  Subject clustering (i.e., the use of measured features to cluster subjects,
such as patients or cells, into multiple groups) is a problem of great
interest. In recent years, many approaches were proposed, among which
unsupervised deep learning (UDL) has received a great deal of attention. Two
interesting questions are (a) how to combine the strengths of UDL and other
approaches, and (b) how these approaches compare to one other.
  We combine Variational Auto-Encoder (VAE), a popular UDL approach, with the
recent idea of Influential Feature PCA (IF-PCA), and propose IF-VAE as a new
method for subject clustering. We study IF-VAE and compare it with several
other methods (including IF-PCA, VAE, Seurat, and SC3) on $10$ gene microarray
data sets and $8$ single-cell RNA-seq data sets. We find that IF-VAE
significantly improves over VAE, but still underperforms IF-PCA. We also find
that IF-PCA is quite competitive, which slightly outperforms Seurat and SC3
over the $8$ single-cell data sets. IF-PCA is conceptually simple and permits
delicate analysis. We demonstrate that IF-PCA is capable of achieving the phase
transition in a Rare/Weak model. Comparatively, Seurat and SC3 are more complex
and theoretically difficult to analyze (for these reasons, their optimality
remains unclear).
