Modularity component analysis clusters data without centering.
problem Clustering data without centering.
method Developed exact linear relation between modularity matrix eigenvectors and singular vectors.
result Modularity component analysis clusters data similarly to PCA but without centering.
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.
Bayesian correlated component analysis identifies brain process similarities across multiple stimulus views.
problem Investigating brain process similarity in responses to multiple views of a stimulus.
method Hierarchical probabilistic model that evaluates universality of spatial networks across multi-view data.
result Bayesian correlated component analysis evaluates favorably against other algorithms and identifies variability in spatial representations.
We present a unifying framework which reduces the construction of probabilistic component analysis techniques to a mere selection of the latent neighbourhood, thus providing an elegant and principled framework for creating novel component analysis models as well as constructing probabilistic equivalents of deterministi…
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.
New ICA method improves on existing techniques.
problem Finding independent components in data.
method Multiple-weighted Independent Component Analysis (MWeICA) based on approximate diagonalization of weighted covariance matrices.
result MWeICA achieves better results than state-of-the-art ICA methods with similar computational time.
Analyzes last few principal components for stock correlations.
problem Identifying highly correlated stocks for better portfolio management.
method Principal component analysis of correlation matrix.
result Last few components contain useful financial information.
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.
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.
RKCA combines sparse dictionary learning and robust component analysis for robust low-rank modeling.
problem Learning robust low-rank representations from noisy data.
method Kronecker-decomposable component analysis (RKCA) with efficient learning algorithm.
result RKCA achieves robustness to gross corruption and low-rank modeling.
Boosting improves ICA for better component recovery.
problem Improving ICA's reliance on prior knowledge of sources.
method Maximizing likelihood via boosting and fixed-point unmixing.
result Boosting-based ICA outperforms existing methods.
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.
A new method removes whitening for better non-Gaussian component analysis.
problem Data covariance matrix ill-conditioning hinders LSNGCA performance.
method Developed a whitening-free least-squares NGCA method.
result Demonstrated superior performance compared to whitened LSNGCA.
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.
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.
DeepCA combines neural networks with component analysis for improved performance.
problem Limited capacity of shallow component analysis in deep learning.
method Deep Component Analysis (DeepCA) with ADNNs for inference.
result Improved performance on various tasks, including depth prediction.
XCAN uses cross-product penalization for sparse matrix factorization.
problem Understanding complex data structures.
method Sparse matrix factorization with a loss function balancing variance and structural preservation.
result Flexible modeling approach for diverse applications.
Scalable psFA for fMRI data extracts sparse components.
problem Extracting neural representations from fMRI data with probabilistic formulation.
method Group level scalable probabilistic sparse factor analysis (psFA) with spatial sparsity, component pruning, and heteroscedastic noise modeling.
result Sparse components similar to group ICA and reduced noise in activated areas.
LNGCA extends ICA to non-Gaussian signals and noise, improving estimation and testing.
problem Modeling multivariate data with non-Gaussian components and Gaussian noise.
method Linear latent factor model, simultaneous estimation of non-Gaussian and Gaussian components, discrepancy maximization, resampling-based test.
result Improved estimation and testing of non-Gaussian components over competing methods.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
The paper uses diffusion approximations to analyze and optimize online principal component estimation.
problem Optimizing online principal component estimation from streaming data.
method Diffusion approximation tools applied to Oja's iteration for principal component analysis.
result The Oja's iteration for the top eigenvector generates a continuous-state discrete-time Markov chain over the unit sphere.
SAMoSSA combines mSSA and AR for accurate time series analysis.
problem Accurately estimating both deterministic and stationary components in time series data.
method Two-stage algorithm: first mSSA for non-stationary components, then AR for stationary residual.
result SAMoSSA provides forecasting consistency and outperforms existing methods.
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…
A new method selects PCA components based on residual memory, outperforming existing techniques.
problem Selecting the optimal number of components in PCA for data with long memory effects.
method Sequentially removes components, stopping when maximum memory accounted for.
result Our method outperforms existing techniques in computational efficiency and accuracy.
Causal Component Analysis aims to recover latent variables with causal relationships.
problem Recover latent variables with causal relationships from observed mixtures.
method Introduces a likelihood-based approach using normalizing flows to estimate unmixing function and causal mechanisms.
result Demonstrates effectiveness through synthetic experiments in CauCA and ICA settings.
Explains eigenvalue and generalized eigenvalue problems with examples.
problem Eigenvalue and generalized eigenvalue problems.
method Introduction and examples from machine learning.
result Solutions to eigenvalue and generalized eigenvalue problems.
Eigen component analysis combines quantum mechanics with machine learning for efficient data analysis.
problem Efficiently extracting linearly separable components from complex data.
method Eigen component analysis (ECA) incorporates quantum mechanics principles into linear learning models.
result ECA outperforms classical linear models and can be integrated with deep neural networks.
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical prob…
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.
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.
The paper improves RPCA for separating sparse and manifold components on noisy data.
problem Separating sparse and manifold components from noisy data.
method Nonlinear Robust Principal Component Analysis (RPCA) framework.
result The method successfully separates sparse and manifold components under noisy data.
Efficiently projects vectors onto top PCA components without explicit PCA.
problem Efficiently project vectors onto top principal components of a matrix.
method Iterative algorithm using ridge regression and polynomial approximation.
result First runtime improvement for principal component regression.
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.
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.
This paper uses PCA for stock price prediction, reducing complexity and improving accuracy.
problem Predicting stock prices from past data using PCA.
method Dimensionality reduction through PCA to project noisy data onto a principle subspace.
result The method improves prediction accuracy and reduces risk.
A method for integrating multiple cancer data sources using kernel principal component analysis.
problem Lack of comprehensive analysis of cancer subtypes from multiple data sources.
method Unsupervised data integration method based on kernel principal component analysis with a scoring function to determine input matrix impact.
result Enables visualization and clustering of integrated data for cancer subtype identification.
Bayesian nonparametric PCA infers the number of significant components.
problem Selecting the number of significant components in PCA is challenging.
method Introduces a Bayesian nonparametric approach using a Stiefel manifold prior and Indian buffet process for uncertainty modeling.
result Proposes a new estimator of the subspace dimension and a refined statistical significance test.
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.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
Improved data analysis with robust SPCA algorithm.
problem Identifying localized spatial structures and disambiguating time scales in low-rank data.
method Formulated as a value-function optimization problem, then extended with randomized linear algebra methods for scalability.
result Robust and efficient sparse principal components in corrupted data.
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.
Proposes MPCA for robust PCA using mode estimation.
problem Outliers sensitivity in PCA.
method Modal Principal Component Analysis (MPCA) based on mode estimation.
result MPCA shows advantages over conventional methods.
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.
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situa…
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
New method separates noisy auto-correlated components from multi-channel measurements.
problem Separating independent auto-correlated components from noisy multi-channel data.
method Simultaneous reconstruction and separation of components considering all channels, using information field theory.
result Significant improvement in signal-to-noise ratio, allowing separations even in high noise conditions.
New techniques solve robust principal component analysis problems.
problem Robust Principal Component Analysis (RPCA) problems.
method Dual smoothing and level set techniques in convex optimization.
result Numerous theoretical and practical improvements for RPCA.