Evolutionary spectral co-clustering

Abstract

Abstract-Co-clustering is the problem of deriving submatrices from the larger data matrix by simultaneously clustering rows and columns of the data matrix. Traditional co-clustering techniques are inapplicable to problems where the relationship between the instances (rows) and features (columns) evolve over time. Not only is it important for the clustering algorithm to adapt to the recent changes in the evolving data, but it also needs to take the historical relationship between the instances and features into consideration. We present ESCC, a general framework for evolutionary spectral co-clustering. We are able to efficiently co-cluster evolving data by incorporation of historical clustering results. Under the proposed framework, we present two approaches, Respect To the Current (RTC), and Respect To Historical (RTH). The two approaches differ in the way the historical cost is computed. In RTC, the present clustering quality is of most importance and historical cost is calculated with only one previous timestep. RTH, on the other hand, attempts to keep instances and features tied to the same clusters between time-steps. Extensive experiments performed on synthetic and real world data, demonstrate the effectiveness of the approach.

Spectral co-clustering ensemble

“…There are also some works on extending spectral approaches to co-clustering [30][31][32]. Spectral approaches transform the problem of co-clustering as a partition problem on a bipartite graph.…”

Evolutionary Soft Co-Clustering

“…3 Evolutionary Soft Co-Clustering Although both co-clustering and evolutionary clustering have been intensively studied, the field of evolutionary co-clustering remains largely unexplored [13]. In addition, prior method (discussed in Section 4) employs singular value decomposition (SVD) in computing the solutions of relaxed problems.…”

“…Following the evolutionary spectral clustering framework in [6], two spectral methods for evolutionary coclustering have been proposed in [13]. In this section, we systematically extend the spectral methods in [13] using two different graph cut criteria, leading to four different methods for capturing the temporal smoothness.…”

“…In this section, we systematically extend the spectral methods in [13] using two different graph cut criteria, leading to four different methods for capturing the temporal smoothness. Our experimental results in Section 5 show that the probabilistic model proposed in this paper consistently outperforms the spectral methods.…”

“…To discover smooth hidden block structures from dynamic data, we systematically study the evolutionary co-clustering of time-varying data matrices. Existing methods are based on the spectral learning framework and do not require the co-clustering indicator matrices to be nonnegative, hindering a probabilistic interpretation of the results [13].…”