Related papers: Sufficient Component Analysis for Supervised Dimen…

Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective…

Recent advances in unsupervised domain adaptation mainly focus on learning shared representations by global distribution alignment without considering class information across domains. The neglect of class information, however, may lead to…

Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical…

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the…

Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and - for a certain type of dynamics…

In semantic segmentation, even state-of-the-art deep learning models fall short of the performance required in certain high-stakes applications such as medical image analysis. In these cases, performance can be improved by allowing a model…

Suppose the data consist of a set $S$ of points $x_j$, $1\leq j \leq J$, distributed in a bounded domain $D\subset R^N$, where $N$ is a large number. An algorithm is given for finding the sets $L_k$ of dimension $k\ll N$, $k=1,2,...K$, in a…

Sparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or the number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most…

Feature selection from a large number of covariates (aka features) in a regression analysis remains a challenge in data science, especially in terms of its potential of scaling to ever-enlarging data and finding a group of scientifically…

Sufficient dimension reduction (SDR) is an effective tool for regression models, offering a viable approach to address and analyze the nonlinear nature of regression problems. This paper introduces the itdr R package, a comprehensive and…

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…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

Different unsupervised models for dimensionality reduction like PCA, LLE, Shannon's mapping, tSNE, UMAP, etc. work on different principles, hence, they are difficult to compare on the same ground. Although they are usually good for…

Evaluating side-channel analysis (SCA) security is a complex process, involving applying several techniques whose success depends on human engineering. Therefore, it is crucial to avoid a false sense of confidence provided by non-optimal…

Missing data present challenges in data analysis. Naive analyses such as complete-case and available-case analysis may introduce bias and loss of efficiency, and produce unreliable results. Multiple imputation (MI) is one of the most widely…

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…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…