scale statistical modeling, reducing data size through subsampling is essential for balancing computational efficiency and statistical accuracy. We propose a new method, Principal Component Analysis guided Quantile Sampling…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented…

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…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

We consider the problem of recovering elements of a low-dimensional model from linear measurements. From signal and image processing to inverse problems in data science, this question has been at the center of many applications. Lately,…

Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…

We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data. Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties. We…