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In statistics and data mining, affinity propagation (AP) is a clustering algorithm based on the concept of "message passing" between data points. Unlike clustering algorithms such as k-means or k-medoids, AP does not require the number of clusters to be determined or estimated before running the algorithm. Like k-medoids, AP finds "exemplars", members of the input set that are representative of clusters.

Algorithm

Let x₁ through xₙ be a set of data points, with no assumptions made about their internal structure, and let s be a function that quantifies the similarity between any two points, that is s(xᵢ, xⱼ) > s(xᵢ, xₖ) iff xⱼ is more similar to xᵢ than xₖ.

The algorithm proceeds by alternating two message passing steps, to update two matrices:

• The "responsibility" matrix R has values r(i, k) that quantify how suited xₖ is to serve as the exemplar for xᵢ, relative to other candidate exemplars for xᵢ.
• The "availability" matrix A contains values a(i, k) represents how "appropriate" it would be for xᵢ to pick xₖ as its exemplar, taking into account other points' preference for xₖ as an exemplar.

Both matrices are initialized to all zeroes, and can be viewed as log-probability tables. The algorithm then performs the following updates iteratively:

• First, responsibility updates are sent around: $r(i,k)\leftarrow s(i,k)-{\max }_{k^{\prime }\ne k}\{a(i,k^{\prime })+s(i,k^{\prime })\}$
• Then, availability is updated per

$a(i,k)\leftarrow \min (0,r(k,k)+\sum _{i^{\prime }\in ̸\{i,k\}}\max (0,r(i^{\prime },k)))$ for $i\ne k$ and

$a(k,k)\leftarrow \sum _{i^{\prime }\ne k}\max (0,r(i^{\prime },k))$.

Applications

The inventors of affinity propagation showed it is better for certain computer vision and computational biology tasks, e.g. clustering of pictures of human faces and identifying regulated transcripts, than k-means, even when k-means was allowed many random restarts and initialized using PCA. Affinity propagation has been successfully used to solve problems in a wide range of areas, including vision, genomics, genetic networks, biology, circuit design, nuclear physics, biochemistry, nanotechnology, geology, anthropology, economics and financial modelling. In many applications it works better than other techniques, but it is not guaranteed to work better than other methods. For example, a study comparing AP and Markov clustering on protein interaction graph partitioning found Markov clustering to work better for that problem.

References

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