Several Remarks on Dissimilarities and Ultrametrics

We investigate the relationships between tolerance relations, equivalence relations, and ultrametrics. The set of spheres associated to an ultrametric space has a tree structure that rejects a hierarchy on the set of equivalences associated to that space. We show that every ultrametric defined on a finite space is a linear combination of binary ultrametric and we introduce the notion of ultrametricity for dissimilarities, which has applications in many data mining problems

On Partition Metric Space, Index Function, and Data Compression

We discuss a metric structure on the set of partitions of a finite set induced by the Gini index and two applications of this metric: the identification of determining sets for index functions using techniques that originate in machine learning, and a data compression algorithm

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era

On Generalized Entropy and Entropic Metrics

Starting from an axiomatization of a generalization of Shannon entropy we introduce a set of axioms for a parametric family of distances over sets of partitions of finite sets. This family includes some well-known metrics used in data mining and in the study of finite functions.

Metric-Entropy Pairs on Lattices

We introduce the notion of ∧- and ∨-pairs of functions on lattices as an abstraction of the notions of metric and its related entropy for probability distributions. This approach allows us to highlight the relationships that exist between various properties of metrics and entropies and opens the possibility of extending these concepts to other algebraic structures

Pharmacotherapy of diabetes related ocular diseases

Pharmacotherapy of diabetes related ocular diseases.egységes, osztatlanáltalános orvosango