Relational patterns of gene expression via non-metric multidimensional scaling analysis

Abstract

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. 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 clear-cut as those by nMDS without preprocessing.

Multivariate regression analysis of distance matrices for testing associations between gene expression patterns and related variables

“…In fact, because the proposed procedure can be used to analyze each gene in a univariate manner, it extends traditional univariate procedures. In addition, unlike other approaches, the proposed approach does not require a reduction of the data via principal components (40), cluster (6), factor (41), or multidimensional scaling analysis (42). The proposed analysis procedure also differs from related procedures, such as GSEA and globalTest (43,44), in that it can be used to emphasize the multivariate nature of the expression values of many genes in the same pathway and treats the system being interrogated as a whole and does not consider each individual gene in a univariate analysis which then considers the result of the univariate analyses in aggregate.…”

Nonmetric Multidimensional Scaling Corrects for Population Structure in Association Mapping With Different Sample Types

“…Statistically, however, because the information compression capability of PCA is generally weak a small number of dimensions may not be able to capture most of the overall variation even when the data are in fact on a very low dimensional manifold (Taguchi and Oono 2005). Thus, PCA may fail to properly correct for population structure in certain situations (Kimmel et al 2007 also been used to account for population structure (Kraakman et al 2004;Epstein et al 2007), and their performance requires further investigation.Multidimensional scaling (MDS) is a major branch of multivariate analysis that has been widely used to visualize hidden relations among objects in data (Borg and Groenen 2005) and has been applied to genomic data to unravel relational patterns among genes from time series DNA microarray data (Taguchi and Oono 2005;Tzeng et al 2008). The essence of MDS is to find the configuration of points compatible with the given dissimilarity relations among them, and the resulting configuration should visually exhibit the structures or relations hidden in the original data.…”

“…The PCA method makes it computationally feasible to handle a large number of markers (tens of thousands) and correct for subtle population stratification (Hunter et al 2007;Wellcome Trust Case Control Consortium 2007;Yeager et al 2007). Statistically, however, because the information compression capability of PCA is generally weak a small number of dimensions may not be able to capture most of the overall variation even when the data are in fact on a very low dimensional manifold (Taguchi and Oono 2005). Thus, PCA may fail to properly correct for population structure in certain situations (Kimmel et al 2007).…”

“…Multidimensional scaling (MDS) is a major branch of multivariate analysis that has been widely used to visualize hidden relations among objects in data (Borg and Groenen 2005) and has been applied to genomic data to unravel relational patterns among genes from time series DNA microarray data (Taguchi and Oono 2005;Tzeng et al 2008). The essence of MDS is to find the configuration of points compatible with the given dissimilarity relations among them, and the resulting configuration should visually exhibit the structures or relations hidden in the original data.…”

Complexity of type 2 diabetes mellitus data sets emerging from nutrigenomic research: A case for dimensionality reduction?

“…A multivariate technique that aims to summarize a large number of variables with a small number of factors [164] Multi-dimensional Scaling (MDS) MDS is a dimentsionality reduction method that tries to preserve the interpoint distance between points in the low-dimensional space [165] Principal Component Analysis (PCA) Find the n dimensions that explain most of the variance.…”