Related papers: Multivariate distance matrix regression for a mani…

Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…

This paper considers the problem of manifold functional multiple regression with functional response, time--varying scalar regressors, and functional error term displaying Long Range Dependence (LRD) in time. Specifically, the error term is…

Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression…

Distance metric learning can be viewed as one of the fundamental interests in pattern recognition and machine learning, which plays a pivotal role in the performance of many learning methods. One of the effective methods in learning such a…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

We propose the use of the vector-valued distance to compute distances and extract geometric information from the manifold of symmetric positive definite matrices (SPD), and develop gyrovector calculus, constructing analogs of vector space…

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image…

Recently, there has been a growing need in analyzing data on manifolds owing to their important role in diverse fields of science and engineering. In the literature of manifold-valued data analysis up till now, however, only a few works…

Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…

A new, coordinate-free (geometric) approach to multivariate statistical analysis. General multivariate linear models and linear hypotheses are defined in geometric form. A method of constructing statistical criteria is defined for linear…

This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…

Information visualization significantly enhances human perception by graphically representing complex data sets. The variety of visualization designs makes it challenging to efficiently evaluate all possible designs catering to users'…

In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…

Multidimensional Scaling (MDS) is a classic technique that seeks vectorial representations for data points, given the pairwise distances between them. However, in recent years, data are usually collected from diverse sources or have…

Leveraging geodesic distances and the geometrical information they convey is key for many data-oriented applications in imaging. Geodesic distance computation has been used for long for image segmentation using Image based metrics. We…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or…

A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents various dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian…

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as…