Sample Size Evaluation and Comparison of K-Means Clusterings of RNA-Seq Gene Expression Data

The process by which DNA is transformed into gene products, such as RNA and proteins, is called gene expression. Gene expression profiling quantifies the expression of genes (amount of RNA) in a particular tissue at a particular time. Two commonly used high-throughput techniques for gene expression analysis are DNA microarrays and RNA-Seq, with RNA-Seq being the newer technique based on high-throughput sequencing. Statistical analysis is needed to deal with complex datasets — one commonly used statistical tool is clustering. Clustering comparison is an existing area dedicated to comparing multiple clusterings from one or more clustering algorithms. However, there has been limited application of cluster comparisons to clusterings of RNA-Seq gene expression data. In particular, cluster comparisons are useful in order to test the differences between clusterings obtained using a single algorithm when using different samples for clustering. Here we use a metric for cluster comparisons that is a variation of existing metrics. The metric is simply the minimal number of genes that need to be moved from one cluster to another in one given clustering to produce another given clustering. As the metric only has genes (or elements) as units, it is easy to interpret for RNA-Seq analysis. Moreover, three different algorithmic techniques — brute force, branch-and-bound, and maximal bipartite matching — for computing the proposed metric exactly are compared in terms of time to compute, with bipartite matching being significantly more time efficient. This metric is then applied to the important issue of understanding the effect of increasing the number of RNA-Seq samples to clusterings. Three datasets were used where a large number of samples were available: mouse embryonic stem cell tissue data, Drosophila melanogaster data from multiple tissues and micro-climates, and a mouse multi-tissue dataset. For each, a reference clustering was computed from all of the samples, and then it was compared to clusterings created from smaller subsets of the samples. All clusterings were created using a standard heuristic K-means clustering algorithm, while also systematically varying the numbers of clusters, and also using both Euclidean distance and Manhattan distance. The clustering comparisons suggest that for the three large datasets tested, there seems to be a limited impact of adding more RNA-Seq samples on K-means clusterings using both Euclidean distance and Manhattan distance (Manhattan distance gives a higher variation) beyond some small number of samples. That is, the clusterings compiled based on a limited number of samples were all either quite similar to the reference clustering or did not improve as additional samples were added. These findings were the same for different numbers of clusters. The methods developed could also be applied to other clustering comparison problems