An effective algorithm for mining 3-clusters in vertically partitioned data

Abstract

Conventional clustering algorithms group similar data points together along one dimension of a data table. Bi-clustering simultaneously clusters both dimensions of a data table. 3-clustering goes one step further and aims to concurrently cluster two data tables that share a common set of row labels, but whose column labels are distinct. Such clusters reveal the underlying connections between the elements of all three sets. We present a novel algorithm that discovers 3-clusters across vertically partitioned data. Our approach presents two new and important formulations: first we introduce the notion of a 3-cluster in partitioned data; and second we present a mathematical formulation that measures the quality of such clusters. Our algorithm discovers high quality, arbitrarily positioned, overlapping clusters, and is efficient in time. These results are exhibited in a comprehensive study on real datasets.

Triclustering Algorithms for Three-Dimensional Data Analysis

“…Subspace clustering also can be applied on alternative data structures: (1) relational data Banerjee et al 2007;Bekkerman et al 2005;Gao et al 2006;Chiaravalloti et al 2006;Balasubramanian et al 2016), (2) vertical partitioned data (Alqadah and Bhatnagar 2008), and (3) time-annotated graphs (Guigourès et al 2015).…”

“…Second, 2D biological data have been augmented into 3D data by distributing the observed values along a third dimension given by annotations from knowledge bases. Alqadah and Bhatnagar (2008) applied triclustering over disease-gene-GO term expression data to unravel associations between diseases and the regulated biological processes, cellular components, and molecular functions. Li and Tuck (2009) analyzed gene-sample-regulator expression data, where binding information was incorporated to create the third dimension.…”

“…Zudin et al (2015) triclustered user-tag-bookmark data to find groups of users coherently assigning similar tags on shared bookmarks. Alqadah and Bhatnagar (2008) applied triclustering over sparse keyword-ad campaign-site data. The same authors also introduced the problem of finding static communities from context-conditional social networks (individual-individual-issue data) to gain insight on consensual or disjoint views within a community on certain issues (such as Republican-Democrat views on political issues).…”

Algorithm for low-variance biclusters to identify coregulation modules in sequencing datasets

“…This helps divide the search space into independent sub-spaces of the search space at each level. This approach has been successfully adopted in [30] and [3] for searching biclusters in binary datasets.…”

“…A lattice of partially ordered closed biclusters is an efficient model of the search space in which a search algorithm may look for desirable closed biclusters. This approach has been adopted for finding biclusters in binary datasets [3,7,6,30] and our work in this paper is the first attempt to advance the same idea to datasets with real-values entries in the cells.…”