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In contrast with Mercer kernel-based approaches as used e.g., in Kernel Principal Component Analysis (KPCA), it was previously shown that Singular Value Decomposition (SVD) inherently relates to asymmetric kernels and Asymmetric Kernel…

We study a distributed Principal Component Analysis (PCA) framework where each worker targets a distinct eigenvector and refines its solution by updating from intermediate solutions provided by peers deemed as "superior". Drawing intuition…

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Model merging combines multiple fine-tuned models into a single model by adding their weight updates, providing a lightweight alternative to retraining. Existing methods primarily target resolving conflicts between task updates, leaving the…

Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue…

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

We propose a compression based continual task learning method that can dynamically grow a neural network. Inspired from the recent model compression techniques, we employ compression-aware training and perform low-rank weight approximations…

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

The growing adoption of IoT systems in industries like transportation, banking, healthcare, and smart energy has increased reliance on sensor networks. However, anomalies in sensor readings can undermine system reliability, making real-time…

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

This paper is devoted to proposing a general weighted low-rank recovery model and designing a fast SVD-free computational scheme to solve it. First, our generic weighted low-rank recovery model unifies several existing approaches in the…

We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\reals^d$. A simple and…

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the…

The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for…

Support vector classification (SVC) with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with…

This paper considers the problem of updating the rank-k truncated Singular Value Decomposition (SVD) of matrices subject to the addition of new rows and/or columns over time. Such matrix problems represent an important computational kernel…

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…