An Ensemble Clusterer Framework based on Valid and Diverse Basic Small Clusters

Clustering ensemble is a new problem where it is aimed to extract a clustering out of a pool of base clusterings. The pool of base clusterings is sometimes referred to as ensemble. An ensemble is to be considered to be a suitable one, if its members are diverse and any of them has a minimum quality. The method that maps an ensemble into an output partition (called also as consensus partition) is named consensus function. The consensus function should find a consensus partition that all of the ensemble members agree on it as much as possible. In this paper, a novel clustering ensemble framework that guarantees generation of a pool of the base clusterings with the both conditions (diversity among ensemble members and high-quality members) is introduced. According to its limitations, a novel consensus function is also introduced. We experimentally show that the proposed clustering ensemble framework is scalable, efficient and general. Using different base clustering algorithms, we show that our improved base clustering algorithm is better. Also, among different consensus functions, we show the effectiveness of our consensus function. Finally, comparing with the state of the art, we find that the clustering ensemble framework is comparable or even better in terms of scalability and efficacy.

Social Network Optimization for Cluster Ensemble Selection

This paper studies the cluster ensemble selection problem for unsupervised learning. Given a large ensemble of clustering solutions, our goal is to select a subset of solutions to form a smaller yet better performing cluster ensemble than using all available solutions. The common way of aggregating the chosen solutions is accumulating the information of the selected results to a similarity matrix. This paper suggests transforming the similarity matrix to a modularity matrix and then applying a new consensus function which optimizes modularity measure in it. We represent the modularity maximization problem as a 0-1 quadratic program which can be exactly solved for small datasets. We also established a new greedy algorithm, namely sum linkage, to optimize the objective function specially for large scale datasets in a very short time. We show that the proposed consensus partition gets much closer to the actual cluster structure than the partitions obtained from the direct application of common cluster ensemble methods. The promising results compared with other most cited consensus functions show the excellent efficiency of the proposed method.

Extensive Analysis on Generation and Consensus Mechanisms of Clustering Ensemble: A Survey

<p class="PreformattedText">Data analysis plays a prominent role in interpreting various phenomena. Data mining is the process to hypothesize useful knowledge from the extensive data. Based upon the classical statistical prototypes the data can be exploited beyond the storage and management of the data. Cluster analysis a primary investigation with little or no prior knowledge, consists of research and development across a wide variety of communities. Cluster ensembles are melange of individual solutions obtained from different clusterings to produce final quality clustering which is required in wider applications. The method arises in the perspective of increasing robustness, scalability and accuracy. This paper gives a brief overview of the generation methods and consensus functions included in cluster ensemble. The survey is to analyze the various techniques and cluster ensemble methods.</p>

Axioms for Consensus Functions on then-Cube

Apvalue of a sequenceπ=(x1,x2,…,xk)of elements of a finite metric space(X,d)is an elementxfor which∑i=1kdp(x,xi)is minimum. Thelp–function with domain the set of all finite sequences onXand defined bylp(π)={x: xis apvalue ofπ}is called thelp–function on(X,d). Thel1andl2functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of thelp–functions on then-cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.