In the simple case that there is an only element a(i,j) either 0 or 1 in the binary matrix A, a Bicluster is equal to a biclique in the corresponding bipartite graph.
In the complex case, the element in matrix A is used to compute the quality of a given Bicluster and solve the more restricted version of the problem.
[13] It requires either large computational effort or the use of lossy heuristics to short-circuit the calculation.
In tangible data, these entries a(i,j) may be represented with the form n(i,j) + μ where n(i,j) denotes the noise.
There are, however, other algorithms, without the normalization step, that can find Biclusters which have rows and columns with different approaches.
In Cheng and Church's theorem, a Bicluster is defined as a subset of rows and columns with almost the same score.
More recently, IMMD-CC[22] is proposed that is developed based on the iterative complexity reduction concept.
IMMD-CC is able to identify co-cluster centroids from highly sparse transformation obtained by iterative multi-mode discretization.
Recent proposals have addressed the Biclustering problem in the specific case of time-series gene expression data.
This restriction leads to a tractable problem and enables the development of efficient exhaustive enumeration algorithms such as CCC-Biclustering[23] and e-CCC-Biclustering.
The e-CCC-Biclustering algorithm uses approximate expressions to find and report all maximal CCC-Bicluster's by a discretized matrix A and efficient string processing techniques.
These algorithms are also applied to solve problems and sketch the analysis of computational complexity.
There is an ongoing debate about how to judge the results of these methods, as Biclustering allows overlap between clusters and some algorithms allow the exclusion of hard-to-reconcile columns/conditions.
Not all of the available algorithms are deterministic and the analyst must pay attention to the degree to which results represent stable minima.
Because this is an unsupervised classification problem, the lack of a gold standard makes it difficult to spot errors in the results.
One approach is to utilize multiple Biclustering algorithms, with the majority or super-majority voting amongst them to decide the best result.
Matrix elements Dij denote occurrence of word j in document i. Co-clustering algorithms are then applied to discover blocks in D that correspond to a group of documents (rows) characterized by a group of words(columns).
Instead of explicitly clustering rows and columns alternately, they consider higher-order occurrences of words, inherently taking into account the documents in which they occur.
According to the cover coefficient concept number of clusters can also be roughly estimated by the following formula
In contrast to other approaches, FABIA is a multiplicative model that assumes realistic non-Gaussian signal distributions with heavy tails.
FABIA utilizes well understood model selection techniques like variational approaches and applies the Bayesian framework.