Microarray Time-Series Data Clustering via Multiple Alignment of Gene Expression Profiles

Abstract

Genes with similar expression profiles are expected to be functionally related or co-regulated. In this direction, clustering microarray time-series data via pairwise alignment of piece-wise linear profiles has been recently introduced. We propose a k-means clustering approach based on a multiple alignment of natural cubic spline representations of gene expression profiles. The multiple alignment is achieved by minimizing the sum of integrated squared errors over a time-interval, defined on a set of profiles. Preliminary experiments on a well-known data set of 221 pre-clustered Saccharomyces cerevisiae gene expression profiles yields excellent results with 79.64% accuracy.

New approaches to clustering microarray time-series data using multiple expression profile alignment

“…In [14], we have introduced a multiple alignment approach for continuously integrable profiles. In this section, we extend that multiple alignment approach to piecewise linear profiles.…”

“…Additionally, we should also note that the error between x(t) and the shiftedŷ(t) = y(t) − a min is zero [14].…”

“…The solution a min i for each a i , 1 ≤ i ≤ s, is given by the following theorem whose proof and other related theoretical results can be found in [14].…”

“…Using natural cubic spline interpolations, in [14], we reformulated the pairwise gene expression profile alignment problem of [13] in terms of integrals of arbitrary functions. We then generalized the pairwise alignment formulae of [13] from the case of piecewise linear functions to profiles that are represented by any continuous integrable functions on a finite interval.…”

“…The procedure for extending pairwise profile alignment to multiple profile alignment is similar to the one described in [14], except that in this case we have used piecewise linear profiles instead of natural cubic spline profiles. We combine k-means clustering with our multiple alignment approaches to cluster microarray time-series data.…”