Motivation: Comparisons of microbiome communities across populations are often based on pairwise distance measures (beta-diversity). Standard analyses (principal coordinate plots, permutation tests, kernel methods) require access to primary data if another investigator wants to add or compare independent data. We propose using standard reference measurements to simplify microbiome beta-diversity analyses, to make them more transparent, and to facilitate independent validation and comparisons across studies. Results: Using stool and nasal reference sets from the Human Microbiome Project (HMP), we computed mean distances (actually Bray-Curtis or Pearson correlation dissimilarities) to each reference set for each new sample. Thus, each new sample has two mean distances that can be plotted and analyzed with classical statistical methods. To test the approach, we studied independent (not reference) HMP subjects. Simple Hotelling tests demonstrated statistically significant differences in mean distances to reference sets between all pairs of body sites (stool, skin, nasal, saliva and vagina) at the phylum, class, order, family and genus levels. Using the distance to a single reference set was usually sufficient, but using both reference sets always worked well. The use of reference sets simplifies standard analyses of beta-diversity and facilitates the independent validation and combining of such data because others can compute distances to the same reference sets. Moreover, standard statistical methods for survival analysis, logistic regression and other procedures can be applied to vectors of mean distances to reference sets, thereby greatly expanding the potential uses of beta-diversity information. More work is needed to identify the best reference sets for particular applications. Availability and implementation: https://github.com/NCI-biostats/microbiome-fixed-reference. Supplementary information: Supplementary data are available at Bioinformatics online.

Abstract Motivation: With the increasing number of gene expression databases, the need for more powerful analysis and visualization tools is growing. Many techniques have successfully been applied to unravel latent similarities among genes and/or experiments. Most of the current systems for microarray data analysis use statistical methods, hierarchical clustering, self-organizing maps, support vector machines, or k-means clustering to organize genes or experiments into ‘meaningful’ groups. Without prior explicit bias almost all of these clustering methods applied to gene expression data not only produce different results, but may also produce clusters with little or no biological relevance. Of these methods, agglomerative hierarchical clustering has been the most widely applied, although many limitations have been identified. Results: Starting with a systematic comparison of the underlying theories behind clustering approaches, we have devised a technique that combines tree-structured vector quantization and partitive k-means clustering (BTSVQ). This hybrid technique has revealed clinically relevant clusters in three large publicly available data sets. In contrast to existing systems, our approach is less sensitive to data preprocessing and data normalization. In addition, the clustering results produced by the technique have strong similarities to those of self-organizing maps (SOMs). We discuss the advantages and the mathematical reasoning behind our approach. Availability: The BTSVQ system is implemented in Matlab R12 using the SOM toolbox for the visualization and preprocessing of the data http://www.cis.hut.fi/projects/somtoolbox/ BTSVQ is available for non-commercial use http://www.uhnres.utoronto.ca/ta3/BTSVQ Contact: [email protected] Keywords: microarray data clustering and visulization; self-organizing maps, partitive k-means clustering; lung cancer.