Improved K-means clustering algorithms : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Computer Science, Massey University, New Zealand

K-means clustering algorithm is designed to divide the samples into subsets with the goal that maximizes the intra-subset similarity and inter-subset dissimilarity where the similarity measures the relationship between two samples. As an unsupervised learning technique, K-means clustering algorithm is considered one of the most used clustering algorithms and has been applied in a variety of areas such as artificial intelligence, data mining, biology, psychology, marketing, medicine, etc. K-means clustering algorithm is not robust and its clustering result depends on the initialization, the similarity measure, and the predefined cluster number. Previous research focused on solving a part of these issues but has not focused on solving them in a unified framework. However, fixing one of these issues does not guarantee the best performance. To improve K-means clustering algorithm, one of the most famous and widely used clustering algorithms, by solving its issues simultaneously is challenging and significant. This thesis conducts an extensive research on K-means clustering algorithm aiming to improve it. First, we propose the Initialization-Similarity (IS) clustering algorithm to solve the issues of the initialization and the similarity measure of K-means clustering algorithm in a unified way. Specifically, we propose to fix the initialization of the clustering by using sum-of-norms (SON) which outputs the new representation of the original samples and to learn the similarity matrix based on the data distribution. Furthermore, the derived new representation is used to conduct K-means clustering. Second, we propose a Joint Feature Selection with Dynamic Spectral (FSDS) clustering algorithm to solve the issues of the cluster number determination, the similarity measure, and the robustness of the clustering by selecting effective features and reducing the influence of outliers simultaneously. Specifically, we propose to learn the similarity matrix based on the data distribution as well as adding the ranked constraint on the Laplacian matrix of the learned similarity matrix to automatically output the cluster number. Furthermore, the proposed algorithm employs the L2,1-norm as the sparse constraints on the regularization term and the loss function to remove the redundant features and reduce the influence of outliers respectively. Third, we propose a Joint Robust Multi-view (JRM) spectral clustering algorithm that conducts clustering for multi-view data while solving the initialization issue, the cluster number determination, the similarity measure learning, the removal of the redundant features, and the reduction of outlier influence in a unified way. Finally, the proposed algorithms outperformed the state-of-the-art clustering algorithms on real data sets. Moreover, we theoretically prove the convergences of the proposed optimization methods for the proposed objective functions

On Parallelization of Categorical Data Clustering

We study parallelization of categorical data clustering algorithms in an MPI platform. Clustering such data has been a daunting task even for sequential algorithms, mainly due to the challenges in finding suitable similarity/distance measures. We propose a parallel version of the k-modes algorithm, called PV3, which maintains the same clustering quality as produced by the sequential approach while achieving reasonable speed-ups. PV3 is programmed to ensure deterministic processing in a parallel environment. To produce better clustering results, we then develop an initialization method called Revised Density Method (RDM) based on the notion of density. Additionally, we develop variants of the RDM method to further enhance its performance. we then study effective ways to parallelize RDM and its variants. To further exploit parallelism opportunities, we develop an Ensemble Parallelizing Process (EPP) framework. This framework can be used with any desired initialization/clustering algorithms with different levels of parallelism. Using our different RDM initialization techniques along with the PV3 algorithm in the EPP framework, we then build an RDM realization of EPP, called RDM EPP. The result of our numerous experiments using benchmark categorical datasets indicate the quality metric of RDM EPP to be among the top three sequential k-modes based clustering algorithms. In terms of speed up, the results indicate to be 7 times faster for some datasets, though much larger datasets are required for a more comprehensive scalability study of RDM EPP