I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from University of California. The idea is to use the notion of Total Correlation based on the entropy measures. It is appealing due to its simplicity and no tuning of large number of hyperparameters.

The paper about hierarchical representations (the most recent, builds on the top of the previous measures). http://arxiv.org/pdf/1410.7404.pdf

I would like to suggest you a relatively recent technique for automatic structure extraction from categorical variable data (this includes binary). The method is called CorEx from Greg van Steeg from University of Southern California. The idea is to use the notion of Total Correlation based on the entropy measures. It is appealing due to its simplicity and no tuning of large number of hyperparameters.

The paper about hierarchical representations (the most recent, builds on the top of the previous measures). http://arxiv.org/pdf/1410.7404.pdf