Efficient k-nearest neighbors search in graph space

The k-nearest neighbors classifier has been widely used to classify graphs in pattern recognition. An unknown graph is classified by comparing it to all the graphs in the training set and then assigning it the class to which the majority of the nearest neighbors belong. When the size of the database is large, the search of k-nearest neighbors can be very time consuming. On this basis, researchers proposed optimization techniques to speed up the search for the nearest neighbors. However, to the best of our knowledge, all the existing works compared the unknown graph to each train graph separately and thus none of them considered finding the k nearest graphs from a query as a single problem. In this paper, we define a new problem called multi graph edit distance to which k-nearest neighbor belongs. As a first algorithm to solve this problem, we take advantage of a recent exact branch-and-bound graph edit distance approach in order to speed up the classification stage. We extend this algorithm by considering all the search spaces needed for the dissimilarity computation between the unknown and the training graphs as a single search space. Results showed that this approach drastically outperformed the original approach under limited time constraints. Moreover, the proposed approach outperformed fast graph edit distance algorithms in terms of average execution time especially when the number of graphs is tremendous. (C) 2018 Published by Elsevier B.V.