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

From patterned response dependency to structured covariate dependency: categorical-pattern-matching

Data generated from a system of interest typically consists of measurements from an ensemble of subjects across multiple response and covariate features, and is naturally represented by one response-matrix against one covariate-matrix. Likely each of these two matrices simultaneously embraces heterogeneous data types: continuous, discrete and categorical. Here a matrix is used as a practical platform to ideally keep hidden dependency among/between subjects and features intact on its lattice. Response and covariate dependency is individually computed and expressed through mutliscale blocks via a newly developed computing paradigm named Data Mechanics. We propose a categorical pattern matching approach to establish causal linkages in a form of information flows from patterned response dependency to structured covariate dependency. The strength of an information flow is evaluated by applying the combinatorial information theory. This unified platform for system knowledge discovery is illustrated through five data sets. In each illustrative case, an information flow is demonstrated as an organization of discovered knowledge loci via emergent visible and readable heterogeneity. This unified approach fundamentally resolves many long standing issues, including statistical modeling, multiple response, renormalization and feature selections, in data analysis, but without involving man-made structures and distribution assumptions. The results reported here enhance the idea that linking patterns of response dependency to structures of covariate dependency is the true philosophical foundation underlying data-driven computing and learning in sciences.Comment: 32 pages, 10 figures, 3 box picture

ACCAMS: Additive Co-Clustering to Approximate Matrices Succinctly

Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple insight that an additive model of co-clusterings allows one to approximate matrices efficiently. This allows us to build a concise model that, per bit of model learned, significantly beats all factorization approaches to matrix approximation. Even more surprisingly, we find that summing over small co-clusterings is more effective in modeling matrices than classic co-clustering, which uses just one large partitioning of the matrix. Following Occam's razor principle suggests that the simple structure induced by our model better captures the latent preferences and decision making processes present in the real world than classic co-clustering or matrix factorization. We provide an iterative minimization algorithm, a collapsed Gibbs sampler, theoretical guarantees for matrix approximation, and excellent empirical evidence for the efficacy of our approach. We achieve state-of-the-art results on the Netflix problem with a fraction of the model complexity.Comment: 22 pages, under review for conference publicatio