Table 2 BicPAMS: input data, major parameters, and output models

Input: Data

P1 Matrix

The accepted file formats include attribute-relation files (.ARFF) and standard matrix files (such as.TXT). The first line of standard matrix files should specify the column identifiers, while the first entry of each line should specify the row identifier. Tabular data can be either delimited by tabs, spaces or commas.

P2 Network

BicPAMS accepts any input file format (such as.TXT or.SIG) assuming that: the first line specifies the column identifiers, and each other line specifies an interaction/entry within the network. An entry specifies the nodes and the association strength. Entries can be either delimited by tabs, spaces or commas. In addition to the file, the column index identifying the first node, second node and association strength needs to be inputted. Illustrating, for a network with header “idProteinA,nameProteinA,idProteinB,nameProteinB,weight”, the user should fix (node1,node2,score) indexes as (0,2,4) or (1,3,4). Finally, the user can specify whether each entry is directional from the first node towards the second node or bidirectional. Bidirectional entries increase the density of the network.

Desirable Biclustering Models

P3 Coherency Assumption

The coherency assumption defines the correlation of values within a bicluster. In constant models, an observed pattern (possibly containing different items) is preserved across rows (or columns). In additive or multiplicative models, shifting or scaling factors are allowed per row (or column) in order to allow meaningful variations of the original pattern. In order-preserving models, the values per row induce the same ordering across columns. A plaid model considers the cumulative effect of the contributions from multiple biclusters on areas where their rows and columns overlap. Previous models can further accommodate symmetric factors.

P4 Coherency Strength

The number of items determines the allowed deviations from expected values. Illustrating, a gene expression matrix parameterized with 5 items will have 2 levels of activation ({1,2}), 2 levels of repression ({-1,-2}) and 1 level of unchanged expression ({0}). By going beyond the differential values, BicPAMS enables the discovery of non-trivial yet coherent and meaningful correlations. To maintain consistency, additive (multiplicative) models should be used with an uneven (even) number of items. When considering order-preserving models, the number of items should be increased to balance the degree of co-occurrences versus precedences.

P5 Quality

This field specifies the maximum number of allowed noisy/missing elements (determining the minimum overlapping threshold for merging procedures). The tolerance of biclusters to noise can be additionally addressed using noise handlers (see mapping options) and alternative postprocessing procedures.

P15 Pattern Representation

Closed patterns (default option) enable the discovery of maximal biclusters (biclusters that cannot be extended without the need of removing rows and columns). Maximal patterns gives a preference towards flattened biclusters, possibly neglecting both vertical and smaller biclusters. Finally, the use of simple/all frequent patterns leads to biclustering solutions with a high number of biclusters (possibly contained by another bicluster), which can be useful to guide postprocessing steps. As the user specifies one of these three options, the available pattern miners are dynamically updated.

P16 Orientation

Coherency can be either observed across rows (default) or columns (searches are applied on the transposed matrix). When the number of columns highly exceeds the number of rows (or vice-versa when searches are applied on the transposed matrix), pattern miners with vertical data formats such as Eclat should be preferred.

Output

Upon successfully running BicPAMS, a textual and graphical display of the outputs is provided. The user can select the level of details associated with the outputted biclustering solution (statistics only, list of rows and columns per bicluster, disclosure of values per bicluster).