Fast Implementations of Markov Clustering for Protein Sequence Grouping

Abstract

Two efficient versions of a Markov clustering algorithm are proposed, suitable for fast and accurate grouping of protein sequences. First, the essence of the matrix splitting approach consists in optimal reordering of rows and columns in the similarity matrix after every iteration, transforming it into a matrix with several compact blocks along the diagonal, and zero similarities outside the blocks. These blocks are treated separately in later iterations, thus significantly reducing the overall computational load. Alternately, a special sparse matrix architecture is employed to represent the similarity matrix of the Markov clustering algorithm, which also helps getting rid of a severe amount of unnecessary computations. The proposed algorithms were tested to classify sequences of protein databases like SCOP95. The proposed solutions achieve a speed-up factor in the range 15-300 compared to the conventionally implemented Markov clustering, depending on input data size and parameter settings, without damaging the partition accuracy. The convergence is usually reached in 40-50 iterations. Combining the two proposed approaches brings us close to the 1000 times speed-up ratio.

This work was supported by the Hungarian National Research Funds (OTKA) under grant no. PD103921, the Hungarian Academy of Science through the János Bolyai Fellowship Program.