Related papers: A nonlinear aggregation type classifier
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…
In distributed classification, each learner observes its environment and deduces a classifier. As a learner has only a local view of its environment, classifiers can be exchanged among the learners and integrated, or merged, to improve…
We prove that any optimal, independent, and zero unanimous fuzzy classification aggregation function of a continuum of individual classifications of $m\ge 3$ objects into $2\le p\le m$ types must be a weighted arithmetic mean. We also…
When data is of an extraordinarily large size or physically stored in different locations, the distributed nearest neighbor (NN) classifier is an attractive tool for classification. We propose a novel distributed adaptive NN classifier for…
We investigate a problem in which each member of a group of learners is trained separately to solve the same classification task. Each learner has access to a training dataset (possibly with overlap across learners) but each trained…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
Numbers and numerical vectors account for a large portion of data. However, recently the amount of string data generated has increased dramatically. Consequently, classifying string data is a common problem in many fields. The most widely…
This correspondence studies the basic problem of classifications - how to evaluate different classifiers. Although the conventional performance indexes, such as accuracy, are commonly used in classifier selection or evaluation,…
Many real-world machine learning applications are characterized by a huge number of features, leading to computational and memory issues, as well as the risk of overfitting. Ideally, only relevant and non-redundant features should be…
Someone knowledgeable in nonstandard analysis may get the feeling that in the nonlinear theory of generalized functions, too often one works directly on the nets and spends effort to obtain results that should be clear from general…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
Ordinal data are often seen in real applications. Regular multicategory classification methods are not designed for this data type and a more proper treatment is needed. We consider a framework of ordinal classification which pools the…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…
This article, addressed to a general audience of functional analysts, is intended to be an illustration of a few basic principles from `noncommutative functional analysis', more specifically the new field of {\em operator spaces.} In our…