Biclustering

Biclustering, block clustering, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix.The term was first introduced by Boris Mirkin to name a technique introduced many years earlier, in 1972, by J. A. Hartigan. Biclustering, block clustering, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix.The term was first introduced by Boris Mirkin to name a technique introduced many years earlier, in 1972, by J. A. Hartigan. Given a set of m {displaystyle m} samples represented by an n {displaystyle n} -dimensional feature vector, the entire dataset can be represented as m {displaystyle m} rows in n {displaystyle n} columns (i.e., an m × n {displaystyle m imes n} matrix). The biclustering algorithm generates biclusters – a subset of rows which exhibit similar behavior across a subset of columns, or vice versa. Biclustering was originally introduced by J. A. Hartigan in 1972. The term biclustering was later used by Mirkin. This algorithm was not generalized until 2000 when Y. Cheng and G. M. Church proposed a biclustering algorithm based on variance and applied it to biological gene expression data. Their paper is still the most important literature in the gene expression biclustering field. In 2001 and 2003, I.S. Dhillon put forward two algorithms applying biclustering to files and words. One version was based on bipartite spectral graph partitioning. The other was based on information theory. Dhillon assumed the loss of mutual information during biclustering was equal to the Kullback–Leibler-distance (KL-distance) between P and Q. P means the distribution of files and feature words before biclustering. Q is the distribution after biclustering. KL-distance is for measuring the difference between two random distributions. KL = 0 when the two distributions are the same and KL increases as the difference increases. Thus, the aim of the algorithm was to find the minimum KL-distance between P and Q. In 2004, Arindam Banerjee used a weighted-Bregman distance instead of KL-distance to design a biclustering algorithm which was suitable for any kind of matrix, unlike the KL-distance algorithm.