On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,786 papers · 148 categories

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48 results for “Euclidean PCA”

Principal symmetric space analysismath.ST

Develops PCA for symmetric spaces using geodesic submanifolds.

problem PCA for data on Riemannian symmetric spaces.

method Totally geodesic submanifolds for approximation.

result Illustrated on n-spheres, Grassmannians, n-tori and polyspheres.

PCA Riemannian symmetric spaces geodesic submanifolds Euclidean PCA

2019-08-13abs ↗pdf ↗

Efficient convex PCA with applications to Wasserstein GPCA and ranked datastat.CO

Convex PCA improves Euclidean PCA for convex data subsets.

problem Improving PCA for convex data subsets.

method Developed new theoretical results and a numerical implementation for finite dimensional convex PCA.

result Finite dimensional convex PCA approximates Wasserstein GPCA and ranked compositional data.

Convex PCA Wasserstein space Wasserstein GPCA Ranked data Hilbert space

2022-11-05abs ↗pdf ↗

Barycentric Subspace Analysis on Manifoldsmath.ST

This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly defined as the locus of points which are weighted means of $k+1$ reference points.…

2016-07-11abs ↗pdf ↗

Probabilistic Geometric Principal Component Analysis with application to neural datacs.LG

PGPCA improves PCA for nonlinear data in neuroscience.

problem Nonlinear data distribution in neuroscience.

method Developed PGPCA for nonlinear manifolds, incorporating EM algorithm.

result PGPCA outperforms PPCA in modeling data around nonlinear manifolds.

neuroscience dimensionality reduction nonlinear manifold Probabilistic Geometric PCA EM algorithm

2025-09-22abs ↗pdf ↗

Spherical Principal Component Analysiscs.LG

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for anal…

2019-03-16abs ↗pdf ↗

Principal Component Analysis Using Structural Similarity Index for Imageseess.IV

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

problem Lack of principled assessment methods for image fidelity and similarity.

method Defines an image structure subspace using SSIM, proposes ISCA and kernel ISCA.

result Demonstrates improved image subspace learning using SSIM.

Principal Component Analysis Structural Similarity Index Image Subspace Image Quality Assessment Manifold Learning

2019-08-25abs ↗pdf ↗

Principal Component Analysis in Space Formsstat.ML

PCA adapted for curved spaces improves data analysis.

problem PCA's limitations in curved spaces.

method Space Form PCA (SFPCA) for Riemannian manifolds.

result SFPCA provides faster and more accurate subspaces estimation.

PCA space forms Riemannian manifolds affine subspaces curvature

2023-01-06abs ↗pdf ↗

Improving the Accuracy of Principal Component Analysis by the Maximum Entropy Methodstat.ML

Improved PCA accuracy using maximum entropy method.

problem Accuracy issues in classical PCA.

method Model uncertainty with random variables, apply Maximum Entropy Method.

result Improved estimates of distances between data items.

PCA maximum entropy distance estimation approximate nearest neighbor

2019-07-24abs ↗pdf ↗

Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Datastat.ML

Paper improves robust PCA for noisy, outlier, and missing data.

problem Robust PCA with noise, outliers, and missing data.

method Bridging convex and nonconvex optimization.

result Near-optimal statistical accuracy for robust PCA.

robust PCA convex optimization nonconvex optimization matrix estimation missing data

2020-01-15abs ↗pdf ↗

Riemannian Principal Component Analysisstat.ML

R-PCA extends PCA to Riemannian manifolds for structured data.

problem Applying PCA to data on Riemannian manifolds without vector space operations.

method Adapting PCA to Riemannian manifolds by equipping data with local metrics.

result Unified approach for dimensionality reduction and statistical analysis on manifolds.

Riemannian manifolds Principal Component Analysis Geodesic Analysis Structured data Local metrics

2025-05-30abs ↗pdf ↗

Efficient coordinate-descent for orthogonal matrices through Givens rotationscs.LG

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we…

2013-12-02abs ↗pdf ↗

Structured Sampling for Robust Euclidean Distance Geometrycs.LG

Paper tackles robust Euclidean distance estimation with sparse outliers.

problem Estimating point positions from corrupted distance measurements.

method Proposes a novel algorithm using Nyström method and robust PCA.

result Achieves accurate recovery with minimal anchors and sparse outliers.

Euclidean distance geometry robust PCA sparse outliers Nyström method robust estimation

2024-12-14abs ↗pdf ↗

Efficient fair PCA for fair representation learningstat.ML

Simplifies fair PCA with fast, efficient solution.

problem Learning fair low-rank approximations of data.

method Conceptually simple approach with analytic solution.

result Faster and similar results to existing fair PCA methods.

fair PCA principal component analysis kernel PCA manifold optimization

2023-02-26abs ↗pdf ↗

Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysisq-fin.ST

KAN-PCA improves asset return analysis by capturing more variance than classical PCA during market crises.

problem Inefficient classical PCA during market crises when correlations between assets change dramatically.

method KAN-PCA uses KAN (Kolmogorov-Arnold Networks) with B-spline functions to learn nonlinear projections.

result KAN-PCA achieves a higher reconstruction R^2 (66.57%) compared to classical PCA (62.99%) on 20 S&P 500 stocks.

asset return analysis market crises PCA nonlinear factor decomposition spectral approach

2026-03-30abs ↗pdf ↗

Fair principal component analysis (PCA): minorization-maximization algorithms for Fair PCA, Fair Robust PCA and Fair Sparse PCAstat.ML

New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.

problem Fair Principal Component Analysis (FPCA) to ensure fairness in PCA solutions.

method Iterative MM algorithm with SDP reformulation to quadratic program.

result Algorithm monotonically improves fairness objectives at each iteration.

Fair PCA Robust PCA Sparse PCA MM algorithm SDP reformulation

2023-05-10abs ↗pdf ↗

The

φ

-PCA Framework: A Unified and Efficiency-Preserving Approach with Robust Variantsstat.ME

Unified framework improves PCA for outliers and distributed data.

problem Outliers and limitations in PCA for large-scale applications.

method φ-PCA framework that retains PCA efficiency and adds robustness.

result HM-PCA achieves optimal robustness and efficiency.

PCA robustness distributed outliers efficiency

2025-10-15abs ↗pdf ↗

TL-PCA: Transfer Learning of Principal Component Analysiscs.LG

TL-PCA uses transfer learning to improve PCA performance with limited target data.

problem PCA performance is limited with scarce target data.

method Transfer learning approach to PCA (TL-PCA) that combines source task knowledge with target task data.

result Improved PCA representation for dimensionality reduction with limited target data.

transfer learning PCA dimensionality reduction limited data eigendecomposition

2024-10-14abs ↗pdf ↗

Bucketed PCA Neural Networks with Neurons Mirroring Signalscs.LG

Bucketed PCA-NN outperforms DNNs by 96% on MNIST.

problem Benchmarking deep neural networks for supervised classification.

method Applies PCA to individual buckets constructed in two phases, retains neural network architecture, and uses neurons that mirror input signals.

result Bucketed PCA-NN achieves 96% accuracy on MNIST, similar to DNNs.

PCA Neural Networks Bucketing Classification Accuracy

2021-08-02abs ↗pdf ↗

A Deep-Learning-Based Geological Parameterization for History Matching Complex Modelsstat.ML

A new low-dimensional parameterization based on principal component analysis (PCA) and convolutional neural networks (CNN) is developed to represent complex geological models. The CNN-PCA method is inspired by recent developments in computer vision using deep learning. CNN-PCA can be viewed as a generalization of an ex…

2018-07-07abs ↗pdf ↗

Anchor PCAstat.ML

Anchor PCA improves robustness in multi-domain PCA.

problem PCA on pooled data can focus on spurious directions.

method Anchor PCA focuses on shared directions of variation.

result Anchor PCA outperforms pooling and worst-case alternatives.

PCA multi-domain robustness dimension reduction

2026-06-04abs ↗pdf ↗

Fair PCA, One Component at a Timecs.LG

A new method for fair PCA ensures balanced error across groups.

problem Balancing approximation error across different groups in multi-group data.

method Iterative method to compute fair principal components minimizing max group-wise reconstruction error.

result Preserves the containment property of standard PCA and reduces to standard PCA for single-group data.

fair PCA min-max fairness principal components group-wise error containment property

2025-03-27abs ↗pdf ↗

Unsupervised and Supervised Principal Component Analysis: Tutorialstat.ML

This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, an…

2019-06-01abs ↗pdf ↗

Rethinking PCA Through Dualitycs.LG

Revisits PCA with new formulations and insights.

problem Improving PCA formulations and understanding.

method Difference-of-convex (DC) framework, kernelizability, out-of-sample applicability, simultaneous iteration, DCA perspective.

result PCA-like problems are kernelizable and have new optimization perspectives.

PCA kernelization difference-of-convex simultaneous iteration QR algorithm

2025-10-20abs ↗pdf ↗

Log-Ratio Propagation on the Simplex: A Theory of Cellwise Contamination for Compositional Datastat.ML

A theory of cellwise contamination for compositional data using log-ratios.

problem Contamination in compositional data analysis.

method Develops a theory combining contamination model and propagation theorem.

result Reduction in cellwise breakdown value by

(D-1)/D

for certain estimators.

compositional data log-ratios contamination cellwise robustness PCA

2026-05-29abs ↗pdf ↗

σ

-PCA: a building block for neural learning of identifiable linear transformationscs.LG

Proposes $σ$ -PCA to learn identifiable linear transformations without whitening.

problem Cannot identify axes with equal variances in PCA.

method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.

result Eliminates subspace rotational indeterminacy in PCA.

PCA linear transformations rotational indeterminacy statistical independence whitening

2023-11-22abs ↗pdf ↗

Empirical Bayes Covariance Decomposition, and a Solution to the Multiple Tuning Problem in Sparse PCAstat.ME

Solution to sparse PCA tuning problem using Empirical Bayes.

problem Sparse PCA multiple tuning problem (MTP).

method Empirical Bayes covariance decomposition for penalized PCA.

result Empirical Bayes approach efficiently solves MTP in sparse PCA.

sparse PCA multiple tuning problem Empirical Bayes covariance decomposition penalized PCA

2023-12-06abs ↗pdf ↗

Shapley Values of Reconstruction Errors of PCA for Explaining Anomaly Detectionstat.ML

Method calculates Shapley values for PCA reconstruction errors to explain anomaly detection.

problem Explaining PCA-based anomaly detection results.

method Utilizes probabilistic PCA view to compute Shapley values of reconstruction errors.

result Shapley values are more advantageous than raw errors for explaining anomalies.

PCA Anomaly Detection Shapley Values Reconstruction Errors Probabilistic PCA

2019-09-08abs ↗pdf ↗

PCA++: How Uniformity Induces Robustness to Background Noise in Contrastive Learningstat.ML

PCA++ improves robustness to background noise in contrastive learning.

problem Recovering shared signal subspaces from positive pairs in high-dimensional data with structured background noise.

method PCA++ uses hard uniformity-constrained contrastive learning to enforce identity covariance on projected features.

result PCA++ outperforms standard PCA and alignment-only PCA+ in simulations and real-world datasets.

contrastive learning PCA robustness background noise signal recovery

2025-11-15abs ↗pdf ↗

Empirical Bayes PCA in high dimensionsstat.ME

EB-PCA reduces noise in high-dimensional PCA by estimating a joint prior distribution.

problem High-dimensional PCA noise in samples comparable to or larger than data.

method Empirical Bayes PCA using Kiefer-Wolfowitz MLE, random matrix theory, and AMP algorithm.

result EB-PCA achieves Bayes-optimal accuracy in spiked models and significantly improves over PCA in simulations and real data.

PCA Bayesian High dimensions Empirical Bayes AMP algorithm

2020-12-21abs ↗pdf ↗

Black-Box

k

-to-

1

-PCA Reductions: Theory and Applicationsmath.NA

New analysis improves black-box $k$ -PCA algorithms, reducing parameter loss.

problem Designing efficient

k

-PCA algorithms with black-box access to a 1-PCA oracle.

method Black-box deflation methods, analyzing ePCA and cPCA approximations.

result Deflation methods suffer no asymptotic parameter loss for

k

-cPCA in feasible regimes.

k-PCA black-box deflation methods approximation parameter loss

2024-03-06abs ↗pdf ↗

Kernel PCA with the Nyström methodstat.ML

Derives kernel PCA with Nyström method for scalability.

problem Scalability of kernel PCA.

method Nyström method for kernel PCA.

result Provides scalable alternative to full kernel PCA.

Nyström method kernel PCA scalability PCA kernel methods

2021-09-12abs ↗pdf ↗

Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCAcs.LG

We develop efficient algorithms for robust PCA that handle outliers.

problem Finding principal components in datasets with outliers.

method Nearly-linear time and streaming algorithms for robust PCA.

result Near-optimal error guarantees for robust PCA with nearly-linear time and memory usage.

PCA robustness outliers streaming algorithms

2023-05-04abs ↗pdf ↗

Cauchy Principal Component Analysiscs.LG

Principal Component Analysis (PCA) has wide applications in machine learning, text mining and computer vision. Classical PCA based on a Gaussian noise model is fragile to noise of large magnitude. Laplace noise assumption based PCA methods cannot deal with dense noise effectively. In this paper, we propose Cauchy Princ…

2014-12-19abs ↗pdf ↗

Principal Component Analysis Based on T

\ell_1

-norm Maximizationcs.LG

A new PCA method using T $\ell_1$ -norm outperforms existing methods.

problem Outliers and noise sensitivity in classical PCA.

method PCA based on T

\ell_1

-norm maximization.

result The method outperforms PCA-

\ell_p

\ell_p

SPCA, and PCA in numerical experiments.

PCA T$\ell_1$-norm robustness outliers noise

2020-05-23abs ↗pdf ↗

Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpointstat.ML

New fair PCA method using streaming algorithms with statistical guarantees.

problem Perform PCA while ensuring fair projected distributions.

method Formulated new notion PAFO learnability, proposed fair noisy power method (FNPM) for memory efficiency.

result First statistical guarantee for fair PCA in streaming setting.

fair PCA streaming algorithms PAFO learnability FNPM

2023-10-28abs ↗pdf ↗

PCA-Guided Quantile Sampling: Preserving Data Structure in Large-Scale Subsamplingstat.ME

PCA-Guided Quantile Sampling preserves data structure in large datasets.

problem Preserving data structure in large-scale subsampling.

method PCA QS uses leading principal components to guide stratified sampling.

result PCA QS maintains statistical and geometric structure without distorting semantics.

PCA quantile sampling data structure large-scale machine learning

2025-06-23abs ↗pdf ↗

Mean-Shift PCA by Knockoff Meanstat.ML

A method to remove mean-shift noise from PCA using knockoffs.

problem High sensitivity of PCA to mean-shift contamination in high-dimensional data.

method Introducing knockoff mean-shift perturbation to separate and remove mean-shift components from PCA.

result The mean-shift spikes are spectrally separable from stable eigenvalues, allowing for robust PCA.

PCA mean-shift knockoff robustness spectral stability

2026-05-25abs ↗pdf ↗

AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flowcs.LG

AgFlow speeds up model selection in penalized PCA.

problem Efficient model selection in penalized PCA for HDLSS settings.

method Implicit regularization effect of gradient flow to reduce computation complexity.

result AgFlow achieves the complete solution path of L2-penalized PCA.

PCA penalized PCA model selection gradient flow HDLSS

2021-10-07abs ↗pdf ↗

Convergence and complexity of block majorization-minimization for constrained block-Riemannian optimizationmath.OC

New algorithm for nonconvex optimization on constrained Riemannian manifolds converges quickly.

problem Optimization on constrained Riemannian manifolds.

method Block majorization-minimization (BMM) for smooth nonconvex objectives with Riemannian constraints.

result Converges to stationary points within

O(ε^{-2})

iterations.

nonconvex optimization Riemannian manifolds block majorization-minimization constrained optimization convergence analysis

2023-12-16abs ↗pdf ↗

PCA of high dimensional random walks with comparison to neural network trainingstat.ML

One technique to visualize the training of neural networks is to perform PCA on the parameters over the course of training and to project to the subspace spanned by the first few PCA components. In this paper we compare this technique to the PCA of a high dimensional random walk. We compute the eigenvalues and eigenvec…

2018-06-22abs ↗pdf ↗

GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysisstat.ML

GT-PCA improves PCA for image and time series data.

problem Lack of robustness to transformations in PCA.

method GT-PCA is a neural network that estimates components invariant to specific transformations.

result GT-PCA outperforms alternative methods in synthetic and real data experiments.

dimensionality reduction principal component analysis transform-invariant neural networks image analysis

2024-01-28abs ↗pdf ↗

Monitoring multimode processes: a modified PCA algorithm with continual learning abilitystat.ML

Modified PCA algorithm with continual learning preserves features of previous modes for multimode process monitoring.

problem Catastrophic forgetting of previous modes in monitoring models for successive modes.

method Modified PCA algorithm with elastic weight consolidation (EWC) to preserve features of previous modes.

result PCA-EWC algorithm effectively monitors multimode processes without performance decrease.

PCA continual learning multimode processes catastrophic forgetting elastic weight consolidation

2020-12-13abs ↗pdf ↗

Operator learning with PCA-Net: upper and lower complexity boundscs.LG

PCA-Net combines PCA and neural networks for operator approximation, with new bounds on complexity.

problem Developing approximation theory for PCA-Net architecture.

method Combines PCA and neural networks, derives universal approximation results and lower bounds on complexity.

result PCA-Net can overcome the curse of parametric complexity for specific operators.

PCA-Net operator learning neural networks approximation theory lower bounds

2023-03-28abs ↗pdf ↗

Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergencestat.ML

A new dynamical formulation of log-PCA captures local principal modes of geodesic variations.

problem Learning principal variations of random probability measures under Wasserstein geometry.

method Introducing a new dynamical formulation of log-PCA as a variational approach.

result Deriving a general statistical convergence rate for empirical WT-PCA.

log-PCA Wasserstein geometry principal variations statistical convergence

2026-06-15abs ↗pdf ↗

Matrix Normal PCA for Interpretable Dimension Reduction and Graphical Noise Modelingcs.LG

MN-PCA models structured noise in data and feature spaces.

problem Complex and structured noise in real-world data.

method Matrix normal distribution for structured noise modeling, generalized Mahalanobis distance approximation.

result MN-PCA obtains a low-rank data representation and structured noise simultaneously.

PCA Matrix normal distribution structured noise generalized Mahalanobis distance Wasserstein distance

2019-11-25abs ↗pdf ↗

Supervised Discriminative Sparse PCA for Com-Characteristic Gene Selection and Tumor Classification on Multiview Biological Datacs.LG

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the so-called sparse PCA, which focuses on seeking sparse loadings. However, the performance…

2019-05-28abs ↗pdf ↗

Latent Space Exploration Using Generative Kernel PCAcs.LG

Generative Kernel PCA explores latent spaces for data interpretation and novelty detection.

problem Exploring latent spaces of datasets for better data interpretation.

method Generative Kernel PCA using hidden and visible units similar to Restricted Boltzmann Machines.

result Gradually moving in the latent space allows for interpretation of components and detection of novel patterns.

Kernel PCA latent space novelty detection data interpretation Restricted Boltzmann Machines

2021-05-28abs ↗pdf ↗

Comparison of PCA with ICA from data distribution perspectivestat.ML

We performed an empirical comparison of ICA and PCA algorithms by applying them on two simulated noisy time series with varying distribution parameters and level of noise. In general, ICA shows better results than PCA because it takes into account higher moments of data distribution. On the other hand, PCA remains quit…

2017-09-29abs ↗pdf ↗