Fuzzy k-means clustering with crisp regions

Abstract

approach given by Miyamoto and Mukaidono [3]. The regularization approach can also provide the fuzzy c l w tering with crisp regions by introducing the quadratic regularizing function, for example (151). Our approach differs from the regularization approach, and then results are different. In the regularization approach, the meaning of the regularking function is not necwarily Instead of the regularizing function we introduce an explicit classification function which can be interpreted ezcr ilV A n e w h z z Y k-means clustering m&hod is Proposed by introducing crisp regions of clusters. &~u n d a r~~~ Of the redom are determined hYPerbolas admembenhiP are given b y one o r zero in each region. The area between crisp regiom is a fuzzy region, where membership MIues are P r o P o r t i o n d to distances t o crisp regions-A new method is a direct extension of the traditional hard k-means.

Fuzzy Clustering for Image Segmentation Using Generic Shape Information

“…GK, FCS and FCES algorithms were initialised using random membership values μ . FKR used a fuzzy k-means (FKM) [22] algorithm, while for the FKE algorithm the same initialisation approach in [11] was used, namely 10 iterations of FKM followed by 10 iterations of FKR. For the proposed FCGS algorithm, while any clustering algorithm can be used for initialization with Bspline, the GK algorithm (Algorithm 1) was selected because it consistently provided the highest percentage of superior results for all the test images used in the experiments in comparison to FKR, FCS, FKE and FCES.…”

A clustering approach for identifying approachable locations using terrestrial surface transport

“…The algorithm has well-defined boundaries between different clusters but there may be situations when the same data point is assigned to more than one cluster. For handling such situations, fuzzy k-means clustering algorithm [13] was proposed. In fuzzy k-means algorithm the data point can belong to more than one cluster.…”

A Modified Fuzzy K-means Clustering using Expectation Maximization

“…An improvement of K-means using the fuzzy logic theory was done by Looney [7] in which the concept of fuzziness has been used to improve K-means. Another improvement of fuzzy K-means with crisp regions was done by Watanabe [8]. Fuzzy K-means improves the basic K-means in finding good centers for clusters.…”

“…A large number of seeds can generally lead to an optimal solution, but again this cannot be guaranteed. Improvements to the K-means algorithm were made which dealt with some problems in the simple Kmeans [7,8]. K-means however is not considered as the best choice for clustering due it its time performance and requirements.…”

“…An improvement to this approach was to start with a huge random population of seeds [8]. This has been shown to find better seeds, since the initial seeds are more than K, and are distributed in the data set.…”