arXiv research

New algorithms separate singing voices from accompaniment using complex and quaternionic principal component pursuit.

Paper extends principal component pursuit to hypercomplex numbers for improved audio data analysis.

We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…

Paper develops efficient AltMin algorithm for SRPCP robust matrix recovery.

In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold" refers to the topology properties of the structure. The approximating manifold is …

We extend the theoretical analysis of a recently proposed single subspace learning algorithm, called Dual Principal Component Pursuit (DPCP), to the case where the data are drawn from of a union of hyperplanes. To gain insight into the properties of the $\ell_1$ non-convex problem associated with DPCP, we develop a geo…

This paper presents a remarkably simple, yet powerful, algorithm termed Coherence Pursuit (CoP) to robust Principal Component Analysis (PCA). As inliers lie in a low dimensional subspace and are mostly correlated, an inlier is likely to have strong mutual coherence with a large number of data points. By contrast, outli…

A new robust PCA estimator combining M-estimators and minimum divergence estimators.

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed reconstruction error. By directly minimizing over the Stiefel manifold, we avoid deflatio…

Denise learns a function to quickly decompose covariance matrices robustly.

Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be solved in polynomial time via a natural convex relaxation, known as Compressive …

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting where each point has …

New algorithm rSVDdpd improves robustness and scalability for video surveillance background modeling.

Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and hyper-parameter tuning. Traditional high-dimensional data reduction techniques, …

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …

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

Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To addre…

Generalizes PCA to maximize any convex function of components.

Sparse principal component analysis (PCA) involves nonconvex optimization for which the global solution is hard to obtain. To address this issue, one popular approach is convex relaxation. However, such an approach may produce suboptimal estimators due to the relaxation effect. To optimally estimate sparse principal su…

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

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

Efficient private matrix analysis algorithms for recent variants.

Autoencoders reveal principal component subspaces.

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 PCR method using SVD with sparse regularization.

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…

In many applications that require matrix solutions of minimal rank, the underlying cost function is non-convex leading to an intractable, NP-hard optimization problem. Consequently, the convex nuclear norm is frequently used as a surrogate penalty term for matrix rank. The problem is that in many practical scenarios th…

Essential principal components simplify spectral analysis with minimal training data.

A new method for sparse regression using principal components.

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

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

Proposes a fair PCA algorithm that balances reconstruction loss and fairness.

Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…

QAPCA uses quantum annealing for robust PCA.

New supervised and unsupervised NFLTs for elliptical distributions.

Two new PCA variants improve financial data analysis.

Improved estimation of multiple principal components using manifold optimization and iterative deflation techniques.

NGCA identifies non-Gaussian components in multidimensional data.

CPCR mitigates bias in PCR for overparameterized models.

This paper analyzes how errors accumulate in PCA's deflation method.

Paper presents a faster classical algorithm for principal component regression.

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…

The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem ${\mathcal{NP}}$-hard. In this work, we prove that, if the matrix is positive semidefinite and its …

The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurem…

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…

The paper uses PCA and HMM to forecast stock returns outperforming buy-and-hold.

Study explores K-means clustering of variables and its relation to PCA.

This paper compares and analyzes random projections and column sub-sampling for dimension reduction in regression.