Quantum Clustering of Microarray Data in a Truncated SVD Space
Axel, I. and Horn, D.
School of Physics and Astronomy, Tel Aviv University
We describe the application of a novel clustering method to microarray
expression data. Its first stage involves compression of dimensions that
can be achieved by applying SVD to the gene-sample matrix in microarray
problems.
Thus the data (samples or genes) can be represented by vectors in a
truncated space of low dimensionality, 4 and 5 in the examples studied
here. We find it preferable to project all vectors onto the unit sphere
before applying our clustering algorithm, the quantum clustering method.
Although the method is not hierarchical, it can be modified to allow
hierarchy in terms of its free scale parameter.
We test our method on three data sets and obtain promising results. On
cancer cell data we obtain a dendrogram that reflects correct groupings
of cells. In an AML/ALL data set we obtain very good clustering of samples
into four classes of the data. Finally, in clustering of genes in yeast cell
cycle data we obtain four groups in a problem that is estimated to contain
five families.