  Motivation:Microarray experiments result in large scale data sets that
require extensive mining and refining to extract useful information. We
demonstrate the usefulness of (nonmetric) multidimensional scaling (MDS) method
in analyzing a large number of genes. Applying MDS to the microarray data is
certainly not new, but the existing works are all on small numbers
  (< 100) of points to be analyzed. We have been developing an efficient novel
algorithm for nonmetric multidimensional scaling (nMDS) analysis for very large
data sets as a maximally unsupervised data mining device. We wish to
demonstrate its usefulness in the context of bioinformatics (unraveling
relational patterns among genes from time series data in this paper).
  Results: The Pearson correlation coefficient with its sign flipped is used to
measure the dissimilarity of the gene activities in transcriptional response of
cell-cycle-synchronized human fibroblasts to serum [Iyer {\it et al}., Science
{\bf 283}, 83 (1999)]. These dissimilarity data have been analyzed with our
nMDS algorithm to produce an almost circular relational pattern of the genes.
The obtained pattern expresses a temporal order in the data in this example;
the temporal expression pattern of the genes rotates along this circular
arrangement and is related to the cell cycle. For the data we analyze in this
paper we observe the following. If an appropriate preparation procedure is
applied to the original data set, linear methods such as the principal
component analysis (PCA) could achieve reasonable results, but without data
preprocessing linear methods such as PCA cannot achieve a useful picture.
Furthermore, even with an appropriate data preprocessing, the outcomes of
linear procedures are not as clearcut as those by nMDS without preprocessing.
