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Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

We introduce principal differences analysis (PDA) for analyzing differences between high-dimensional distributions. The method operates by finding the projection that maximizes the Wasserstein divergence between the resulting univariate…

Unsupervised domain adaptation (UDA) aims to transfer and adapt knowledge from a labeled source domain to an unlabeled target domain. Traditionally, subspace-based methods form an important class of solutions to this problem. Despite their…

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…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

Discriminative features play an important role in image and object classification and also in other fields of research such as semi-supervised learning, fine-grained classification, out of distribution detection. Inspired by Linear…

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

Linear discriminant analysis (LDA) is a widely used technique for data classification. The method offers adequate performance in many classification problems, but it becomes inefficient when the data covariance matrix is ill-conditioned.…

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Domain adaptation (DA) aims to generalize a learning model across training and testing data despite the mismatch of their data distributions. In light of a theoretical estimation of upper error bound, we argue in this paper that an…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…

Person re-identification is to seek a correct match for a person of interest across views among a large number of imposters. It typically involves two procedures of non-linear feature extractions against dramatic appearance changes, and…

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…

Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating…

Many variants of unsupervised domain adaptation (UDA) problems have been proposed and solved individually. Its side effect is that a method that works for one variant is often ineffective for or not even applicable to another, which has…

Excessive computational cost for learning large data and streaming data can be alleviated by using stochastic algorithms, such as stochastic gradient descent and its variants. Recent advances improve stochastic algorithms on convergence…

Domain adaptation (DA) is a representation learning methodology that transfers knowledge from a label-sufficient source domain to a label-scarce target domain. While most of early methods are focused on unsupervised DA (UDA), several…