Dominant Set Biclustering Matteo Denitto 1(B ) , Manuele Bicego 1 , Alessandro Farinelli 1 , and Marcello Pelillo 2 1 Department of Computer Science, University of Verona, Verona, Italy matteo.denitto@univr.it 2 ECLT - University of Venice, Venice, Italy Abstract. Biclustering, which can be defined as the simultaneous clus- tering 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 pro- posed approach has been tested by using a well known synthetic microar- ray benchmark, with encouraging results. 1 Introduction Biclustering, also widely known as co-clustering, can be defined as the simul- taneous clustering of both rows and columns of a given data matrix [5, 12, 17]. With respect to clustering, the main differences of biclustering consist in the exploitation of local information (instead of global) to retrieve subsets of rows sharing a “similar” behaviour in a subsets of columns, and vice versa (instead of subsets of rows sharing a similar behaviour among whole the columns). Although bi-clustering was born and mainly applied to analyse gene expression microarray data [5, 22], it has been recently exploited in a more various range of applications from clickstream data [18], passing by recommender systems [19], to different Computer Vision scenarios (such as facial expression recognition [16], motion and plane estimation [8]). Different biclustering techniques have been proposed in the past – for a com- prehensive review please refer to [12, 17, 22, 23] – each one characterized by dif- ferent features, such as computational complexity, effectiveness, interpretability and optimization criterion. Various of such previous approaches are based on the idea of adapting a given clustering technique to the biclustering problem, for example by repeatedly performing rows and columns clustering [10, 14]. This paper follows the above-described research trend, and proposes a novel biclustering algorithm, which extends and adapts to the biclustering scenario the dominant-set based clustering. The concept of dominant set can be depicted from various points of view, since it involves optimization theory, graph theory, c  Springer International Publishing AG, part of Springer Nature 2018 M. Pelillo and E. Hancock (Eds.): EMMCVPR 2017, LNCS 10746, pp. 49–61, 2018. https://doi.org/10.1007/978-3-319-78199-0_4