δ-TRIMAX: Extracting Triclusters and Analysing Coregulation in Time Series Gene Expression Data

Triclustering of Gene Expression Microarray Data Using Coarse-Grained Parallel Genetic Algorithm

“…The evolutionary computation in the form of a multi-objective algorithm has also been employed in the search for triclusters in [13]. Bhar Anirban et al in 2012 presented δ-TRIMAX algorithm [2]. Again in 2013, the same authors applied the δ-TRIMAX algorithm in estrogen-induced breast cancer cell datasets which provides insights into breast cancer prognosis [3].…”

Triclustering Algorithms for Three-Dimensional Data Analysis

“…The variance of values in a tricluster is an illustrative merit function, which when minimized leads to the discovery of subspaces with approximately constant values. Merit functions vary according to the way they are applied: to guide greedy iterative searches (Bhar et al 2012), optimize multiple objectives (Liu et al 2008), or learn parametric models describing the target solution (Amar et al 2015)), for example; -their scope: whether they are used to assess a single tricluster or the overall triclustering solution (Mankad and Michailidis 2014); and the correlation extent: whether they (1) jointly assess the three dimensions (Sim et al 2010a),…”

“…Residue-based functions can be used to guarantee more flexible forms of homogeneity, including coherence assumptions that can accommodate shifts and scales on one, two, or three dimensions. In this context, the mean squared residue (MSR), originally proposed for the biclustering task (Cheng and Church 2000), was extended to guide triclustering algorithms (Bhar et al 2012;Dede and Oğul 2013). Given a real-valued 3D dataset, the elements of a tricluster can be described by…”

“…Complementary works combine merit functions with additional criteria to handle further challenges, such as high imbalance on the number of objects per dimension (e.g., thousands of genes for dozens of samples and time points in gene-sample-time data) (Bhar et al 2012) or arbitrarily high overlapping areas ). Gutiérrez-Avilés and Rubio-Escudero (2014b) extended the 3D MSR to incorporate two new terms controlling both the imbalance on the size of each dimension and the overlapping degree between triclusters.…”

“…Contiguity is used to enhance the consistency and interpretability of the results and reduce the complexity of the triclustering task. The contiguity condition can be relaxed or even disregarded since triclusters can be also meaningfully described by non-contiguous objects as long as the underlying homogeneity captures some form of temporal progression or spatial meaning (Bhar et al 2012;Amar et al 2015). The allowance of gaps between contiguous objects (Ji et al 2007) is a common relaxation to contiguity constraints that can be placed to tolerate local inconsistencies while still preserving desirable homogeneity criteria.…”