arXiv research

Generalizes PCA to maximize any convex function of components.

Paper develops a dual formulation for PCA in Hilbert spaces.

Explains various PCA and SPCA methods with theory and applications.

Kernel PCA explains self-attention mechanisms in deep learning models.

New PCA method detects faults using occupation kernels.

Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.

Explains eigenvalue and generalized eigenvalue problems with examples.

Simplifies fair PCA with fast, efficient solution.

Paper extends RPD for better handling multiple modalities and non-convexity.

Personalized treatment of patients based on tissue-specific cancer subtypes has strongly increased the efficacy of the chosen therapies. Even though the amount of data measured for cancer patients has increased over the last years, most cancer subtypes are still diagnosed based on individual data sources (e.g. gene exp…

New method uses sparse kernel PCA for better outlier detection.

Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…

KPCA improves OoD detection by separating InD and OoD data.

A new method for efficient nonlinear process monitoring using random Bernoulli features.

PCHAL and PCHAR use principal components to speed up HAL and HAR methods.

Proposes an online method for high-dimensional streaming data.

Proposes a method to optimize class mean preservation in kernel-based feature spaces.

Kernelized PCovR reveals structure-property relations in chemistry and materials.

Enhances autoencoders with kernel alignment for better data representation.

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 monitored process is linear, nonlinear PCA models, such as autoencoder models and kern…

Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically a full $n \times n$ kernel matrix is constructed over $n$ data points, but this…

This work analyzes when contrastive models are close to PCA or kernel methods.

Proposes a new PCA method using SSIM for image subspace learning.

Two strategies for embedding new data points from proximity data are explored.

Efficient private matrix analysis algorithms for recent variants.

This study compares DR methods with kernel variations for face image analysis.

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

Additive principal components (APCs for short) are a nonlinear generalization of linear principal components. We focus on smallest APCs to describe additive nonlinear constraints that are approximately satisfied by the data. Thus APCs fit data with implicit equations that treat the variables symmetrically, as opposed t…

The paper introduces a method for interpretable principal component analysis of high-dimensional time series.

This paper aims to develop new techniques to describe joint behavior of stocks, beyond regression and correlation. For example, we want to identify the clusters of the stocks that move together. Our work is based on applying Kernel Principal Component Analysis(KPCA) and Functional Principal Component Analysis(FPCA) to …

A mean function in reproducing kernel Hilbert space, or a kernel mean, is an important part of many applications ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given finite samples, an empirical average is the standard estimate for the true kernel mean. We show that this e…

This work addresses two main issues of the standard Kernel Entropy Component Analysis (KECA) algorithm: the optimization of the kernel decomposition and the optimization of the Gaussian kernel parameter. KECA roughly reduces to a sorting of the importance of kernel eigenvectors by entropy instead of by variance as in K…

Study spectral properties of graph Laplacian for manifold data.

LLMs learn probability density functions in-context, showing distinct learning trajectories.

Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.

Two new PCA variants improve financial data analysis.

Paper introduces RKHM for more explicit variable structures analysis.

New simulations advise caution in choosing principal components for multivariate functional data.

Essential principal components simplify spectral analysis with minimal training data.

In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…

A novel outlier detection method for high-dimensional data.

QAPCA uses quantum annealing for robust PCA.

Paper uses PCA to analyze Chinese sovereign bonds and discusses bond immunization.

Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any dimension major results known for surfaces in space, which in turn yield a method to …

The paper uses diffusion approximations to analyze and optimize online principal component estimation.

We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…

In this paper the exact linear relation between the leading eigenvectors of the modularity matrix and the singular vectors of an uncentered data matrix is developed. Based on this analysis the concept of a modularity component is defined, and its properties are developed. It is shown that modularity component analysis …

HPPCA improves imputation of longitudinal data with missing values.