#Jaccard coefficient xlstat series#

The fact that the vertices being compared appear in the associative set prevents the sets from ever matching. Likewise, vertex 2 appears in vertex 1’s neighbor. Rephrasing that statement, vertex 1 appears in vertex 2’s neighbor set. The issue is that the vertex pairs being compared are reflected in the neighborhood sets. While those similarity scores are mathematically correct according to the algorithm, the resulting similarity score do not match what I would except for a clique. Looking at the Jaccard similarity score between connected vertices A and B, the neighbors of A are. This was a limitation of the initial cuGraph Jaccard implementation and what has been addressed in cuGraph release 0.7. Therefore, being able to compute similarity scores between any pair of vertices is important. The problem with the previous approach is that not all recommendations can come from solely looking at directly connected vertex pairs. But for satellites it is easy to just recommend all connections from their sole neighbor. Note that this approach does not work for vertices with a single connection, also called a satellite, since their similarity score will be zero. The application of triadic closure and similarity should be apparent to anyone that uses social media since those tools remind you constantly that you should connect to a friend of friends. As mentioned, this is a very simple view since there is a range of options for applying additional weights, like only looking within community clusters, that could be added to better select recommendations that will be accepted. Then for a given vertex (example, vertex A) find their neighbors with the highest similar score and recommend neighbors of B that are missing from A. Now back to the application: the basic process starts by first computing the similarity metric (Jaccard or Overlap Coefficient) for all vertex pairs connected by an edge. For our recommendation application, this means that we need to find those unconnected A - B pairs since there is a high change that those users will become friends - it is always good to recommend something that the user will accept. That probability is so high that Granovetter, in his 1973 work on weak-ties, deemed the missing link as the “forbidden triad”, which meant that for Granovetter’s application that you could infer a connection between A and B. Given three people, A, B, and C, see Figure 1 if A and C are friends (connected), and B and C are friends, then there is a high probability that A and B will connect. Within the field of social network analysis, there is the concept of Triadic Closure, which was first introduced by sociologists Georg Simmel in 1908. the number of common elements) over the size of the union of set A and set B (i.e. Given two sets, A and B, the Jaccard Similarity is defined as the size of the intersection of set A and set B (i.e. The Jaccard Similarity, also called the Jaccard Index or Jaccard Similarity Coefficient, is a classic measure of similarity between two sets that was introduced by Paul Jaccard in 1901. Let’s start with a quick introduction to the similarity metrics (warning math ahead). Those two algorithms fall into the category of similarity metrics and lead to the topic of this blog, which is to discuss the difference between the two algorithms and why I think one is better than the other. Of interest to this discussion is the expansion of the Jaccard Similarity metric to allow for comparisons of any pair of vertices, and the addition of the Overlap Coefficient algorithm. The RAPIDS cuGraph 0.7 release adds several new features.

It should also be noted that I approach graph analysis from a social network perspective and tend to use the social science theory and terms, but I have been trying to use ‘vertex’ rather than ‘node’. If there is interest in a graph analytic primer, please leave me a comment below. I am assuming that the reader has a basic understanding of graph theory and graph analytics.

#Jaccard coefficient xlstat series#

There are a wide range of graph applications and algorithms that I hope to discuss through this series of blog posts, all with a bias toward what is in RAPIDS cuGraph.