Table 1 Recent breakthroughs on pattern-based biclustering: algorithms and tackled limitations

Constant Models BicPAM [11]

Putative functional modules robust to noise, such as co-expressed genes with a regulatory pattern given by possibly different expression levels across a subset of conditions.

Algorithms consistently combining preprocessing, pattern mining (itemsets and association rules) and postprocessing procedures to guarantee the flexibility and robustness of the outputs.

Flexible structures; Exhaustive (yet efficient) searches; Tolerance to noise; Parameterizable coherence strength.

Multiplicative and Additive Models BicPAM [11]

Modules with shifting and scaling factors to deal with the distinct responsiveness of biological entities and handle biases introduced by the applied measurement.

Iterative discovery of pattern differences (shifts) and least common divisors (scales), together with pruning strategies, to learn additive and multiplicative models.

Precise modeling of shifting and scaling factors across rows; Flexible structure and parameterizable quality.

Order Preserving Model BicSPAM [12]

Coherent variation of gene expression or molecular concentrations across samples or within a temporal progression (such as stages of a disease or drug response).

Biclustering is parameterized with enhanced sequential pattern miners (by ordering column indexes per row according to the observed values) to flexibly discover noise-tolerant orderings.

Surpasses efficiency and robustness issues of exhaustive peers; Flexible structures with guarantees of optimality, addressing the problems of greedy peers.

Symmetric Bic(S)PAM [11, 12]

Modules associated with biological processes simultaneously capturing activation and repression mechanisms within transcriptomic, proteomic or metabolic data.

Combinatorial sign-adjustments (together with pruning principles) to model symmetries and integrate them with scales, shifts and orderings.

Discovery of non-constant biclusters with symmetries; Parameterizable properties.

Network Modules BicNET [17]

Coherent modules in homo/heterogeneous biological networks with weighted/labeled interactions. Modules able to capture non-trivial forms of behavior and accommodate less-studied biological entities.

Extension of previous contributions towards biological networks. For this end, new data structures and searches are proposed to effectively and efficiently deal with the inherent sparsity of network data.

Discovery of non-dense modules; Robustness to noisy and missing interactions; Scalable for large networks.

Plaid ModelBiP [14]

Overlapping regulatory influence in expression data (cumulative effects that multiple biological processes have on a gene at a particular time) and network data (cumulative effects in interactions belonging to multiple modules).

Extended searches to recover excluded areas (due to cumulative contributions on regions where biclusters overlap) and to remove noisy areas. New composition functions and relaxations to deal with noise and non-linear cumulative effects.

Addresses the exact additive plaid assumption with relaxations; No need for all the data elements to follow a plaid assumption; Models non-constant biclusters.

Constraints BiC2PAM [19]

Biological modules in accordance with user expectations (e.g. non-trivial homogeneity, satisfying a given pattern or preferred regulatory behavior (such as repression)) or with consistent functional terms.

Extended searches to benefit from background knowledge, including: constraints with succinct, anti-monotone and convertible properties, and incorporation of terms from knowledge repositories.

Focus on regions of interest; Efficiency gains; Removal of uninformative values.