Related papers: Parameterized Principal Component Analysis
Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…
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.…
In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
Predictable Feature Analysis (PFA) (Richthofer, Wiskott, ICMLA 2015) is an algorithm that performs dimensionality reduction on high dimensional input signal. It extracts those subsignals that are most predictable according to a certain…
Factor-based forecasting using Principal Component Analysis (PCA) is an effective machine learning tool for dimension reduction with many applications in statistics, economics, and finance. This paper introduces a Supervised Screening and…
In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…
We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…
Principal component analysis (PCA) is a well-established method commonly used to explore and visualise data. A classical PCA model is the fixed effect model where data are generated as a fixed structure of low rank corrupted by noise. Under…
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…
Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…
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…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…
We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by…
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,…
The success of machine learning models relies heavily on effectively representing high-dimensional data. However, ensuring data representations capture human-understandable concepts remains difficult, often requiring the incorporation of…
This paper investigates the intrinsic group structures within the framework of large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. To this…
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…