We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph defined by the consensus matrix and the eigenvalues of the associated transition probability matrix are used to determine the number of clusters. For noisy or high-dimensional data, an iterative technique is presented to refine this consensus matrix in way that encourages a block-diagonal form. It is shown that the resulting consensus matrix is generally superior to existing similarity matrices for this type of spectral analysis.

A novel framework for consensus clustering is presented which has the ability to determine both the number of clusters and a final solution using multiple algorithms. A consensus similarity matrix is formed from an ensemble using multiple algorithms and several values for k. A variety of dimension reduction techniques and clustering algorithms are considered for analysis. For noisy or high-dimensional data, an iterative technique is presented to refine this consensus matrix in way that encourages algorithms to agree upon a common solution. We utilize the theory of nearly uncoupled Markov chains to determine the number, k , of clusters in a dataset by considering a random walk on the graph defined by the consensus matrix. The eigenvalues of the associated transition probability matrix are used to determine the number of clusters. This method succeeds at determining the number of clusters in many datasets where previous methods fail. On every considered dataset, our consensus method provides a final result with accuracy well above the average of the individual algorithms.

Cluster analysis is a field of data analysis that extracts underlying patterns in data. One application of cluster analysis is in text-mining, the analysis of large collections of text to find similarities between documents. We used a collection of about 30,000 tweets extracted from Twitter just before the World Cup started. A common problem with real world text data is the presence of linguistic noise. In our case it would be extraneous tweets that are unrelated to dominant themes. To combat this problem, we created an algorithm that combined the DBSCAN algorithm and a consensus matrix. This way we are left with the tweets that are related to those dominant themes. We then used cluster analysis to find those topics that the tweets describe. We clustered the tweets using k-means, a commonly used clustering algorithm, and Non-Negative Matrix Factorization (NMF) and compared the results. The two algorithms gave similar results, but NMF proved to be faster and provided more easily interpreted results. We explored our results using two visualization tools, Gephi and Wordle.

We explore the geometrical interpretation of the PCA based clustering algorithm Principal Direction Divisive Partitioning (PDDP). We give several examples where this algorithm breaks down, and suggest a new method, gap partitioning, which takes into account natural gaps in the data between clusters. Geometric features of the PCA space are derived and illustrated and experimental results are given which show our method is comparable on the datasets used in the original paper on PDDP.

Cluster Analysis is a field of Data Mining used to extract underlying patterns in unclassified data. Many existing clustering algorithms are inadequate in that they require knowledge of how many clusters exist in the data, otherwise known as k, and that their underlying assumptions make them ineffective in certain situations. The method of Consensus Clustering seeks to rectify the latter problem by incorporating the results of multiple clustering algorithms to achieve one final grouping. We investigate a novel method of Iterative Consensus Clustering (ICC) which solves both issues. The iteration of the consensus clustering technique widens the eigengap associated with the Perron cluster, giving a more definitive, and more accurate, estimation of the number of clusters, k.

Data clustering has various applications in a wide variety of fields ranging from social and biological sciences, to business, statistics, information retrieval, machine learning and data mining. Clustering refers to the process of grouping data based only on information found in the data which describes its characteristics and relationships. Although humans are generally very good at discovering patterns and classifying objects, clustering algorithms are able to discern similarities in data even when humans are not [6]. The main focus of our research has been document clustering, but we will demonstrate that our methods also work nicely on scientific data. In this paper, we propose an adaptation of the clustering algorithm known as Principal Direction Divisive Partitioning (PDDP) developed by Daniel Boley in [2] which is based Principal Components Analysis (PCA). PCA involves the eigenvector decomposition of a data covariance matrix, or equivalently a singular value decomposition (SVD) of a data matrix after mean centering. The name of our adaptation, Principal Direction Gap Partitioning (PDGP), borrows most of its name from PDDP as it follows many of the same steps that PDDP follows. The word “gap” replaces the word “divisive” in reference to how the algorithm splits data along natural gaps at each step. This concept will be further developed in the following sections, but it should be noted that PDGP is still a divisive algorithm in the same way that PDDP is.