Evaluation of Group Homogeneity in Gaussian Mixture Models Using Combined Cluster and Discriminant Analysis

Year 2017, Volume: 2 Issue: 1, 121 - 132, 01.07.2017

Ezgi Nazman , Semra Erbaş

Abstract

Cluster
analysis has been widely used in both data mining as unsupervised learning
method and in statistics as multivariate statistical method which reveals natural
groups underlying data set. However, determining the number
of homogeneous groups regarding
with finite mixture models which provides a natural representation of
heterogeneity due to pairwise overlap is a difficult process. In this study, Gaussian mixture
components which is one of finite mixture models are considered in terms of
group homogeneity. For this purpose,  combined
cluster and linear discriminant analysis is compared with combined cluster and quadratic
discriminant anlysis in order to evaluate correctly classification rates of the
Gaussian mixture components and to determine whether further division of components
is nessessary to obtain homogeneous groups. The comparison has been carried out
by using a simulation study for 81 different scenarios and an illisturative
example is presented.

Keywords

Clustering, Discriminant analysis, Pairwise overlap, Gaussian mixture component

Birleştirilmiş Kümeleme ve Diskriminant Analizi Kullanarak Gauss Karma Modellerde Grup Homojenliğinin Değerlendirilmesi

Abstract

Kümeleme analizi hem gözetimsiz öğrenme olarak veri
madenciliğinde hem de veri seti altında yatan doğal grupları ortaya çıkaran çok
değişkenli istatistiksel bir yöntem olarak istatistikte yaygın olarak
kullanılmaktadır. Ancak, ikili örtüşmeden ötürü
doğal bir heterojenlik temsili ortaya çıkaran sonlu karma modellerine ilişkin
homojen grup sayısını belirlemek zor bir işlemdir. Bu çalışmada, grup
homojenliği açısından sonlu karma modellerden biri olan Gauss karma modelleri
ele alınmıştır. Bu amaçla, Gauss karma bileşenlerin doğru sınıflama oranlarını değerlendirmek ve homojen
grupları elde etmede bileşenlerin daha fazla bölünmesinin gerekli olup
olmadığına karar vermek için birleştirilmiş kümeleme ve lineer diskriminant
analizi ile birleştirilmiş kümeleme ve karesel diskriminant analizi
karşılaştırılmıştır. 

Keywords

Kümeleme, Diskriminant analizi, ikili örtüşme, Gauss Karma Modeller

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