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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…

In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality…

Fair Principal Component Analysis (PCA) is a problem setting where we aim to perform PCA while making the resulting representation fair in that the projected distributions, conditional on the sensitive attributes, match one another.…

A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

Correspondence analysis (CA) is a multivariate statistical tool used to visualize and interpret data dependencies by finding maximally correlated embeddings of pairs of random variables. CA has found applications in fields ranging from…

This study presents the m-arcsinh Kernel ('m-ar-K') Fast Independent Component Analysis ('FastICA') method ('m-ar-K-FastICA') for feature extraction. The kernel trick has enabled dimensionality reduction techniques to capture a higher…

Here we propose FastFCA-AS, an accelerated algorithm for Full-rank spatial Covariance Analysis (FCA), which is a robust audio source separation method proposed by Duong et al. ["Under-determined reverberant audio source separation using a…

We consider a multi-view learning problem known as group independent component analysis (group ICA), where the goal is to recover shared independent sources from many views. The statistical modeling of this problem requires to take noise…

Mixtures of factor analysers (MFA) models represent a popular tool for finding structure in data, particularly high-dimensional data. While in most applications the number of clusters, and especially the number of latent factors within…

Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…

Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Word embeddings represent words as multidimensional real vectors, facilitating data analysis and processing, but are often challenging to interpret. Independent Component Analysis (ICA) creates clearer semantic axes by identifying…

An analysis of the protein content of several crystal forms of proteins has been performed. We apply a new numerical technique, the Independent Component Analysis (ICA), to determine the volume fraction of the asymmetric unit occupied by…

In many data classification problems, there is no linear relationship between an explanatory and the dependent variables. Instead, there may be ranges of the input variable for which the observed outcome is signficantly more or less likely.…

Independent Component Analysis (ICA) is an effective unsupervised tool to learn statistically independent representation. However, ICA is not only sensitive to whitening but also difficult to learn an over-complete basis. Consequently, ICA…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…