Abstract:To determine the number of clusters in the clustering analysis that has a broad range of applied sciences, such as physics, chemistry, biology, engineering, economics etc., many methods have been proposed in the literature. The aim of this paper is to determine the number of clusters of a dataset in a model-based clustering by using an Analytic Hierarchy Process (AHP). In this study, the AHP model has been created by using the information criteria Akaike's Information Criterion (AIC), Approximate Weight of Evidence (AWE), Bayesian Information Criterion (BIC), Classification Likelihood Criterion (CLC), and Kullback Information Criterion (KIC). The achievement of the proposed approach has been tested on common real and synthetic datasets. The proposed approach based on the corresponding information criteria has produced accurate results. The currently produced results have been seen to be more accurate than those corresponding to the information criteria.

Clustering analysis based on a mixture of multivariate normal distributions is commonly used in the clustering of multidimensional data sets. Model selection is one of the most important problems in mixture cluster analysis based on the mixture of multivariate normal distributions. Model selection involves the determination of the number of components (clusters) and the selection of an appropriate covariance structure in the mixture cluster analysis. In this study, the efficiency of information criteria that are commonly used in model selection is examined. The effectiveness of information criteria has been determined according to the success in the selection of the number of components and in the selection of an appropriate covariance matrix.

The aim of this article is to investigate pathological subjects from a population through different physical factors. To achieve this, particle swarm optimization (PSO) and K-means (KM) clustering algorithms have been combined (PSO-KM). Datasets provided by the literature were divided into three clusters based on age and weight parameters and each one of right tibial external rotation (RTER), right tibial internal rotation (RTIR), left tibial external rotation (LTER), and left tibial internal rotation (LTIR) values were divided into three types as Type 1, Type 2 and Type 3 (Type 2 is non-pathological (normal) and the other two types are pathological (abnormal)), respectively. The rotation values of every subject in any cluster were noted. Then the algorithm was run and the produced values were also considered. The values of the produced algorithm, the PSO-KM, have been compared with the real values. The hybrid PSO-KM algorithm has been very successful on the optimal clustering of the tibial rotation types through the physical criteria. In this investigation, Type 2 (pathological subjects) is of especially high predictability and the PSO-KM algorithm has been very successful as an operation system for clustering and optimizing the tibial motion data assessments. These research findings are expected to be very useful for health providers, such as physiotherapists, orthopedists, and so on, in which this consequence may help clinicians to appropriately designing proper treatment schedules for patients.

Sonlu karma modellerde bileşen (küme) sayısının belirlenmesi önemli bir problem olup normal karma modeller, sonlu karma dağılımlarda sıklıkla kullanılmaktadır. Bu çalışmada, çok kriterli karar verme yöntemlerinden biri olan TOPSIS yöntemi ile çok değişkenli veri setinin modellenmesinde yeni bir kümeleme yöntemi önerilmiştir. Önerilen yöntemde, çok değişkenli verinin her bir değişkeni tek değişkenli normal karma dağılımlarla modellenip, bileşen sayısına göre elde edilen bilgi kriteri değerleri kullanılarak bir karar matrisi oluşturulmuştur. Karar matrisi kullanılarak TOPSIS yöntemi ile değişkenlerdeki bileşen sayısı belirlenmiştir. Bileşen bulunmayan homojen değişkenler elenerek boyut indirgenmiş olup heterojen değişkenlerdeki bileşen sayılarına göre oluşabilecek karma modeller için alternatif bileşen sayıları hesaplanmıştır. Alternatif bileşen sayıları içerisinden en uygun bileşen sayısı ve uygun karma model yine TOPSIS yöntemi ile belirlenmiştir. Böylece çok değişkenli veride boyut indirgeme ve değişken seçimi ile küme sayısı tahmini yapılmıştır. Önerilen yaklaşımın başarısı gerçek veri seti üzerinde test edilmiş olup veri setinin küme sayısı doğru olarak belirlenmiştir. Ayrıca bu yaklaşım, gözlemlerin sınıflandırma başarısını da arttırmıştır.