Mining Maximally Banded Matrices in Binary Data

Abstract

Binary data occurs often in several real world applications ranging from social networks to bioinformatics. Extracting patterns from such data has been a focus of fundamental data mining tasks including association rule analysis, sequence mining and bi-clustering. Recently, the utility of banded structures in binary matrices has been pointed out with applications in paleontology, bioinformatics and social networking. A binary matrix has a banded structure if both the rows and columns can be permuted so that the 1's exhibit a staircase pattern down the rows, along the leading diagonal. In this paper we show the correspondence between biclustering and banded structures in matrices; and the MMBS (Mine Maximally Banded Sub-matrices) algorithm is presented as a direct result of this correspondence. The current state of the art algorithm, MBS, only allows for the discovery of a single band and assumes a fixed column permutation. On the other hand MMBS facilitates the discovery of multiple bands that may possibly be overlapping or segmented. Our experimental results, presented here, clearly indicate the advantage of MMBS over MBS with both, synthetic and real data sets.

Segmented nestedness in binary data

“…The problem of finding k fully or almost nested submatrices is an instance of matrix reordering problems, for which many kind of patterns exist [12]. Examples of finding several reorderable patterns in one dataset include, for example, frequent itemsets [9] and maximally banded patterns [1], none of which requires a partitioning of columns. On the other hand, bucket orders [17] represent the data as ordered partitions.…”