Related papers: Joint Characterization of Multiscale Information i…

We discuss the inadequacy of covariances/correlations and other measures in L2 as relative distance metrics under some conditions. We propose a computationally simple heuristic to transform a map based on standard principal component…

Dimension reduction and visualization is a staple of data analytics. Methods such as Principal Component Analysis (PCA) and Multidimensional Scaling (MDS) provide low dimensional (LD) projections of high dimensional (HD) data while…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

This paper examines in detail the geometric structure of principal component analysis (PCA) by considering in detail the distributions of both unrotated and rotated MNIST digits in the space defined by the lowest order PCA components. Since…

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

A major bottleneck of pedestrian detection lies on the sharp performance deterioration in the presence of small-size pedestrians that are relatively far from the camera. Motivated by the observation that pedestrians of disparate spatial…

Modern datasets and models are notoriously difficult to explore and analyze due to their inherent high dimensionality and massive numbers of samples. Existing visualization methods which employ dimensionality reduction to two or three…

Modern data are increasingly both high-dimensional and heteroscedastic. This paper considers the challenge of estimating underlying principal components from high-dimensional data with noise that is heteroscedastic across samples, i.e.,…

We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…

These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…

Studying complex real-world phenomena often involves data from multiple views (e.g. sensor modalities or brain regions), each capturing different aspects of the underlying system. Within neuroscience, there is growing interest in…

In real-world applications of image recognition tasks, such as human pose estimation, cameras often capture objects, like human bodies, at low resolutions. This scenario poses a challenge in extracting and leveraging multi-scale features,…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…

When working with large biological data sets, exploratory analysis is an important first step for understanding the latent structure and for generating hypotheses to be tested in subsequent analyses. However, when the number of variables is…

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…