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.

k近邻分类器已广泛用于对模式识别中的图进行分类。通过将未知图与训练集中的所有图进行比较，然后为该图分配最接近的邻居中的大多数所属于的类别，可以对未知图进行分类。当数据库的大小很大时，搜索k最近邻居可能会非常耗时。在此基础上，研究人员提出了优化技术，以加快对最近邻居的搜索。但是，据我们所知，所有现有作品都分别将未知图形与每个火车图形进行了比较，因此没有人考虑找到k查询中最接近的图形作为一个问题。在本文中，我们定义了一个新问题，称为多图编辑距离，它是k最近邻居所属的。作为解决此问题的第一个算法，我们利用了最近的精确分支和界图编辑距离方法，以加快分类阶段。我们通过考虑未知和训练图之间的差异计算所需的所有搜索空间作为单个搜索空间来扩展该算法。结果表明，在有限的时间限制下，该方法大大优于原始方法。此外，在平均执行时间方面，该方法优于快速图形编辑距离算法，尤其是在图形数量巨大时。