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The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…

Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…

This work includes all the technical details of the Sequential Principal Curves Analysis (SPCA) in a single document. SPCA is an unsupervised nonlinear and invertible feature extraction technique. The identified curvilinear features can be…

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…

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

Probabilistic principal component analysis (PCA) and its Bayesian variant (BPCA) are widely used for dimension reduction in machine learning and statistics. The main advantage of probabilistic PCA over the traditional formulation is…

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

Modeling non-linear temporal trajectories is of fundamental interest in many application areas, such as in longitudinal microbiome analysis. Many existing methods focus on estimating mean trajectories, but it is also often of value to…

Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…

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…

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.…

Artificial neural networks that learn to perform Principal Component Analysis (PCA) and related tasks using strictly local learning rules have been previously derived based on the principle of similarity matching: similar pairs of inputs…

Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…

We study principal component analysis (PCA) for mean zero i.i.d. Gaussian observations $X_1,\dots, X_n$ in a separable Hilbert space $\mathbb{H}$ with unknown covariance operator $\Sigma.$ The complexity of the problem is characterized by…

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…

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…