Entropy-Regularized Fuzzy Clustering for Non-Euclidean Relational Data and Indefinite Kernel Data

2012 ◽  
Vol 16 (7) ◽  
pp. 784-792 ◽  
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Fuzzy Clustering ◽  
Numerical Experiments ◽  
Standard Approach ◽  
Relational Data ◽  
Data Types ◽  
Indefinite Kernel ◽  
Clustering Approach ◽  
Theoretical Results

In this paper, an entropy-regularized fuzzy clustering approach for non-Euclidean relational data and indefinite kernel data is developed that has not previously been discussed. It is important because relational data and kernel data are not always Euclidean and positive semi-definite, respectively. It is theoretically determined that an entropy-regularized approach for both non-Euclidean relational data and indefinite kernel data can be applied without using a β-spread transformation, and that two other options make the clustering results crisp for both data types. These results are in contrast to those from the standard approach. Numerical experiments are employed to verify the theoretical results, and the clustering accuracy of three entropy-regularized approaches for non-Euclidean relational data, and three for indefinite kernel data, is compared.

scholarly journals A Comparative Study on TIBA Imputation Methods in FCMdd-Based Linear Clustering with Relational Data

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Takeshi Yamamoto ◽  
Katsuhiro Honda ◽  
Akira Notsu ◽  
Hidetomo Ichihashi
Keyword(s):  
Comparative Study ◽  
Iterative Algorithm ◽  
Fuzzy Clustering ◽  
Incomplete Data ◽  
Numerical Experiments ◽  
Missing Values ◽  
Relational Data ◽  
Imputation Methods ◽  
Clustering Model ◽  
Linear Cluster

Relational fuzzy clustering has been developed for extracting intrinsic cluster structures of relational data and was extended to a linear fuzzy clustering model based on Fuzzyc-Medoids (FCMdd) concept, in which Fuzzyc-Means-(FCM-) like iterative algorithm was performed by defining linear cluster prototypes using two representative medoids for each line prototype. In this paper, the FCMdd-type linear clustering model is further modified in order to handle incomplete data including missing values, and the applicability of several imputation methods is compared. In several numerical experiments, it is demonstrated that some pre-imputation strategies contribute to properly selecting representative medoids of each cluster.

Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data

2011 ◽  
Vol 15 (8) ◽  
pp. 1050-1056 ◽  
Author(s):  
Takeshi Yamamoto ◽  
◽  
Katsuhiro Honda ◽  
Akira Notsu ◽  
Hidetomo Ichihashi
Keyword(s):  
Fuzzy Clustering ◽  
Real World ◽  
Numerical Experiments ◽  
Document Classification ◽  
Classification Task ◽  
Relational Data ◽  
Real World Applications ◽  
Data Elements ◽  
Euclidean Type ◽  
Linear Cluster

Relational data is common in many real-world applications. Linear fuzzy clustering models have been extended for handling relational data based on Fuzzyc-Medoids (FCMdd) framework. In this paper, with the goal being to handle non-Euclidean data, β-spread transformation of relational data matrices used in Non-Euclidean-type Relational Fuzzy (NERF)c-means is applied before FCMdd-type linear cluster extraction. β-spread transformation modifies data elements to avoid negative values for clustering criteria of distances between objects and linear prototypes. In numerical experiments, typical features of the proposed approach are demonstrated not only using artificially generated data but also in a document classification task with a document-keyword co-occurrence relation.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

scholarly journals An Unsupervised Fuzzy Clustering Approach for Early Screening of COVID-19 from Radiological Images

2021 ◽  
pp. 1-1
Author(s):  
Weiping Ding ◽  
Shouvik Chakraborty ◽  
Kalyani Mali ◽  
Sankhadeep Chatterjee ◽  
Janmenjoy Nayak ◽  
...  
Keyword(s):  
Fuzzy Clustering ◽  
Early Screening ◽  
Radiological Images ◽  
Clustering Approach ◽  
Unsupervised Fuzzy Clustering

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

Improved fuzzy clustering approach: Application to medical image MRI

2012 ◽  
Author(s):  
Noureddine El Harchaoui ◽  
Samir Bara ◽  
Mounir Ait Kerroum ◽  
Ahmed Hammouch ◽  
Mohamed Ouadou ◽  
...  
Keyword(s):  
Fuzzy Clustering ◽  
Medical Image ◽  
Clustering Approach

A Convergence Analysis of the MINRES Method for Some Hermitian Indefinite Systems

2017 ◽  
Vol 7 (4) ◽  
pp. 827-836
Author(s):  
Ze-Jia Xie ◽  
Xiao-Qing Jin ◽  
Zhi Zhao
Keyword(s):  
Convergence Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Coefficient Matrix ◽  
Indefinite Systems ◽  
Indefinite Linear Systems ◽  
Theoretical Results

AbstractSome convergence bounds of the minimal residual (MINRES) method are studied when the method is applied for solving Hermitian indefinite linear systems. The matrices of these linear systems are supposed to have some properties so that their spectra are all clustered around ±1. New convergence bounds depending on the spectrum of the coefficient matrix are presented. Some numerical experiments are shown to demonstrate our theoretical results.

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