Related papers: Sparse Functional Principal Component Analysis in …

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…

The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method…

Non-gaussian component analysis (NGCA) introduced in offered a method for high dimensional data analysis allowing for identifying a low-dimensional non-Gaussian component of the whole distribution in an iterative and structure adaptive way.…

Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…

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,…

Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…

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…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…

Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and…

Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…

Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when…