For Boolean (i.e., categorical with two classes) features, a good alternative to using PCA consists in using Multiple Correspondence Analysis (MCA), which is simply the extension of PCA to categorical variables (see related thread). For some background about MCA, the papers are Husson et al. (2010), or Abdi and Valentin (2007). An excellent R package to perform MCA is FactoMineR. It provides you with tools to plot two-dimensional maps of the loadings of the observations on the principal components, which is very insightful.
Below are two map examples from one of my past research projects (plotted with ggplot2). I had only about 60 observations and it gave good results. The first map represents the observations in the space PC1-PC2, the second map in the space PC3-PC4... The variables are also represented in the map, which helps with interpreting the meaning of the dimensions. Collecting the insight from several of these maps can give you a pretty nice picture of what's happening in your data.
On the website linked above, you will also find information about a novel procedure, HCPC, which stands for Hierarchical Clustering on Principal Components, and which might be of interest to you. Basically, this method works as follows:
- perform a MCA,
- retain the first $k$ dimensions (where $k<p$, with $p$ your original number of features). This step is useful in that it removes some noise, and hence allows a more stable clustering,
- perform an agglomerative (bottom-up) hierarchical clustering in the space of the retained PCs. Since you use the coordinates of the projections of the observations in the PC space (real numbers), you can use the Euclidean distance, with Ward's criterion for the linkage (minimum increase in within-cluster variance). You can cut the dendogram at the height you like or let the R function cut if or you based on some heuristic,
- (optional) stabilize the clusters by performing a K-means clustering. The initial configuration is given by the centers of the clusters found at the previous step.
Then, you have lots of ways to investigate the clusters (most representative features, most representative individuals, etc.)