arXiv research

Unified framework improves PCA for outliers and distributed data.

One-shot algorithm for feature-distributed kernel PCA reduces communication costs.

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…

Two derivations of PCA for distributional data.

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

We develop efficient algorithms for robust PCA that handle outliers.

A new algorithm reduces data dimensionality and decorrelation in a distributed setting.

Convex PCA improves Euclidean PCA for convex data subsets.

The paper analyzes the excess risk of PCA and provides a precise characterization.

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…

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data. PCA performs well in the presence of moderate noise and even with missing data, b…

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

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…

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of independent identical Gaussian noise. Probabilistic PCA (PPCA) and its variants have been…

RFPCA improves robustness of FPCA for matrix data.

KPCA improves OoD detection by separating InD and OoD data.

We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCA-based anomaly detection is applied, care must be taken in computing…

Solution to sparse PCA tuning problem using Empirical Bayes.

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

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal. In the probabilistic interpretation of low-rank PCA, the data has a normal multiv…

New fair PCA method using streaming algorithms with statistical guarantees.

Probabilistic Autoencoder learns latent space weights' distribution.

A new method for distributed PCA using matrix β-mean.

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

Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use profile. Principal Component Analysis (PCA), is the classical way of dimensional redu…

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

Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate covariates, and suggest post-processing transformations to improve interpretability of lat…

A new robust PCA method uses Innovation Search and Leverage Scores.

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantag…

Performance of nuclear threat detection systems based on gamma-ray spectrometry often strongly depends on the ability to identify the part of measured signal that can be attributed to background radiation. We have successfully applied a method based on Principal Component Analysis (PCA) to obtain a compact null-space m…

This paper tackles distributed estimation of the top-L eigenspace in PCA for large data sets.

Attention learns PCA on Gaussian data, proving its connection to principal component analysis.

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three as…

ALPCAH improves PCA for noisy data by estimating sample-wise noise variances.

Kernel PCA helps analyze multivariate extremes and clusters them effectively.

Paper optimizes PCA for fairness using MMD and Stiefel manifold optimization.

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm scalability and model interpretability are difficult to achieve, not to mention the preval…

Low-precision streaming PCA estimates the leading eigenvector with limited precision.

New combinatorial method for sparse PCA works beyond spiked identity model.

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further establish its rate of convergence and show how it relates to the number of nodes emp…

Paper improves Oja's algorithm for Markovian data streams.

PCA is often used in anomaly detection and statistical process control tasks. For bivariate data, we prove that the minor projection (the least varying projection) of the PCA-rotated data is the most sensitive to distributional changes, where sensitivity is defined by the Hellinger distance between distributions before…

Paper develops methods for PCA inference with missing data and heteroskedastic noise.

Improved online PCA algorithm learns from evolving norm of parameter vector.

We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the minimax estimation error for the leading eigenvector when it belongs to an $\ell_q$ …

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem …

Paper develops inference methods for low-rank tensors without debiasing.

A central problem of random matrix theory is to understand the eigenvalues of spiked random matrix models, introduced by Johnstone, in which a prominent eigenvector (or "spike") is planted into a random matrix. These distributions form natural statistical models for principal component analysis (PCA) problems throughou…