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Additive principal components (APCs for short) are a nonlinear generalization of linear principal components. We focus on smallest APCs to describe additive nonlinear constraints that are approximately satisfied by the data. Thus APCs fit…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and…
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors…
Eigenvector localization refers to the situation when most of the components of an eigenvector are zero or near-zero. This phenomenon has been observed on eigenvectors associated with extremal eigenvalues, and in many of those cases it can…
Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of…
A core task in multi-modal learning is to integrate information from multiple feature spaces (e.g., text and audio), offering modality-invariant essential representations of data. Recent research showed that, classical tools such as {\it…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
Clustering is an essential data mining tool that aims to discover inherent cluster structure in data. For most applications, applying clustering is only appropriate when cluster structure is present. As such, the study of clusterability,…
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…
We present an unsupervised learning analysis of correlation hierarchies in the quarter-filled simple and extended Hubbard models by applying principal component analysis (PCA) to exact-diagonalization (ED) data on 3x4 and 4x4 cylindrical…
In this paper, we consider clustering based on principal component analysis (PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical reasons why PCA is effective for clustering HDLSS data. First, we derive a geometric…
It is shown that the Principal Component Analysis applied to azimuthal single-particle distributions allows to perform flow analysis in ways that are analogous to the traditional approaches based on multi-particle correlations. In…
Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…
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…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…