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Principal Component Analysis (PCA) is a widely used technique in machine learning, data analysis and signal processing. With the increase in the size and complexity of datasets, it has become important to develop low-space usage algorithms…

As one of the newest members in the field of artificial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data,…

We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…

Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…

Learning the graphical structure of Bayesian networks is key to describing data-generating mechanisms in many complex applications but poses considerable computational challenges. Observational data can only identify the equivalence class…

Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the…

Understanding feature representation for deep neural networks (DNNs) remains an open question within the general field of explainable AI. We use principal component analysis (PCA) to study the performance of a k-nearest neighbors classifier…

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…

We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…

Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…

Sparse PCA is a widely used technique for high-dimensional data analysis. In this paper, we propose a new method called low-rank principal eigenmatrix analysis. Different from sparse PCA, the dominant eigenvectors are allowed to be dense…

We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Distributed Principal Component Analysis (PCA) has been studied to deal with the case when data are stored across multiple machines and communication cost or privacy concerns prohibit the computation of PCA in a central location. However,…

The increasing integration of data science techniques into quantitative finance has enabled more systematic and data-driven approaches to portfolio construction. This paper investigates the use of Principal Component Analysis (PCA) in…

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential…

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to variables, the…

We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a…