Cosine distance as vector distance function for k-means
I have a graph of N vertices where each vertex represents a place. Also I have vectors, one per user, each one of N coefficients where the coefficient's value is the duration in seconds spent at the corresponding place or 0 if that place was not visited. E.g. for the graph: the vector: v1 = {100, 50, 0 30, 0} would mean that we spent: 100secs at vertex 1 50secs at vertex 2 and 30secs at vertex 4 (vertices 3 & 5 where not visited, thus the 0s). I want to run a k-means clustering and I've chosen cosine_distance = 1 - cosine_similarity as the metric for the distances, where the formula for cosine