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Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…

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 most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

We study semiparametric factor models in high-dimensional panels where the factor loadings consist of a nonparametric component explained by observed covariates and an idiosyncratic component capturing unobserved heterogeneity. A key…

Data collection often results in records that have missing values or variables. This investigation compares 3 different data imputation models and identifies their merits by using accuracy measures. Autoencoder Neural Networks, Principal…

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

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…

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…

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…

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

Motivated by the previously developed multilevel aggregation method for solving structural analysis problems a novel two-level aggregation approach for efficient iterative solution of Principal Component Analysis (PCA) problems is proposed.…

Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…

We propose a novel exemplar selection approach based on Principal Component Analysis (PCA) and median sampling, and a neural network training regime in the setting of class-incremental learning. This approach avoids the pitfalls due to…

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…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…