相关论文: A co-kurtosis PCA based dimensionality reduction w…

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…

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…

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher…

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…

High-dimensional biological data often exhibit a severe mismatch between feature dimensionality and sample size, making reliable classification difficult in extremely small-data regimes. In these settings, kernel methods can lose…

The in silico exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools gained a lot of…

Parallel-wound no-insulation (PW-NI) high-temperature superconducting (HTS) coils significantly reduce charging delay while maintaining excellent self-protection capability, demonstrating great potential for high-field applications.…

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…

Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Retrieval-Augmented Generation enhances language models by retrieving relevant information from external knowledge bases, relying on high-dimensional vector embeddings typically stored in float32 precision. However, storing these embeddings…

This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored. While computing measures of uncertainty for nonlinear/nonconvex estimators is in…

Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In simple, homogeneous missingness settings with a noise level of constant order, we show that an existing inverse-probability weighted…

Dimensionality reduction is a classical technique widely used for data analysis. One foundational instantiation is Principal Component Analysis (PCA), which minimizes the average reconstruction error. In this paper, we introduce the…

PCA is widely used in health and care research to analyze complex HD datasets, such as patient health records, genetic data, and medical imaging. By reducing dimensionality, PCA helps identify key patterns and trends, which can aid in…

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and improve the accuracy of modeling. In this study, a new framework of modeling is suggested. Compared with other popular methods,…

Artificial neural networks (ANN) have been shown to be flexible and effective function estimators for identification of nonlinear state-space models. However, if the resulting models are used directly for nonlinear model predictive control…

In recent work, robust Principal Components Analysis (PCA) has been posed as a problem of recovering a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from their sum, $\mathbf{M}:= \mathbf{L} + \mathbf{S}$ and a provably exact…