Explains various PCA and SPCA methods with theory and applications.
problem No specific problem stated; focuses on explaining methods.
method Explains PCA, SPCA, kernel PCA, and kernel SPCA methods with theory and applications.
result Comprehensive coverage of PCA and SPCA methods with theory and applications.
New method optimizes PCA for better prediction and variance.
problem Improve PCA for better prediction and variance.
method Jointly optimize prediction error and variance explained.
result Our method outperforms existing approaches in both prediction and variance.
New supervised and unsupervised NFLTs for elliptical distributions.
problem Understanding unsupervised No Free Lunch Theorems for elliptical distributions.
method Proved two equally optimal strategies for elliptical distributions, inspired PRIM-based bump-hunting algorithms.
result Optimal strategies for selecting principal components based on variance or volume.
Study on reducing dimensionality in high-dimensional regression with kernel methods and stability analysis.
problem Analyzing errors in high-dimensional regression with dimensionality reduction and kernel regression.
method Derive a stability result for kernel regression with Wasserstein distance and apply it to PCA to deduce convergence rates.
result Two-step procedure yields useful convergence rates in semi-supervised settings.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…
New method disentangles hidden data structures using HSIC and supervision.
problem Tackles the challenge of interpreting high-dimensional data.
method Supervised Independent Subspace Principal Component Analysis (sisPCA) using HSIC.
result Identifies and separates hidden data structures effectively.
Paper proposes SDDP for improving time series forecasting with high-dimensional predictors.
problem Improving time series forecasting with high-dimensional predictors.
method SDDP framework that incorporates target variable and lagged observations into factor extraction process.
result SDDP improves predictive accuracy in time series forecasting.
A simple self-supervised model for tensor RPCA using deep unfolding.
problem Tensor robust principal component analysis (RPCA) challenges in practical applications.
method Deep unfolding with only four hyperparameters.
result Competitive or superior performance compared to supervised methods, even in data-starved scenarios.
AugmentedPCA improves PCA with supervised or adversarial objectives.
problem Lack of reproducible linear analogs for deep latent factor models.
method Augments PCA with supervised or adversarial objectives.
result Improves downstream classification performance and identifies cancer-related genes.
Spofe bridges statistical rigor and interpretability in feature extraction from tabular data.
problem Ensuring statistical rigor and interpretability in feature extraction from complex tabular data.
method Spofe combines kernel principal components and sparse polynomial functions with a multi-objective knockoff selection procedure.
result Spofe consistently outperforms other methods in feature selection for regression and classification tasks.
Efficient private matrix analysis algorithms for recent variants.
problem Private analysis of recent matrix updates.
method Identifying sufficient conditions on positive semidefinite matrices.
result First efficient differentially private algorithms for various matrix analysis tasks.
Is all of machine learning supervised to some degree? The field of machine learning has traditionally been categorized pedagogically into supervised vs unsupervised learning; where supervised learning has typically referred to learning from labeled data, while unsupervised learning has typically referred to learning …
Enhances functional classifier performance with new tree-based methods and unbiased feature importance assessment.
problem Challenges of high-dimensional functional data and biased feature importance assessment.
method Augmented functional classification trees and random forests with ad-hoc conditional permutations for unbiased feature importance.
result Significant enhancement in predictive power of functional classifiers through new feature importance assessment.
The paper introduces a method for interpretable principal component analysis of high-dimensional time series.
problem Inconsistent and difficult-to-interpret principal component estimates in high-dimensional regimes.
method Localized sparse principal component analysis of spectral density matrices in frequency domain.
result Efficient algorithm for sparse-localized estimates of principal subspaces.
Generalizes PCA to maximize any convex function of components.
problem Finding a principal vector that maximizes a convex function of components.
method Gradient ascent algorithm for solving the generalized PCA problem; fixed points of neural networks for kernel version.
result Solutions can be obtained as fixed points of simple neural networks.
Survey of SDR methods for high-dimensional regression and embedding.
problem Reducing dimensionality in high-dimensional data.
method Involves both statistical and machine learning approaches, covering inverse and forward regression methods.
result Supervised Kernel Dimension Reduction is equivalent to supervised PCA.
Study optimal spectral estimator for semi-supervised node classification.
problem Semi-supervised node classification on CSBM with limited labels.
method Spectral estimator inspired by PCA, graph ridge regression, GCN.
result Achieves information-theoretical threshold for exact recovery.
Two new PCA variants improve financial data analysis.
problem Numerical instability and nonstationarity in PCA for finance.
method Iterated and exponentially weighted moving PCA variants using Ogita-Aishima iteration.
result Improved stability and adaptability in financial data analysis.
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
ACA identifies and explains anomalies in data.
problem Explaining anomalies in non-supervised data analysis.
method Abnormal Component Analysis (ACA) using data depth.
result ACA provides a linear explanation for anomalies.
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…
QAPCA uses quantum annealing for robust PCA.
problem Outliers in data skew L2-norm principal components.
method Quantum annealing for L1-norm optimization.
result QAPCA's reconstruction error is comparable to L1-BF.
Paper uses PCA to analyze Chinese sovereign bonds and discusses bond immunization.
problem Analyzing factors affecting Chinese sovereign bond yield changes.
method Applied Principal Component Analysis (PCA) on bond yield data.
result Identified principal factors influencing Chinese sovereign bond yield changes.
Unified method learns latent spaces from labeled data.
problem Identifying low-dimensional latent structures in high-dimensional data.
method Nonlinear multiple-response regression within an index model context.
result Unified method offers better interpretability and reduced computational complexity.
Looped transformers with LN converge to power method for principal component prediction.
problem Understanding how transformers learn algorithmic procedures.
method Study of principal component prediction with looped linear transformers and layer normalization.
result Gradient descent trains looped transformers with LN to implement the power method for principal component prediction.
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 …
We propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso (ℓ1) sparsity penalty with a quadratic penalty that shrinks the coefficient vector toward the leading principal components of …
New PCA method for derivatives problems.
problem Reducing dimensionality in derivatives pricing models.
method Supervised Principal Component Analysis (PCA)
result Improved accuracy in machine learning applications.
Unified framework for scale-invariant representation learning using MAPCA.
problem Learning invariant representations in data.
method Metric-Aware Principal Component Analysis (MAPCA) based on generalized eigenproblem.
result MAPCA provides a unified geometric language for various self-supervised learning objectives.
Though there is a growing body of literature on fairness for supervised learning, the problem of incorporating fairness into unsupervised learning has been less well-studied. This paper studies fairness in the context of principal component analysis (PCA). We first present a definition of fairness for dimensionality re…
A new PCA method robust to outliers using Median of Means.
problem PCA's failure to detect true structure in noisy data.
method Median of Means (MoM) approach for robust PCA.
result Achieves optimal convergence rates without assumptions on outliers.
Direct contextual policy search methods learn to improve policy parameters and simultaneously generalize these parameters to different context or task variables. However, learning from high-dimensional context variables, such as camera images, is still a prominent problem in many real-world tasks. A naive application o…
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.
PCA-based MTL improves performance with reduced computation.
problem Negative transfer in multi-task learning.
method Random matrix approach to PCA-based MTL with counter-measures.
result Simple counter-measures prevent negative transfer and improve performance.
Study explores K-means clustering of variables and its relation to PCA.
problem Exploring the relationship between K-means clustering of variables and PCA.
method Apply PCA to original data and K-means to transposed data, quantify variable contributions to principal components.
result Identifies how variable clusters contribute to principal components identified by PCA.
Paper develops a dual formulation for PCA in Hilbert spaces.
problem Characterizing probabilistic PCA in Hilbert spaces.
method Dual formulation for probabilistic PCA in Hilbert spaces.
result Generative framework for kernel methods developed.
UMAP compared to other methods for dimensionality reduction.
problem Comparing UMAP to other dimensionality reduction techniques.
method Comprehensive evaluation of UMAP and other methods.
result Supervised UMAP performs well for classification but not for regression.
The paper uses PCA and HMM to forecast stock returns outperforming buy-and-hold.
problem Predicting stock returns accurately.
method Applied PCA to covariance matrix of S&P 500 stocks, used HMM on principal components, and forecasted stock returns.
result The model outperforms buy-and-hold strategy in terms of annualized Sharpe ratio.
Proposes an online method for high-dimensional streaming data.
problem Increasing variable dimensions with sample size in online kernel sliced inverse regression.
method Introduces approximate linear dependence condition and dictionary variable sets to address the problem. Transforms into online generalized eigen-decomposition problem and uses stochastic optimization for updates.
result Achieves close performance to batch processing kernel sliced inverse regression.
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal …
A new method uses Gram matrix for efficient multivariate functional principal components.
problem Efficiently estimating eigencomponents of multidimensional functional datasets.
method Proposes using inner-product matrix to estimate eigenelements of multivariate and multidimensional functional datasets.
result Established relationship between eigenelements of covariance operator and inner-product matrix.
Kernelized PCovR reveals structure-property relations in chemistry and materials.
problem Understanding structure-property relations in complex systems.
method Kernel Principal Covariates Regression (kernel PCovR) with sparsification.
result Kernelized PCovR effectively reveals and predicts structure-property relations.
RandNet learns from compressed image data, improving efficiency and accuracy.
problem Efficiency and accuracy in training neural networks with large datasets.
method RandNet uses compressed random measurements of images to train neural networks efficiently.
result RandNet achieves comparable accuracy to full data training with minimal loss.
Two derivations of PCA for distributional data.
problem PCA for datasets of distributions.
method Two derivations: variance maximization and reconstruction error minimization.
result Closed-form solution for distributional PCA.
In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor objects that belong to different classes do not share common features after the redu…
Improved convergence speed of principal component analysis through modified learning rules.
problem Slow convergence for covariance matrices with close eigenvalues.
method Introduced an additional term to the objective function to mitigate convergence issues.
result Significantly improved convergence speed confirmed through simulations.