Discovering Non-redundant Overlapping Biclusters on Gene Expression Data

IEEE Trans. Knowl. Data Eng.

et al. 2017

Abstract-Rank data, in which each row is a complete or partial ranking of available items (columns), is ubiquitous. Among others, it can be used to represent preferences of users, levels of gene expression, and outcomes of sports events. It can have many types of patterns, among which consistent rankings of a subset of the items in multiple rows, and multiple rows that rank the same subset of the items highly. In this article, we show that the problems of finding such patterns can be formulated within a single generic framework that is based on the concept of semiring matrix factorisation. In this framework, we employ the max-product semiring rather than the plus-product semiring common in traditional linear algebra. We apply this semiring matrix factorisation framework on two tasks: sparse rank matrix factorisation and rank matrix tiling. Experiments on both synthetic and real world datasets show that the framework is capable of discovering different types of structure as well as obtaining high quality solutions.

Section: Comparison To Bi-clusteringmentioning

confidence: 99%

Semiring Rank Matrix Factorization

IEEE Trans. Knowl. Data Eng.

et al. 2017

“…Inequalities (14) and (15) are introduced to remove the absolute operator of the summations in Equation (12). Inequalities (16) and (17) are due to Theorem 1. Inequality (18) ensures that the reconstructed matrix is a rank matrix.…”

Section: Sparse Rmf Using Integer Linear Programmingmentioning

confidence: 99%

“…Since large noise levels may conversely affect the performance of the algorithms, we use a dataset also used for the previous experiments, with p = 0.05 (low noise level). We ran all algorithms on this dataset and took the first seven Ranked tile 37% 41% 39% CoreNode [16] Numerical Coherent values bicluster 30% 8% 19% FABIA [13] Numerical Coherent values bicluster 99% 51% 75% Plaid [12] Numerical Coherent values bicluster 91% 46% 67% SAMBA [14] Numerical Coherent evolution bicluster 52% 9% 31% ISA [15] Numerical Coherent values bicluster 43% 17% 30% CC [10] Numerical Coherent values bicluster 7% 5% 6% Spectral [11] Numerical Coherent values bicluster --tiles/bi-clusters they produced, which have the highest scores (SAMBA) or largest sizes (all other). For most of the benchmarked algorithms, we used their default values.…”

Section: Data Generationmentioning

confidence: 99%

Rank Matrix Factorisation

Advances in Knowledge Discovery and Data Mining

et al. 2015

We introduce the problem of rank matrix factorisation (RMF). That is, we consider the decomposition of a rank matrix, in which each row is a (partial or complete) ranking of all columns. Rank matrices naturally appear in many applications of interest, such as sports competitions. Summarising such a rank matrix by two smaller matrices, in which one contains partial rankings that can be interpreted as local patterns, is therefore an important problem. After introducing the general problem, we consider a specific instance called Sparse RMF, in which we enforce the rank profiles to be sparse, i.e., to contain many zeroes. We propose a greedy algorithm for this problem based on integer linear programming. Experiments on both synthetic and real data demonstrate the potential of rank matrix factorisation.

“…Data type Pattern Precision Recall F1 Our algorithm Ranks Ranked tile 88% 83% 86% CoreNode [9] Numerical Coherent values bicluster 43% 72% 58% FABIA [7] Numerical Coherent values bicluster 40% 24% 32% Plaid [6] Numerical Coherent values bicluster 90% 6% 48% SAMBA [3] Numerical Coherent evolution bicluster 67% 3% 35% ISA [8] Numerical Coherent values bicluster 64% 44% 54% CC [4] Numerical Coherent values bicluster 35% 22% 29% Spectral [5] Numerical Coherent values bicluster --- Diverse query-based ranked tiling Finally, we use the same dataset, with p = 0.2, to illustrate diverse query-based ranked tiling. Figure 4a shows a query consisting of two columns, and Figure 4b shows the two discovered ranked tiles given that query.…”

Section: Algorithmmentioning

confidence: 99%

Ranked Tiling

Machine Learning and Knowledge Discovery in Databases

et al. 2014

Tiling is a well-known pattern mining technique. Traditionally, it discovers large areas of ones in binary databases or matrices, where an area is defined by a set of rows and a set of columns. In this paper, we introduce the novel problem of ranked tiling, which is concerned with finding interesting areas in ranked data. In this data, each transaction defines a complete ranking of the columns. Ranked data occurs naturally in applications like sports or other competitions. It is also a useful abstraction when dealing with numeric data in which the rows are incomparable. We introduce a scoring function for ranked tiling, as well as an algorithm using constraint programming and optimization principles. We empirically evaluate the approach on both synthetic and real-life datasets, and demonstrate the applicability of the framework in several case studies. One case study involves a heterogeneous dataset concerning the discovery of biomarkers for different subtypes of breast cancer patients. An analysis of the tiles by a domain expert shows that our approach can lead to the discovery of novel insights.