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In recent years, machine learning models have been increasingly applied to spectroscopic datasets for chemical and biomedical analysis. For their successful adoption, particularly in clinical and safety-critical settings, professionals and…
Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering latent structure in data by separating mixed signals into their independent sources. While substantial progress has been made in…
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to…
Robust PCA is a standard tool for learning a linear subspace in the presence of sparse corruption or rare outliers. What about robustly learning manifolds that are more realistic models for natural data, such as images? There have been…
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to…
Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…
Learning representations of multimodal data that are both informative and robust to missing modalities at test time remains a challenging problem due to the inherent heterogeneity of data obtained from different channels. To address it, we…
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
Principal component analysis (PCA) is an exploratory tool widely used in data analysis to uncover dominant patterns of variability within a population. Despite its ability to represent a data set in a low-dimensional space, the…
Sequence data is challenging for machine learning approaches, because the lengths of the sequences may vary between samples. In this paper, we present an unsupervised learning model for sequence data, called the Integrated Sequence…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Recovering linear subspaces from data is a fundamental and important task in statistics and machine learning. Motivated by heterogeneity in Federated Learning settings, we study a basic formulation of this problem: the principal component…
Weakly-supervised anomaly detection aims at learning an anomaly detector from a limited amount of labeled data and abundant unlabeled data. Recent works build deep neural networks for anomaly detection by discriminatively mapping the normal…
We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a…
A unified representation space in multi-modal learning is essential for effectively integrating diverse data sources, such as text, images, and audio, to enhance efficiency and performance across various downstream tasks. Recent binding…
No-Reference Point Cloud Quality Assessment (NR-PCQA) aims to objectively assess the human perceptual quality of point clouds without relying on pristine-quality point clouds for reference. It is becoming increasingly significant with the…
Accurate extraction of molecular representations is a critical step in the drug discovery process. In recent years, significant progress has been made in molecular representation learning methods, among which multi-modal molecular…
Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…