ABSTRACT
The spectral biclustering algorithm was proposed by Kluger et al. (2003) as a method to identify subsets of features and conditions with checkerboard structure. A checkerboard structure can be described as a combination of constantbiclusters in a single data matrix. Figure 7.1 shows an example of a data matrix with 9 biclusters in a checkerboard structure. According to Madeira and Oliveira (2004) the algorithm is designed to identify non-overlapping biclusters and other types of biclusters apart from constant clusters that might not be detected by the algorithm. It is a multiplicative algorithm based on a singular value decomposition (SVD) of the data matrix and requires a normalisation step in order to uncover the underlying checkerboard structures. Figure 7.1 illustrates the multiplicative structure of the signal in the normalized data matrix. Each element in the de-noised data matrix is assumed to be a multiplication of elements in two vectors u and v, Aij = ui × vj . More details about the bicluster’s configuration are given in Section 7.3.
