Combining Multiple Clusterings via Crowd Agreement Estimation and Multi-Granularity Link Analysis

The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability to weight the base clusterings without access to the original data and can be affected significantly by the low-quality, or even ill clusterings. Secondly, they generally focus on the instance level or cluster level in the ensemble system and fail to integrate multi-granularity cues into a unified model. To address these two limitations, this paper proposes to solve the clustering ensemble problem via crowd agreement estimation and multi-granularity link analysis. We present the normalized crowd agreement index (NCAI) to evaluate the quality of base clusterings in an unsupervised manner and thus weight the base clusterings in accordance with their clustering validity. To explore the relationship between clusters, the source aware connected triple (SACT) similarity is introduced with regard to their common neighbors and the source reliability. Based on NCAI and multi-granularity information collected among base clusterings, clusters, and data instances, we further propose two novel consensus functions, termed weighted evidence accumulation clustering (WEAC) and graph partitioning with multi-granularity link analysis (GP-MGLA) respectively. The experiments are conducted on eight real-world datasets. The experimental results demonstrate the effectiveness and robustness of the proposed methods.Comment: The MATLAB source code of this work is available at: https://www.researchgate.net/publication/28197031

DeepCluE: Enhanced Image Clustering via Multi-layer Ensembles in Deep Neural Networks

Deep clustering has recently emerged as a promising technique for complex data clustering. Despite the considerable progress, previous deep clustering works mostly build or learn the final clustering by only utilizing a single layer of representation, e.g., by performing the K-means clustering on the last fully-connected layer or by associating some clustering loss to a specific layer, which neglect the possibilities of jointly leveraging multi-layer representations for enhancing the deep clustering performance. In view of this, this paper presents a Deep Clustering via Ensembles (DeepCluE) approach, which bridges the gap between deep clustering and ensemble clustering by harnessing the power of multiple layers in deep neural networks. In particular, we utilize a weight-sharing convolutional neural network as the backbone, which is trained with both the instance-level contrastive learning (via an instance projector) and the cluster-level contrastive learning (via a cluster projector) in an unsupervised manner. Thereafter, multiple layers of feature representations are extracted from the trained network, upon which the ensemble clustering process is further conducted. Specifically, a set of diversified base clusterings are generated from the multi-layer representations via a highly efficient clusterer. Then the reliability of clusters in multiple base clusterings is automatically estimated by exploiting an entropy-based criterion, based on which the set of base clusterings are re-formulated into a weighted-cluster bipartite graph. By partitioning this bipartite graph via transfer cut, the final consensus clustering can be obtained. Experimental results on six image datasets confirm the advantages of DeepCluE over the state-of-the-art deep clustering approaches.Comment: To appear in IEEE Transactions on Emerging Topics in Computational Intelligenc

Paradigm of tunable clustering using binarization of consensus partition matrices (Bi-CoPaM) for gene discovery

Copyright @ 2013 Abu-Jamous et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Clustering analysis has a growing role in the study of co-expressed genes for gene discovery. Conventional binary and fuzzy clustering do not embrace the biological reality that some genes may be irrelevant for a problem and not be assigned to a cluster, while other genes may participate in several biological functions and should simultaneously belong to multiple clusters. Also, these algorithms cannot generate tight clusters that focus on their cores or wide clusters that overlap and contain all possibly relevant genes. In this paper, a new clustering paradigm is proposed. In this paradigm, all three eventualities of a gene being exclusively assigned to a single cluster, being assigned to multiple clusters, and being not assigned to any cluster are possible. These possibilities are realised through the primary novelty of the introduction of tunable binarization techniques. Results from multiple clustering experiments are aggregated to generate one fuzzy consensus partition matrix (CoPaM), which is then binarized to obtain the final binary partitions. This is referred to as Binarization of Consensus Partition Matrices (Bi-CoPaM). The method has been tested with a set of synthetic datasets and a set of five real yeast cell-cycle datasets. The results demonstrate its validity in generating relevant tight, wide, and complementary clusters that can meet requirements of different gene discovery studies.National Institute for Health Researc

Relaxation dynamics of maximally clustered networks

We study the relaxation dynamics of fully clustered networks (maximal number of triangles) to an unclustered state under two different edge dynamics---the double-edge swap, corresponding to degree-preserving randomization of the configuration model, and single edge replacement, corresponding to full randomization of the Erd\H{o}s--R\'enyi random graph. We derive expressions for the time evolution of the degree distribution, edge multiplicity distribution and clustering coefficient. We show that under both dynamics networks undergo a continuous phase transition in which a giant connected component is formed. We calculate the position of the phase transition analytically using the Erd\H{o}s--R\'enyi phenomenology

Evolution in the Clustering of Galaxies for Z < 1

Measuring the evolution in the clustering of galaxies over a large redshift range is a challenging problem. For a two-dimensional galaxy catalog, however, we can measure the galaxy-galaxy angular correlation function which provides information on the density distribution of galaxies. By utilizing photometric redshifts, we can measure the angular correlation function in redshift shells (Brunner 1997, Connolly et al. 1998) which minimizes the galaxy projection effect, and allows for a measurement of the evolution in the correlation strength with redshift. In this proceedings, we present some preliminary results which extend our previous work using more accurate photometric redshifts, and also incorporate absolute magnitudes, so that we can measure the evolution of clustering with either redshift or intrinsic luminosity.Comment: 6 pages, 6 figures requires paspconf.sty. To be published in "Photometric Redshifts and High Redshift Galaxies", eds. R. Weymann, L. Storrie-Lombardi, M. Sawicki & R. Brunner, (San Francisco: ASP Conference Series

Coupling geometry on binary bipartite networks: hypotheses testing on pattern geometry and nestedness

Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the intrinsic structures of the system, so that the coupling geometry should be taken as information contents, or even the nonparametric minimum sufficient statistics of the network data. Then pertinent null and alternative hypotheses, such as nestedness, are to be formulated according to the macrostate. That is, any efficient testing statistic needs to be a function of this coupling geometry. These conceptual architectures and mechanisms are by and large still missing in community ecology literature, and rendered misconceptions prevalent in this research area. Here the algorithmically computed coupling geometry is shown consisting of deterministic multiscale block patterns, which are framed by two marginal ultrametric trees on row and column axes, and stochastic uniform randomness within each block found on the finest scale. Functionally a series of increasingly larger ensembles of matrix mimicries is derived by conforming to the multiscale block configurations. Here matrix mimicking is meant to be subject to constraints of row and column sums sequences. Based on such a series of ensembles, a profile of distributions becomes a natural device for checking the validity of testing statistics or structural indexes. An energy based index is used for testing whether network data indeed contains structural geometry. A new version block-based nestedness index is also proposed. Its validity is checked and compared with the existing ones. A computing paradigm, called Data Mechanics, and its application on one real data network are illustrated throughout the developments and discussions in this paper