Principal Component Analysis
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Related Articles from SNS
A Robust Optimization Approach to Sparse Principal Component Analysis
arXiv:2606.03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data. Existing methods address this by promoting sparsity through explicit $\ell_1$-penalties, but these are not obvious to tune due to the unsupervised nature of the task. In contrast, we propose Adversarial PCA (AdvPCA), which leverages robust optimization to achieve sparsity by...
Enhancing Blind Source Separation with Dissociative Principal Component Analysis
arXiv:2411.12321v2 Announce Type: replace Abstract: Principal component analysis (PCA) and its sparse variants (sPCA) are widely used as a precursor to independent component analysis (ICA) for blind source separation (BSS). However, sPCA typically relies on a deflation strategy that extracts components sequentially and imposes orthogonality between them. When the underlying sources overlap, this discards the cross component structure that ICA depends on, degrading separation.
On the Wasserstein Geodesic Principal Component Analysis of probability measures
arXiv:2506.04480v2 Announce Type: replace-cross Abstract: This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best capture the modes of variation of the underlying dataset. We first address the case of a collection of Gaussian distributions, and show how to lift the computations in the space of invertible linear maps.
CPCANet: Deep Unfolding Common Principal Component Analysis for Domain Generalization
Announce Type: replace Abstract: Domain Generalization (DG) aims to learn representations that remain robust under out-of-distribution (OOD) shifts and generalize effectively to unseen target domains. While recent invariant learning strategies and architectural advances have achieved strong performance, explicitly discovering a structured domain-invariant subspace through second-order statistics remains underexplored. In this work, we propose CPCANet, a novel framework grounded in Common...
What Does Debiasing Really Remove? A Geometric Study of PCA-Based Gender Debiasing in Word Embeddings
Announce Type: new Abstract: Debiasing methods based on principal component analysis (PCA) are broadly used to reduce gender bias in word embeddings used in LLMs, yet it remains unclear what aspects of bias they actually remove and how destructive this process is. These methods are based on the understanding that bias resides in a low-dimensional subspace, with the assumption that most of it can be captured by a few principal components. In this work, we conduct a systematic geometric...
Machine-learning surrogate model for one-dimensional GaAs/Al$_{0.3}$Ga$_{0.7}$As distributed Bragg reflector spectra
arXiv:2606.08108v1 Announce Type: new Abstract: We present a Gaussian-process (GP) surrogate model for the normal-incidence reflectance spectrum of one-dimensional GaAs/Al$_{0.3}$Ga$_{0.7}$ distributed Bragg reflectors (DBRs). A Latin-hypercube dataset of 1500 transfer-matrix-method (TMM) simulations is used to train and evaluate the model. Principal component analysis reduces the spectral output to 26 components; one GP is fitted per component.
Anchor PCA
arXiv:2606.06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data.
Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation
arXiv:2505.10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample. We analyze a compressed variant of Oja's algorithm for estimating the principal eigenvector of the data covariance matrix using only two adaptive measurements per sample. At each iteration, we observe one measurement along the current estimate and one in a random...
Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA
Announce Type: replace-cross Abstract: We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works have established that acceleration can improve convergence rates compared to the standard Noisy Power Method, these guarantees require overly restrictive upper bounds on the magnitude of the perturbations, limiting their...
Dimensionality Reduction for Cyberattack Classification: A Comparative Evaluation of PCA and Linear Predictive Coding
arXiv:2606.05584v1 Announce Type: new Abstract: High-dimensional feature representations are widely used in machine learning-based cyberattack detection systems. However, they increase computational complexity and may hinder deployment in resource-constrained environments. In this paper, we investigate feature compression techniques for cyberattack classification by comparing two dimensionality reduction approaches: Principal Component Analysis (PCA) and Linear Predictive Coding (LPC).