Related papers: Principal Differences Analysis: Interpretable Char…

Recent works in self-supervised learning have shown impressive results on single-object images, but they struggle to perform well on complex multi-object images as evidenced by their poor visual grounding. To demonstrate this concretely, we…

Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…

Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…

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…

Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

Linear discriminant analysis (LDA) is an important classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of…

When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…

We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…

In this paper, we propose a new variant of Linear Discriminant Analysis to overcome underlying drawbacks of traditional LDA and other LDA variants targeting problems involving imbalanced classes. Traditional LDA sets assumptions related to…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

Deep neural networks are known to be vulnerable to adversarial attacks (AA). For an image recognition task, this means that a small perturbation of the original can result in the image being misclassified. Design of such attacks as well as…

The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…