Related papers: Spatial Depth-Based Classification for Functional …

Many applications, such as system identification, classification of time series, direct and inverse problems in partial differential equations, and uncertainty quantification lead to the question of approximation of a non-linear operator…

Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…

In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In…

Deep neural networks have revolutionized medical image analysis and disease diagnosis. Despite their impressive performance, it is difficult to generate well-calibrated probabilistic outputs for such networks, which makes them…

In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…

The design of high-resolution and cross-term (CT) free time-frequency distributions (TFDs) has been an open problem. Classical kernel based methods are limited by the trade-off between TFD resolution and CT suppression, even under optimally…

Accurate prediction of spatially dependent functional data is critical for various engineering and scientific applications. In this study, a spatial functional deep neural network model was developed with a novel non-linear modeling…

Conventional Computed Tomography (CT) imaging recognition faces two significant challenges: (1) There is often considerable variability in the resolution and size of each CT scan, necessitating strict requirements for the input size and…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…

Kernel-based classification methods, particularly the support vector machine (SVM), are among the most common algorithms for hyperspectral data classification. The Radial Basis function (RBF) kernel has earned great popularity in…

Several data mining problems are characterized by data in high dimensions. One of the popular ways to reduce the dimensionality of the data is to perform feature selection, i.e, select a subset of relevant and non-redundant features.…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

Manifold structure learning is often used to exploit geometric information among data in semi-supervised feature learning algorithms. In this paper, we find that local discriminative information is also of importance for semi-supervised…

Kernel Stein discrepancy (KSD) is a widely used kernel-based measure of discrepancy between probability measures. It is often employed in the scenario where a user has a collection of samples from a candidate probability measure and wishes…

Kernel density estimation (KDE) has become a popular method for visual analysis in various fields, such as financial risk forecasting, crime clustering, and traffic monitoring. KDE can identify high-density areas from discrete datasets.…

We have developed and tested a spatial scan statistic for categorical, functional data (CFSS) - a data structure within which current approaches cannot identify spatial clusters. Our methodology combines an encoding scheme for categorical,…

Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…

We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…

We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…