Relational patterns of gene expression via nonmetric multidimensional   scaling analysis
  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. 
Y.-h. Taguchi and Y. Oono