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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 establish minimax convergence rates for classification of functional data and for nonparametric regression with functional design variables. The optimal rates are of logarithmic type under smoothness constraints on the functional density…

Data classification, the process of analyzing data and organizing it into categories, is a fundamental computing problem of natural and artificial information processing systems. Ideally, the performance of classifier models would be…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

Deep neural networks (DNNs) trained with the logistic loss (i.e., the cross entropy loss) have made impressive advancements in various binary classification tasks. However, generalization analysis for binary classification with DNNs and…

Bayes classifiers for functional data pose a challenge. This is because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…

The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some…

We establish optimal convergence rates up to a log-factor for a class of deep neural networks in a classification setting under a restraint sometimes referred to as the Tsybakov noise condition. We construct classifiers in a general setting…

We consider the problem of clustering functional data while jointly selecting the most relevant features for classification. This problem has never been tackled before in the functional data context, and it requires a proper definition of…

Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework…

A functional distance ${\mathbb H}$, based on the Hausdorff metric between the function hypographs, is proposed for the space ${\mathcal E}$ of non-negative real upper semicontinuous functions on a compact interval. The main goal of the…

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…

Machine learning classifiers' capability is largely dependent on the scale of available training data and limited by the model overfitting in data-scarce learning tasks. To address this problem, this work proposes a novel framework of Meta…

A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…

We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent,…

We investigate the problem of classification in the presence of unknown class-conditional label noise in which the labels observed by the learner have been corrupted with some unknown class dependent probability. In order to obtain finite…

Statistical Linkage Learning (SLL) is a part of many state-of-the-art optimizers. The purpose of SLL is to discover variable interdependencies. It has been shown that the effectiveness of SLL-using optimizers is highly dependent on the…

The property of conformal predictors to guarantee the required accuracy rate makes this framework attractive in various practical applications. However, this property is achieved at a price of reduction in precision. In the case of…