I tried to cluster my data using spectral clustering algorithm. Before applying clustering algorithm, I used PCA on the data, which gave me 4 PC accounting for 95% of variation. After that I plotted eigenvalues for the clusters for two datasets (as I need to analyse them separately). From the plots it's not so obvious that 4 clusters is the right choice (index is a number of clusters). What would be your recommendation for choosing the number of clusters? Also, what is the best approach in choosing number of neighbors considered?Thank you.
You said you're doing spectral clustering. This means you're constructing a similarity matrix, a graph Laplacean, etc. If you don't see the sharp drop in eigenvalues at 4, then maybe you should alter the parameters of your similarity matrix (i.e. if it's a Gassian kernel, alter the bandwidth; if it's KNN, alter the k, etc).