Matteo Denitto

Biclustering of expression microarray data using affinity propagation

Biclustering, namely simultaneous clustering of genes and samples, represents a challenging and important research line in the expression microarray data analysis. In this paper, we investigate the use of Affinity Propagation, a popular clustering method, to perform biclustering. Specifically, we cast Affinity Propagation into the Couple Two Way Clustering scheme, which allows to use a clustering technique to perform biclustering. We extend the CTWC approach, adapting it to Affinity Propagation, by introducing a stability criterion and by devising an approach to automatically assemble couples of stable clusters into biclusters. Empirical results, obtained in a synthetic benchmark for biclustering, show that our approach is extremely competitive with respect to the state of the art, achieving an accuracy of 91% in the worst case performance and 100% accuracy for all tested noise levels in the best case.

A biclustering approach based on factor graphs and the max-sum algorithm

Biclustering represents an intrinsically complex problem, where the aim is to perform a simultaneous row- and column-clustering of a given data matrix. Some recent approaches model this problem using factor graphs, so to exploit their ability to open the door to efficient optimization approaches for well designed function decompositions. However, while such models provide promising results, they do not scale to data matrices of reasonable size. In this paper, we take a step towards addressing this issue, by proposing a novel approach to biclustering based on factor graphs, which yields high quality solutions and scales more favorably than previous methods. Specifically, we cast biclustering as the sequential search for a single bicluster, and propose a binary and compact factor graph that can be solved efficiently using the max-sum algorithm. The proposed approach has been tested and compared with state-of-the-art methods on four datasets (two synthetic and two real world data), providing encouraging results with respect both to previous approaches based on factor graphs and to other state-of-the-art methods. HighlightsA novel compact Factor Graph for Biclustering is proposed.The approach exploits Max-Sum and the message passing scheme for the optimization.Closed form message updates have been derived (derivation included in the paper).The proposed method favorably compares with current state-of-the-art.

A Binary Factor Graph Model for Biclustering

Biclustering, which can be defined as the simultaneous clustering of rows and columns in a data matrix, has received increasing attention in recent years, particularly in the field of Bioinformatics e.g. for the analysis of microarray data. This paper proposes a novel biclustering approach, which extends the Affinity Propagation [1] clustering algorithm to the biclustering case. In particular, we propose a new exemplar based model, encoded as a binary factor graph, which allows to cluster rows and columns simultaneously. Moreover, we propose a linear formulation of such model to solve the optimization problem using Linear Programming techniques. The proposed approach has been tested by using a well known synthetic microarray benchmark, with encouraging results.

Multiple Structure Recovery via Probabilistic Biclustering

Multiple Structure Recovery (MSR) represents an important and challenging problem in the field of Computer Vision and Pattern Recognition. Recent approaches to MSR advocate the use of clustering techniques. In this paper we propose an alternative method which investigates the usage of biclustering in MSR scenario. The main idea behind the use of biclustering approaches to MSR is to isolate subsets of points that behave “coherently” in a subset of models/structures. Specifically, we adopt a recent generative biclustering algorithm and we test the approach on a widely accepted MSR benchmark. The results show that biclustering techniques favorably compares with state-of-the-art clustering methods.

Biclustering with a quantum annealer

Several problem in Artificial Intelligence and Pattern Recognition are computationally intractable due to their inherent complexity and the exponential size of the solution space. One example of such problems is biclustering, a specific clustering problem where rows and columns of a data-matrix must be clustered simultaneously. Quantum information processing could provide a viable alternative to combat such a complexity. A notable work in this direction is the recent development of the D-Wave computer, whose processor has been designed to the purpose of solving Quadratic Unconstrained Binary Optimization (QUBO) problems. In this paper, we investigate the use of quantum annealing by providing the first QUBO model for biclustering and a theoretical analysis of its properties (correctness and complexity). We empirically evaluated the accuracy of the model on a synthetic data-set and then performed experiments on a D-Wave machine discussing its practical applicability and embedding properties.

Dominant Set Biclustering

Biclustering, which can be defined as the simultaneous clustering of rows and columns in a data matrix, has received increasing attention in recent years, being applied in many scientific scenarios (e.g. bioinformatics, text analysis, computer vision). This paper proposes a novel biclustering approach, which extends the dominant-set clustering algorithm to the biclustering case. In particular, we propose a new way of representing the problem, encoded as a graph, which allows to exploit dominant set to analyse both rows and columns simultaneously. The proposed approach has been tested by using a well known synthetic microarray benchmark, with encouraging results.

Spike and slab biclustering

Abstract Biclustering refers to the problem of simultaneously clustering the rows and columns of a given data matrix, with the goal of obtaining submatrices where the selected rows present a coherent behaviour in the selected columns, and vice-versa. To face this intrinsically difficult problem, we propose a novel generative model, where biclustering is approached from a sparse low-rank matrix factorization perspective. The main idea is to design a probabilistic model describing the factorization of a given data matrix in two other matrices, from which information about rows and columns belonging to the sought for biclusters can be obtained. One crucial ingredient in the proposed model is the use of a spike and slab sparsity-inducing prior, thus we term the approach spike and slab biclustering (SSBi). To estimate the parameters of the SSBi model, we propose an expectation-maximization (EM) algorithm, termed SSBiEM, which solves a low-rank factorization problem at each iteration, using a recently proposed augmented Lagrangian algorithm. Experiments with both synthetic and real data show that the SSBi approach compares favorably with the state-of-the-art.

A Quantum Annealing Approach to Biclustering

Several problem in Artificial Intelligence and Pattern Recognition are computationally intractable due to their inherent complexity and the exponential size of the solution space. One example of such problems is biclustering, a specific clustering problem where rows and columns of a data-matrix must be clustered simultaneously. Quantum information processing could provide a viable alternative to combat such a complexity. A notable work in this direction is the recent development of the D-Wave™ computer, whose processor is able to exploit quantum mechanical effects in order to perform quantum annealing. The question motivating this work is whether the use of this special hardware is a viable approach to efficiently solve the biclustering problem. As a first step towards the solution of this problem, we show a feasible encoding of biclustering into the D-Wave™ quantum annealing hardware, and provide a theoretical analysis of its correctness.