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This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection…

We provide and critically analyze a framework to learn critical behavior in classical partition functions through the application of non-parametric methods to data sets of thermal configurations. We illustrate our approach in phase…

We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…

Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

This paper introduces the Class-wise Principal Component Analysis, a supervised feature extraction method for hyperspectral data. Hyperspectral Imaging (HSI) has appeared in various fields in recent years, including Remote Sensing.…

Multivariate imputation by chained equations (MICE) is one of the most popular approaches to address missing values in a data set. This approach requires specifying a univariate imputation model for every variable under imputation. The…

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal…

Compressive learning forms the exciting intersection between compressed sensing and statistical learning where one exploits forms of sparsity and structure to reduce the memory and/or computational complexity of the learning task. In this…

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…

The next generation of weak lensing surveys will trace the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. Along with constraining the dynamics of dark energy, they will probe the…

In computer vision most iterative optimization algorithms, both sparse and dense, rely on a coarse and reliable dense initialization to bootstrap their optimization procedure. For example, dense optical flow algorithms profit massively in…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would…

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…