Growing a graph matching from a handful of seeds

Abstract

Is it possible to use only the graph structures to establish the true matching between the nodes? Percolation Graph MatchingPercolation graph matching (PGM) algorithms start from an initial seed set and iteratively match pairs with at least r neighbouring seed-pairsDark green nodes are initial seeds Light green nodes are the new matched pairs after the first three iterations Question: Size of the final matching vs. size of the initial seed set? Model and Performance GuaranteeUsing the theory of bootstrap percolation [Janson et al, 2010] Bi(G; t, s): a random bigraph model to generate two correlated graphs with overlapping vertex sets [Pedarsani and Grossglauser, 2011; Kazemi et al., 2015] Bi( ; t, s)Edge samplingTheorem: For Bi(G(n, p); t, s) with fixed s and t, there exists a threshold a t,s,r for size of the correct pairs in the initial seed set such that:1. if a/a t,s,r < 1, the percolation process dies young 2. if a/a t,s,r ≥ 1 + , the percolation process matches almost all the nodes correctly Aggressive Percolation Graph MatchingState-of-the-art PGM algorithms needs many seeds Finding many seeds is difficult and expensive: how to grow a graph matching with a handful of seeds?Addition of many wrong pairs to the initial seed set have a negligible effect on the performance of PGM:Expand the initial seed set to a larger noisy set In the new noisy seed pairs there are more correct pairs ExpandWhenStuckExpand the candidate pairs by many noisy pairs whenever the percolation process stuck

PROPER: global protein interaction network alignment through percolation matching

“…In this regard, one main category of network alignment algorithms, known as percolation graph matching (PGM), assumes that there is side information in the form of a seed set of pre-matched node couples. In this class of algorithms, the alignment starts with a small set of initial seed couples and percolates to other node couples, i.e., they build the alignment incrementally between nodes of the two networks [45, 48, 53–55]. …”

“…We use the ideas from PGM algorithms (mainly [45]) to design our PROPER ( PRO tein-protein interaction network alignment based on PER colatin) algorithm.…”

“…We argue the suitability of our algorithm by analyzing its performance in a bigraph-sampling model of network evolution [42–44]. For this random-bigraph model, we use the results of [43, 45] to guarantee the performance of our algorithm.…”

When can two unlabeled networks be aligned under partial overlap?

“…When merging graph data, one remedy is to rely on structural information rather than on explicit vertex labels or vertex features to match two (or several) graphs. This network reconciliation problem has received significant attention recently: Social networks can be aligned by structural information [3], [4], [10], [13], [17], [19], [21], [26], with applications in network deanonymization [11], [12], [18], [20], [25]; protein-interaction network matching allows us to find proteins with common functions in different species [14], [15], [22]; graph matching has many applications in pattern recognition and machine vision [5], e.g., finding similar images in a database by matching segment-adjacency graphs [7], [16], [24].…”

A Literature Survey and Classifications on Data Deanonymisation

“…This study used auxiliary information from the same target domain, crawling Flickr, but generating an evolved version. Also these studies [31,32,[37][38][39] used seeding based deanonymisation techniques. Another study [39] presents a new graph matching algorithm that relies on smaller seeds than other methods.…”