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Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant…
Principal Component Analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in Statistics, Machine Learning, Computer Vision, and related fields. However, PCA is well-known…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
Principal component analysis (PCA) defines a reduced space described by PC axes for a given multidimensional-data sequence to capture the variations of the data. In practice, we need multiple data sequences that accurately obey individual…
Neural operator learning has emerged as a powerful approach for solving partial differential equations (PDEs) in a data-driven manner. However, applying principal component analysis (PCA) to high-dimensional solution fields incurs…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…
Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix…
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…
Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA). Prior studies have demonstrated that linear autoencoders (LAEs) can recover the ordered, axis-aligned principal components of PCA by…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
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 study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…
Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…
Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis~(PPGA) has been proposed to generalize conventional principal component analysis…
Principal component analysis (PCA) is fundamental to statistical machine learning. It extracts latent principal factors that contribute to the most variation of the data. When data are stored across multiple machines, however, communication…