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Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

Independent component analysis (ICA) is a computational method for separating a multivariate signal into subcomponents assuming the mutual statistical independence of the non-Gaussian source signals. The classical Independent Components…

The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It…

Contrast enhanced ultrasound is a radiation-free imaging modality which uses encapsulated gas microbubbles for improved visualization of the vascular bed deep within the tissue. It has recently been used to enable imaging with unprecedented…

Canonical correlation analysis (CCA) is a multivariate statistical method which describes the associations between two sets of variables. The objective is to find linear combinations of the variables in each data set having maximal…

Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…

The accumulation of time-series data and the absence of labels make time-series Anomaly Detection (AD) a self-supervised deep learning task. Single-normality-assumption-based methods, which reveal only a certain aspect of the whole…

We have updated and applied a convolutional neural network (CNN) machine learning model to discover and characterize damped Ly$\alpha$ systems (DLAs) based on Dark Energy Spectroscopic Instrument (DESI) mock spectra. We have optimized the…

Factor analysis and principal component analysis (PCA) are used in many application areas. The first step, choosing the number of components, remains a serious challenge. Our work proposes improved methods for this important problem. One of…

As a non-linear extension of the classic Linear Discriminant Analysis(LDA), Deep Linear Discriminant Analysis(DLDA) replaces the original Categorical Cross Entropy(CCE) loss function with eigenvalue-based loss function to make a deep neural…

Some state-of-art multimedia source encoders produce embedded source bit streams that upon the reliable reception of only a fraction of the total bit stream, the decoder is able reconstruct the source up to a basic quality. Reliable…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Corner detection is a vital operation in numerous computer vision applications. The Chord-to-Point Distance Accumulation (CPDA) detector is recognized as the contour-based corner detector producing the lowest localization error while…

This work, for the first time, introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular maximization over a ground set of size $n$ subject to a knapsack constraint, $\mathsf{DLA}$ and…

We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…

The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…

The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under…

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…

The automotive industry is currently expanding digital display options with every new model that comes onto the market. This entails not just an expansion in dimensions, resolution, and customization choices, but also the capability to…