Scaling Analysis of the Affinity Propagation Algorithm
Abstract
We analyze and exploit some scaling properties of the Affinity Propagation (AP) clustering algorithm proposed by Frey and Dueck (2007). First we observe that a divide and conquer strategy, used on a large data set hierarchically reduces the complexity O(N^2) to O(N^{(h+2)/(h+1)}), for a data-set of size N and a depth h of the hierarchical strategy. For a data-set embedded in a d-dimensional space, we show that this is obtained without notably damaging the precision except in dimension d=2. In fact, for d larger than 2 the relative loss in precision scales like N^{(2-d)/(h+1)d}. Finally, under some conditions we observe that there is a value s* of the penalty coefficient, a free parameter used to fix the number of clusters, which separate a fragmentation phase (for ss*) of the underlying hidden cluster structure. At this precise point holds a self-similarity property which can be exploited by the hierarchical strategy to actually locate its position. From this observation, a strategy based on AP can be defined to find out how many cluster are present in a given dataset.
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