Comparison of Hard and Fuzzy Clustering Techniques and Selection of Optimal Fuzzifier Parameter: An Application on Household Characteristics and Health Expenditures

Year 2024, Volume: 11 Issue: 1, 17 - 31, 08.01.2024

Songül Çınaroğlu

Abstract

It is a challenging task for decision makers for finding the optimal classification pattern for the dataset obtained from national accounts, such as household budget survey (HBS) data. Fuzzy c-means (FCM) clustering, a fuzzy logic-based clustering algorithm, can be used effectively to find the proper cluster structure of given data sets under uncertainty. In this study, crisp (k-means) and fuzzy (FCM) clustering performances on grouping of households are compared while changing fuzzifier parameter for FCM. The results of the study reveal that FCM clustering performs better when compared with k-means clustering. It is found out that the optimal number of household groups is 5 and further, high cluster validity index scores are obtained when fuzzifier value is 1.5 in FCM clustering. High cluster validity index scores obtained from fuzzy Silhouette is compared to the crisp cluster validity index. The experimental results proved that fuzzy clustering superior grouping ability and it has better validity measures for grouping of households in a national dataset. It is observed that smaller fuzzifier value is a better choice to enhance fitness of fuzzy clustering. It is hoped that future experiments will compare the clustering abilities of FCM using datasets with different sizes and variables under the uncertainty conditions to determine the class boundary.

Keywords

fuzzycmeans, fuzzifier parameter, kmeans, silhouette

Sert ve Bulanık Kümeleme Tekniklerinin Karşılaştırılması ve Optimal Bulanıklaştırıcı Parametresinin Seçimi: Hanehalkı Özellikleri ve Sağlık Harcamaları Üzerine bir Uygulama

Abstract

Hanehalkı bütçe anketi (HBS) verileri gibi ulusal hesaplardan elde edilen veri seti için en uygun sınıflandırma modelini bulmak karar vericiler için zorlu bir görevdir. Bulanık mantık tabanlı bir kümeleme algoritması olan bulanık c-means (FCM) kümeleme, belirsizlik altında verilen veri setlerinin uygun küme yapısını bulmak için etkili bir şekilde kullanılabilir. Bu çalışmada, FCM için bulanıklaştırıcı parametresi değiştirilirken hanehalklarının gruplandırılmasında kesin (k-ortalamalar) ve bulanık (FCM) kümeleme performansları karşılaştırılmıştır. Çalışmanın sonuçları, FCM kümelemesinin k-means kümeleme ile karşılaştırıldığında daha iyi performans gösterdiğini ortaya koymaktadır. FCM kümelemesinde en uygun hane grubu sayısının 5 olduğu ve ayrıca FCM kümelemesinde bulanıklaştırıcı değeri 1.5 olduğunda yüksek küme geçerlilik indeksi puanları elde edildiği görülmüştür. Fuzzy Silhouette den elde edilen yüksek küme geçerlilik indeks değerleri sert küme geçerlilik indeks değerleri ile karşılaştırılmıştır. Deneysel sonuçlar, bulanık kümelemenin üstün gruplama becerisine sahip olduğunu ve ulusal bir veri setinde hane halklarının gruplanması için daha iyi geçerlilik ölçütlerine sahip olduğunu kanıtlamıştır. Bulanık kümelemenin uygunluğunu artırmak için daha küçük bulanıklaştırıcı değerinin daha iyi bir seçim olduğu gözlemlenmiştir. Gelecekte yapılacak çalışmalarda sınıf sınırını belirlemek için belirsizlik koşulları altında farklı boyut ve değişkenlere sahip veri kümelerini kullanarak FCM'nin kümeleme yeteneklerinin karşılaştırılması umulmaktadır.

Keywords

fuzzycmeans, fuzzifier parametresi, kmeans, silhouette

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