FARKLI BAĞLANTI YÖNTEMLERİ İLE HİYERARŞİK KÜMELEME TOPLULUĞU

Kümeleme topluluğu, yüksek kümeleme performansı sağlaması nedeniyle son yıllarda tercih edilen bir teknik haline gelmiştir. Bu çalışmada, Bağlantı-tabanlı Hiyerarşik Kümeleme Topluluğu (BHKT) olarak isimlendirilen yeni bir yaklaşım önerilmektedir. Önerilen yaklaşımda, topluluk elemanları farklı bağlantı yöntemleri kullanarak hiyerarşik kümeleme yapmakta ve sonrasında çoğunluk oylaması ile ortak karar üretmektedir. Çalışmada kullanılan bağlantı yöntemleri: tek bağlantı, tam bağlantı, ortalama bağlantı, merkez bağlantı, Ward yöntemi, komşu birleştirme yöntemi ve ayarlı tam bağlantıdır. Ayrıca çalışmada, farklı boyutlardaki hiyerarşik kümeleme toplulukları incelenmiş ve birbiriyle karşılaştırılmıştır. Deneysel çalışmalarda, hiyerarşik kümeleme toplulukları 8 farklı veri setinde uygulanmış ve tek bir kümeleme algoritmasına göre daha iyi sonuçlar elde edilmiştir

Clustering based on weighted ensemble

The clustering is an ill-posed problem and it has been proven that there is no algorithm that would satisfy all the assumptions about good clustering. This is why numerous clustering algorithms exist, based on various theories and approaches, one of them being the well-known Kohonen’s self-organizing map (SOM). Unfortunately, after training the SOM there is no explicitly obtained information about clusters in the underlying data, so another technique for grouping SOM units has to be applied afterwards. In the thesis, a contribution towards a two-level clustering of the SOM is presented, employing principles of Gravitational Law. The proposed algorithm for gravitational clustering of the SOM (gSOM) is capable of discovering complex cluster shapes, not only limited to the spherical ones, and is able to automatically determine the number of clusters. Experimental comparison with other clustering techniques is conducted on synthetic and real-world data. We show that gSOM achieves promising results especially on gene-expression data. As there is no clustering algorithm that can solve all the problems, it turns out as very beneficial to analyse the data using multiple partitions of them – an ensemble of partitions. Cluster-ensemble methods have emerged recently as an effective approach to stabilize and boost the performance of the single-clustering algorithms. Basically, data clustering with an ensemble involves two steps: generation of the ensemble with single-clustering methods and the combination of the obtained solutions to produce a final consensus partition of the data. To alleviate the consensus step the weighted cluster ensemble was proposed that tries to assess the relevance of ensemble members. One way to achieve this is to employ internal cluster validity indices to perform partition relevance analysis (PRA). Our contribution here is two-fold: first, we propose a novel cluster validity index DNs that extends the Dunn’s index and is based on the shortest paths between the data points considering the Gabriel graph on the data; second, we propose an enhancement to the weighted cluster ensemble approach by introducing the reduction step after the assessment of the ensemble partitions is done. The developed partition relevance analysis with the reduction step (PRAr) yields promising results when plugged in the three consensus functions, based on the evidence accumulation principle. In the thesis we address all the major stages of data clustering: data generation, data analysis using single-clustering algorithms, cluster validity using internal end external indices, and finally the cluster ensemble approach with the focus on the weighted variants. All the contributions are compared to the state-of-art methods using datasets from various problem domains. Results are positive and encourage the inclusion of the proposed algorithms in the machine-learning practitioner’s toolbox