BACKGROUND: Principal component analysis (PCA) has been widely used to visualize high-dimensional metabolomic data in a two- or three-dimensional subspace. In metabolomics, some metabolites (e.g., the top 10 metabolites) have been subjectively selected when using factor loading in PCA, and biological inferences are made for these metabolites. However, this approach may lead to biased biological inferences because these metabolites are not objectively selected with statistical criteria. RESULTS: We propose a statistical procedure that selects metabolites with statistical hypothesis testing of the factor loading in PCA and makes biological inferences about these significant metabolites with a metabolite set enrichment analysis (MSEA). This procedure depends on the fact that the eigenvector in PCA for autoscaled data is proportional to the correlation coefficient between the PC score and each metabolite level. We applied this approach to two sets of metabolomic data from mouse liver samples: 136 of 282 metabolites in the first case study and 66 of 275 metabolites in the second case study were statistically significant. This result suggests that to set the number of metabolites before the analysis is inappropriate because the number of significant metabolites differs in each study when factor loading is used in PCA. Moreover, when an MSEA of these significant metabolites was performed, significant metabolic pathways were detected, which were acceptable in terms of previous biological knowledge. CONCLUSIONS: It is essential to select metabolites statistically to make unbiased biological inferences from metabolomic data when using factor loading in PCA. We propose a statistical procedure to select metabolites with statistical hypothesis testing of the factor loading in PCA, and to draw biological inferences about these significant metabolites with MSEA. We have developed an R package "mseapca" to facilitate this approach. The "mseapca" package is publicly available at the CRAN website.

An efficient method for constructing facial images for use in telecommunication applications is proposed. This method uses a simple 3D feature model, which consists of polygons, which describe the shape of the face, and elastic linear springs, which simulate the natural movements of facial muscles. This method requires only two orthogonal facial images, and could easily be implemented on a relatively low-spec PC. Experimental results showed good results that various facial expressions could be synthesized and displayed from arbitrary directions.

A certain class of variable-length codes with feedback whose codeword lengths are uniformly upper bounded is considered. For this class of variable-length codes, it is shown that the zero-error capacity region for the, single-user and multiuser channels with feedback can be extended up to the ordinary average-error capacity under some conditions, if variable-length codes (semiblock codes) are used in place of fixed-length codes. This condition is different from that of M.V. Burnashev (1976) for variable-length codes with feedback but without any uniform bound on the codeword lengths. It is also shown that the capacity region for variable-length feedback codes coincides with that for fixed-length feedback codes.>