The Suitable Distance Function for Fuzzy C-Means Clustering

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

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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

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