Eliyanto, Joko and Surono, Sugiyarto and Salafudin, Salafudin
(2022)
*The Suitable Distance Function for Fuzzy C-Means Clustering.*
In: AIP Conference Proceedings.

Text
5.0106185.pdf Download (797kB) |

## Abstract

Fuzzy C-Means clustering is a form of clustering based on distance which apply the concept of fuzzy logic. The

clustering process works simultaneously with the iteration process to minimize the objective function. This objective

function is the summation from the multiplication of the distance between the data coordinates to the nearest cluster centroid

with the degree of which the data belong to the cluster itself. Based on the objective function equation, the value of the

objective function will decrease by increasing the number of iteration process. This research provide how we choose the

suitable distance for Fuzzy C-Means clustering. The right distance will meet the optimization problem in the Fuzzy CMeans Clustering method and produce good cluster quality. They are Euclidean, Average, Manhattan, Chebisev,

Minkowski, Minkowski-Chebisev, and Canberra distance. We use five UCI Machine Learning dataset and two random

datasets. We use the Lagrange multiplier method for the optimization of this method. The result quality of the cluster

measure by their accuracy, Davies Bouldin Index, purity, and adjusted rand index. The experiment shows that the Canbera

distances are the best distances which provide the optimum result by producing minimum objective function 378.185. The

suitable distance for the application of the Fuzzy C-Means Clustering method are Euclidean distance, Average distance,

Manhattan distance, Minkowski distance, Minkowski-Chebisev distance, and Canberra distance. These six distances

produce a numerical simulation that derives the objective function fairly constant. Meanwhile, the Chebisev distance shows

the movement of the value of the objective function that fluctuates, so it is not in accordance with the optimization problem

in the Fuzzy C Means Clustering method.

Item Type: | Conference or Workshop Item (Paper) |
---|---|

Subjects: | Q Science > QA Mathematics |

Divisi / Prodi: | Faculty of Applied Science and Technology (Fakultas Sains Dan Teknologi Terapan) > S1-Mathematics (S1-Matematika) |

Depositing User: | Dr Sugiyarto Surono |

Date Deposited: | 06 Dec 2022 04:04 |

Last Modified: | 06 Dec 2022 04:04 |

URI: | http://eprints.uad.ac.id/id/eprint/37845 |

## Actions (login required)

View Item |