An incremental fuzzy algorithm for data clustering problems

Öz

Data Cluster analysis is an important part of data mining. It can be handled as two types, hard and soft clustering. In hard clustering, a dataset is divided into distinct clusters and each data in the dataset belongs to exactly one cluster. On the contrary data can belong to more than one cluster in soft clustering and each data can be associated with each cluster by a membership degree. Incremental algorithms which are developed for hard clustering have two main advantages. They based on the nonsmooth-nonconvex mathematical model which allows significantly reduce the number of variables and they choose one cluster center for each step that leads to obtain better objective function. In this paper, we propose an incremental fuzzy algorithm for soft clustering problems and present results of numerical experiments on 11 real-world datasets. These results demonstrate that the proposed algorithm is efficient for solving the soft clustering problems.

Anahtar Kelimeler

• A fuzzy c-means,global k-means algorithm,fuzzy clustering,nonsmooth optimization

Veri kümeleme problemleri için artımlı bir bulanık algoritma

Öz

Veri kümeleme analizi veri madenciliğinin önemli bir parçasıdır. Kesin ve esnek kümeleme olmak üzere iki sınıfta ele alınabilir. Kesin kümelemede bir veri seti kümelere ayrıldığında herbir veriseti içerisindeki her eleman yalnız ve yalnız bir kümeye ait olabilir.Esnek kümelemede ise kesin kümelemenin aksine her bir eleman belirli bir üyelik derecesi ile birden fazla kümeye ait olabilir. Kesin kümeleme için geliştirilmiş olan artımlı algoritmalar iki ana avantaja sahiptir. 

Bunlardan birincisi sahip olduğu nonsmooth-nonconvex matematiksel model yapısı sayaseinde değişken sayısı önemli ölçüde azaltılabilir. Bunun yanısıra her bir adımda bir tek küme merkezi seçilerek belirli bir k değerine kadar bu devam ettiği için küresel anlamda amaç fonksiyonu için daha iyi değerler elde edilebilir. Bu çalışmada esnek kümeleme problemlerinin çözümü için artımlı bir bulanık algoritma hazırlanmıştır ve algoritmayla gerçek 11 veriseti üzerinde gerçekleştirilen hesaplama denemelerinin sonuçları sunulmuştur. Sonuçlar esnek kümeleme problemlerinin çözümü için hazırlanan algoritmanın yararlılığını göstermektedir.

Anahtar Kelimeler

• Bulanık c-ortalamalar,küresel k-ortalamalar algoritması,nonsmooth optimizasyon

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