Related papers: Multivariate and functional classification using d…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by…

A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…

Despite its extensive development for multivariate data, semi-supervised learning remains underdeveloped for functional data. To address this challenge, we extend the Fermat distance, a density-sensitive metric aligning with the…

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…

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…

The problem of supervised classification (or discrimination) with functional data is considered, with a special interest on the popular k-nearest neighbors (k-NN) classifier. First, relying on a recent result by Cerou and Guyader (2006), we…

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…

The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…

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…

We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful…

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…

We propose an alternative to $k$-nearest neighbors for functional data whereby the approximating neighboring curves are piecewise functions built from a functional sample. Using a locally defined distance function that satisfies…

In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex…

The K-nearest neighbor (KNN) classifier is one of the simplest and most common classifiers, yet its performance competes with the most complex classifiers in the literature. The core of this classifier depends mainly on measuring the…

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest…

The $k$-nearest neighbour ($k$-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the $k$-NN classifier. In this…

In this paper, we introduced some notions on the n-Normed Spaces. Those are bounded k-linear (or multilinear) functionals and k-continuous (or multicontinuous) functions with k \in \mathbb{N}. We defined k-linear functionals under several…