The graph alignment problem calls for finding a matching between the nodes of one graph and those of another graph, in a way that they correspond to each other by some fitness measure. Over the last years, several graph alignment algorithms have been proposed and evaluated on diverse datasets and quality measures. Typically, a newly proposed algorithm is compared to previously proposed ones on some specific datasets, types of noise, and quality measures where the new proposal achieves superiority over the previous ones. However, no systematic comparison of the proposed algorithms has been attempted on the same benchmarks. This paper fills this gap by conducting an extensive, thorough, and commensurable evaluation of state-ofthe- art graph alignment algorithms. Our results highlight the value of overlooked solutions and an unprecedented effect of graph density on performance, hence call for further work.

What is the best way to match the nodes of two graphs? This graph alignment problem generalizes graph isomorphism and arises in applications from social network analysis to bioinformatics. Some solutions assume that auxiliary information on known matches or node or edge attributes is available, or utilize arbitrary graph features. Such methods fare poorly in the pure form of the problem, in which only graph structures are given. Other proposals translate the problem to one of aligning node embeddings, yet, by doing so, provide only a single-scale view of the graph. In this article, we transfer the shape-analysis concept of functional maps from the continuous to the discrete case, and treat the graph alignment problem as a special case of the problem of finding a mapping between functions on graphs. We present GRASP, a method that first establishes a correspondence between functions derived from Laplacian matrix eigenvectors, which capture multiscale structural characteristics, and then exploits this correspondence to align nodes. We enhance the basic form of GRASP by altering two of its components, namely the embedding method and the assignment procedure it employs, leveraging its modular, hence adaptable design. Our experimental study, featuring noise levels higher than anything used in previous studies, shows that the enhanced form of GRASP outperforms scalable state-of-the-art methods for graph alignment across noise levels and graph types, and performs competitively with respect to the best non-scalable ones. We include in our study another modular graph alignment algorithm, CONE, which is also adaptable thanks to its modular nature, and show it can manage graphs with skewed power-law degree distributions.

The problem of graph alignment is to find corresponding nodes between a pair of graphs. Past work has treated the problem in a monolithic fashion, with the graph as input and the alignment as output, offering limited opportunities to adapt the algorithm to task requirements or input graph characteristics. Recently, node embedding techniques are utilized for graph alignment. In this paper, we study two state-of-the-art graph alignment algorithms utilizing node representations, CONE-Align and GRASP, and describe them in terms of an overarching modular framework. In a targeted experimental study, we exploit this modularity to develop enhanced algorithm variants that are more effective in the alignment task.

With the continuous rise of multimedia, the question of how to access large-scale multimedia databases efficiently has become of crucial importance. Given a multimedia database comprising millions of multimedia objects, how to approximate the content-based properties of the corresponding feature representations in order to carry out similarity search efficiently and with high accuracy? In this paper, we propose the concept of gradient-based signatures in order to aggregate content-based features of multimedia objects by means of generative models. We provide theoretical insights into our approach including closed-form expressions for the computation of gradient-based signatures with respect to Gaussian mixture models and additionally investigate different binarization methods for gradient-based signatures in order to query databases comprising millions of multimedia objects with high accuracy in less than one second.