I have a file that can be considered as a matrix with each row representing a measurement of gene expression of different samples (each column is a sample). I want to find those genes with the most interesting patterns of expression across samples. That means that several samples have a similar expression range, another few samples have another range or expression. Basically I'm looking for variability among expression values but I hope to find not just random variation but meaningful patterns that can be used to separate my samples into biologically meaningful groups.
I came up with this naive idea of using standard deviation at each row/gene and find those with highest standard deviation. But this doesn't seem to be a good method at all.
I also thought about taking the 75th and 25th quantile value and do a simple subtraction and report those with the highest difference, maybe top 20% of genes.
I'm struggling with a statistically meaningful method to do this. I kind of feel this problem can be found in different context and there might be some tools/methods made to address it. Does anyone here have a suggestion or comment on the methods I mentioned?