DICLENS: divisive clustering ensemble with automatic cluster number

DCE-IVI: Density-based clustering ensemble by selecting internal validity index

As each clustering algorithm cannot efficiently partition datasets with arbitrary shapes, the thought of clustering ensemble is proposed to consistently integrate clustering results to obtain better division. Most of ensemble research employs a single algorithm with different parameters to clustering. And this can be easily integrated, however it is hardly to divide complex datasets. Other available methods integrate different algorithms, it can divide datasets from different aspects, but fail to take outliers into account, which produces negative effects on the partition results. In order to solve these problems, we clustering datasets with three different density-based algorithms. The innovation of this paper is described as: (1) by setting dynamic thresholds, lower frequency evidence in the co-association matrix is gradually deleted to obtain multiple reconstructed matrices; (2) these reconstructed matrices are analyzed by hierarchical clustering to obtain basic clustering results; (3) an internal validity index is designed by the compactness within clusters and the correlation between clusters, which is used to select the final clustering result. By this innovation, the clustering effect is significantly improved. Finally, a series of experiments are designed, and the results verify the improvement and effectiveness of the proposed technique (DCE-IVI).

Clustering Ensemble Model Based on Self-Organizing Map Network

This paper proposes a clustering ensemble method that introduces cascade structure into the self-organizing map (SOM) to solve the problem of the poor performance of a single clusterer. Cascaded SOM is an extension of classical SOM combined with the cascaded structure. The method combines the outputs of multiple SOM networks in a cascaded manner using them as an input to another SOM network. It also utilizes the characteristic of high-dimensional data insensitivity to changes in the values of a small number of dimensions to achieve the effect of ignoring part of the SOM network error output. Since the initial parameters of the SOM network and the sample training order are randomly generated, the model does not need to provide different training samples for each SOM network to generate a differentiated SOM clusterer. After testing on several classical datasets, the experimental results show that the model can effectively improve the accuracy of pattern recognition by 4%∼10%.

Distribution-Based Cluster Structure Selection

The objective of cluster structure ensemble is to find a unified cluster structure from multiple cluster structures obtained from different datasets. Unfortunately, not all the cluster structures contribute to the unified cluster structure. This paper investigates the problem of how to select the suitable cluster structures in the ensemble which will be summarized to a more representative cluster structure. Specifically, the cluster structure is first represented by a mixture of Gaussian distributions, the parameters of which are estimated using the expectation-maximization algorithm. Then, several distribution-based distance functions are designed to evaluate the similarity between two cluster structures. Based on the similarity comparison results, we propose a new approach, which is referred to as the distribution-based cluster structure ensemble (DCSE) framework, to find the most representative unified cluster structure. We then design a new technique, the distribution-based cluster structure selection strategy (DCSSS), to select a subset of cluster structures. Finally, we propose using a distribution-based normalized hypergraph cut algorithm to generate the final result. In our experiments, a nonparametric test is adopted to evaluate the difference between DCSE and its competitors. We adopt 20 real-world datasets obtained from the University of California, Irvine and knowledge extraction based on evolutionary learning repositories, and a number of cancer gene expression profiles to evaluate the performance of the proposed methods. The experimental results show that: 1) DCSE works well on the real-world datasets and 2) DCSE based on DCSSS can further improve the performance of the algorithm.

Adaptive Fuzzy Consensus Clustering Framework for Clustering Analysis of Cancer Data

Performing clustering analysis is one of the important research topics in cancer discovery using gene expression profiles, which is crucial in facilitating the successful diagnosis and treatment of cancer. While there are quite a number of research works which perform tumor clustering, few of them considers how to incorporate fuzzy theory together with an optimization process into a consensus clustering framework to improve the performance of clustering analysis. In this paper, we first propose a random double clustering based cluster ensemble framework (RDCCE) to perform tumor clustering based on gene expression data. Specifically, RDCCE generates a set of representative features using a randomly selected clustering algorithm in the ensemble, and then assigns samples to their corresponding clusters based on the grouping results. In addition, we also introduce the random double clustering based fuzzy cluster ensemble framework (RDCFCE), which is designed to improve the performance of RDCCE by integrating the newly proposed fuzzy extension model into the ensemble framework. RDCFCE adopts the normalized cut algorithm as the consensus function to summarize the fuzzy matrices generated by the fuzzy extension models, partition the consensus matrix, and obtain the final result. Finally, adaptive RDCFCE (A-RDCFCE) is proposed to optimize RDCFCE and improve the performance of RDCFCE further by adopting a self-evolutionary process (SEPP) for the parameter set. Experiments on real cancer gene expression profiles indicate that RDCFCE and A-RDCFCE works well on these data sets, and outperform most of the state-of-the-art tumor clustering algorithms.

Hybrid fuzzy cluster ensemble framework for tumor clustering from biomolecular data

Cancer class discovery using biomolecular data is one of the most important tasks for cancer diagnosis and treatment. Tumor clustering from gene expression data provides a new way to perform cancer class discovery. Most of the existing research works adopt single-clustering algorithms to perform tumor clustering is from biomolecular data that lack robustness, stability, and accuracy. To further improve the performance of tumor clustering from biomolecular data, we introduce the fuzzy theory into the cluster ensemble framework for tumor clustering from biomolecular data, and propose four kinds of hybrid fuzzy cluster ensemble frameworks (HFCEF), named as HFCEF-I, HFCEF-II, HFCEF-III, and HFCEF-IV, respectively, to identify samples that belong to different types of cancers. The difference between HFCEF-I and HFCEF-II is that they adopt different ensemble generator approaches to generate a set of fuzzy matrices in the ensemble. Specifically, HFCEF-I applies the affinity propagation algorithm (AP) to perform clustering on the sample dimension and generates a set of fuzzy matrices in the ensemble based on the fuzzy membership function and base samples selected by AP. HFCEF-II adopts AP to perform clustering on the attribute dimension, generates a set of subspaces, and obtains a set of fuzzy matrices in the ensemble by performing fuzzy c-means on subspaces. Compared with HFCEF-I and HFCEF-II, HFCEF-III and HFCEF-IV consider the characteristics of HFCEF-I and HFCEF-II. HFCEF-III combines HFCEF-I and HFCEF-II in a serial way, while HFCEF-IV integrates HFCEF-I and HFCEF-II in a concurrent way. HFCEFs adopt suitable consensus functions, such as the fuzzy c-means algorithm or the normalized cut algorithm (Ncut), to summarize generated fuzzy matrices, and obtain the final results. The experiments on real data sets from UCI machine learning repository and cancer gene expression profiles illustrate that 1) the proposed hybrid fuzzy cluster ensemble frameworks work well on real data sets, especially biomolecular data, and 2) the proposed approaches are able to provide more robust, stable, and accurate results when compared with the state-of-the-art single clustering algorithms and traditional cluster ensemble approaches.