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Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Fantasy Premier League (FPL) performance predictors tend to base their algorithms purely on historical statistical data. The main problems with this approach is that external factors such as injuries, managerial decisions and other…
Matrix factor model has been growing popular in scientific fields such as econometrics, which serves as a two-way dimension reduction tool for matrix sequences. In this article, we for the first time propose the matrix elliptical factor…
In an inspiring paper Dubey and M\"uller (DM) extend PCA to the case that observations are metric-valued functions. As an alternative, we develop a kernel PCA approach, which we show is closely related to the DM approach. While kernel…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
Navigating the complex landscape of single-cell transcriptomic data presents significant challenges. Central to this challenge is the identification of a meaningful representation of high-dimensional gene expression patterns that sheds…
Unlike other major professional sports, American football lacks comprehensive statistical ratings for player evaluation that are both reproducible and easily interpretable in terms of game outcomes. Existing methods for player evaluation in…
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…
Predicting performance outcomes has the potential to transform training approaches, inform coaching strategies, and deepen our understanding of the factors that contribute to athletic success. Traditional non-automated data analysis in…
Fantasy basketball has a rich underlying mathematical structure which makes optimal drafting strategy unclear. A central issue for category leagues is how to aggregate a player's statistics from all categories into a single number…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
Point pattern sets arise in many different areas of physical, biological, and applied research, representing many random realizations of underlying pattern formation mechanisms. These pattern sets can be heterogeneous with respect to…
Neurons in higher cortical areas, such as the prefrontal cortex, are known to be tuned to a variety of sensory and motor variables. The resulting diversity of neural tuning often obscures the represented information. Here we introduce a…
In the framework of Symbolic Data Analysis (SDA), distribution-variables are a particular case of multi-valued variables: each unit is represented by a set of distributions (e.g. histograms, density functions or quantile functions), one for…
Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous), pain levels (truncated), mood states (ordinal), and life…
This paper uses Factored Latent Analysis (FLA) to learn a factorized, segmental representation for observations of tracked objects over time. Factored Latent Analysis is latent class analysis in which the observation space is subdivided and…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…