This paper introduces 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 a clustering algorithm. The clustering algorithm used here is the quantum clustering method that has one free scale parameter. Although the method is not hierarchical, it can be modified to allow hierarchy in terms of this scale parameter.