Related papers: On Mahalanobis distance in functional settings

This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More…

The Mahalanobis distance is a classical tool used to measure the covariance-adjusted distance between points in $\bbR^d$. In this work, we extend the concept of Mahalanobis distance to separable Banach spaces by reinterpreting it as a…

Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…

We present analytical expressions for the means and covariances of the sample distribution of the cross-validated Mahalanobis distance. This measure has proven to be especially useful in the context of representational similarity analysis…

A mathematical model for variable selection in functional regression models with scalar response is proposed. By "variable selection" we mean a procedure to replace the whole trajectories of the functional explanatory variables with their…

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the…

The main ideas behind the classical multivariate logistic regression model make sense when translated to the functional setting, where the explanatory variable $X$ is a function and the response $Y$ is binary. However, some important…

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…

We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…

Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…

High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…

For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…

This paper proposes a multivariate nonlinear function-on-function regression model, which allows both the response and the covariates can be multi-dimensional functions. The model is built upon the multivariate functional reproducing kernel…

In this work we study two Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators, namely affine-invariant Riemannian and Log-Hilbert-Schmidt distances, in the context of covariance operators associated…

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…

We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices. The estimator is positive definite by construction, and the…

This paper introduces a theoretical framework that connects neural network linear layers with the Mahalanobis distance, offering a new perspective on neural network interpretability. While previous studies have explored activation functions…

The discussion focuses on metric covariance, a new association measure between paired random objects in a metric space, developed by Dubey and M\"uller, and on its relationship with other similar concepts which have previously appeared in…