Related papers: Finding Representative Points in Multivariate Data…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
Multiway data are becoming more and more common. While there are many approaches to extending principal component analysis (PCA) from usual data matrices to multiway arrays, their conceptual differences from the usual PCA, and the…
In this paper we are interested in studying concise representations of concepts and dependencies, i.e., implications and association rules. Such representations are based on equivalence classes and their elements, i.e., minimal generators,…
We revisit the problem of fair principal component analysis (PCA), where the goal is to learn the best low-rank linear approximation of the data that obfuscates demographic information. We propose a conceptually simple approach that allows…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
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…
Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…
The problem of choosing appropriate values for missing data is often encountered in the data science. We describe a novel method containing both traditional mathematics and machine learning elements for prediction (imputation) of missing…
Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…
We propose novel methods for predictive (sparse) PCA with spatially misaligned data. These methods identify principal component loading vectors that explain as much variability in the observed data as possible, while also ensuring the…
With the growing interest on Network Analysis, Relational Data Mining is becoming an emphasized domain of Data Mining. This paper addresses the problem of extracting representative elements from a relational dataset. After defining the…
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…
Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. It extends principal component analysis (PCA) and can extract important and complicated components with small…
Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation…
Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…