Vincenzo Carletti

Graph edit distance as a quadratic assignment problem

Definition of the equivalence between assignments and edit paths.Graph edit distance formulation as a quadratic assignment problem.New quadratic cost function for computing graph edit distance.Improvement of the accuracy of the approximation of graph edit distance.Approximation computable in reasonable time. The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in error-correcting graph matching. It is defined from an optimal sequence of edit operations (edit path) transforming one graph into another. Unfortunately, the exact computation of this measure is NP-hard. In the last decade, several approaches were proposed to approximate the GED in polynomial time, mainly by solving linear programming problems. Among them, the bipartite GED received much attention. It is deduced from a linear sum assignment of the nodes of the two graphs, which can be efficiently computed by Hungarian-type algorithms. However, edit operations on nodes and edges are not handled simultaneously, which limits the accuracy of the approximation. To overcome this limitation, we propose to extend the linear assignment model to a quadratic one. This is achieved through the definition of a family of edit paths induced by assignments between nodes. We formally show that the GED, restricted to the paths in this family, is equivalent to a quadratic assignment problem. Since this problem is NP-hard, we propose to compute an approximate solution by adapting two algorithms: Integer Projected Fixed Point method and Graduated Non Convexity and Concavity Procedure. Experiments show that the proposed approach is generally able to reach a more accurate approximation of the exact GED than the bipartite GED, with a computational cost that is still affordable for graphs of non trivial sizes.

Audio surveillance using a bag of aural words classifier

In this paper we propose a novel approach for the audio-based detection of events. The approach adopts the bag of words paradigm, and has two main advantages over other techniques present in the literature: the ability to automatically adapt (through a learning phase) to both short, impulsive sounds and long, sustained ones, and the ability to work in noisy environments where the sounds of interest are superimposed to background sounds possibly having similar characteristics. The proposed method has been experimentally validated on a large database of sounds, including several kinds of background noise, which are superimposed to the sounds to be recognized. The obtained performance has been compared with the results of another audio event detection algorithm from the literature, showing a significant improvement.

Approximate Graph Edit Distance Computation Combining Bipartite Matching and Exact Neighborhood Substructure Distance

Graph edit distance corresponds to a flexible graph dissimilarity measure. Unfortunately, its computation requires an exponential complexity according to the number of nodes of both graphs being compared. Some heuristics based on bipartite assignment algorithms have been proposed in order to approximate the graph edit distance. However, these heuristics lack of accuracy since they are based either on small patterns providing a too local information or walks whose tottering induce some bias in the edit distance calculus. In this work, we propose to extend previous heuristics by considering both less local and more accurate patterns using subgraphs defined around each node.

Recognition of Human Actions from RGB-D Videos Using a Reject Option

In this paper we propose a method for recognizing human actions by using depth images acquired through a Kinect sensor. The depth images are represented through the combination of three sets of well-known features, respectively based on Hu moments, depth variations and the

Performance Comparison of Five Exact Graph Matching Algorithms on Biological Databases

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Report on the First Contest on Graph Matching Algorithms for Pattern Search in Biological Databases

transform, an enhanced version of the Radon transform. A GMM classifier is adopted and finally a reject option is introduced in order to improve the overall reliability of the system. The proposed approach has been tested over two datasets, the Mivia and the MHAD, showing very promising results.

Introducing VF3: A new algorithm for subgraph isomorphism

Graphs are a powerful data structure that can be applied to several problems in bioinformatics. Graph matching, in its diverse forms, is an important operation on graphs, involved when there is the need to compare two graphs or to find substructures into larger structures. Many graph matching algorithms exist, and their relative efficiency depends on the kinds of graphs they are applied to. In this paper we will consider some popular and freely available matching algorithms, and will experimentally compare them on graphs derived from bioinformatics applications, in order to help the researchers in this field to choose the right tool for the problem at hand.

Challenging the Time Complexity of Exact Subgraph Isomorphism for Huge and Dense Graphs with VF3

Graphs are a powerful data structure that can be applied to several problems in bioinformatics, and efficient graph matching is often a tool required for several applications that try to extract useful information from large databases of graphs. While graph matching is in general a NP-complete problem, several algorithms exist that can be fast enough on practical graphs. However, there is no single algorithm that is able to outperform the others on every kind of graphs, and so it is of paramount importance to assess the algorithms on graphs coming from the actual problem domain. To this aim, we have organized the first edition of the Contest on Graph Matching Algorithms for Pattern Search in Biological Databases, hosted by the ICPR2014 Conference, so as to provide an opportunity for comparing state-of-the-art matching algorithms on a new graph database built using several kinds of real-world graphs found in bioinformatics applications. The participating algorithms were evaluated with respect to both their computation time and their memory usage. This paper will describe the contest task and databases, will provide a brief outline of the participating algorithms, and will present the results of the contest.

Automatic detection of long term parked cars

Several graph-based applications require to detect and locate occurrences of a pattern graph within a larger target graph. Subgraph isomorphism is a widely adopted formalization of this problem. While subgraph isomorphism is NP-Complete in the general case, there are algorithms that can solve it in a reasonable time on the average graphs that are encountered in specific real-world applications. In 2015 we introduced one such algorithm, VF2Plus, that was specifically designed for the large graphs encountered in bioinformatics applications. VF2Plus was an evolution of VF2, which had been considered for many years one of the fastest available algorithms. In turn, VF2Plus proved to be significantly faster than its predecessor, and among the fastest algorithms on bioinformatics graphs. In this paper we propose a further evolution, named VF3, that adds new improvements specifically targeted at enhancing the performance on graphs that are at the same time large and dense, that are currently the most problematic case for the state-of-the-art algorithms. The effectiveness of VF3 has been experimentally validated using several publicly available datasets, showing a significant speedup with respect to its predecessor and to the other most advanced state-of-the-art algorithms.

VF2 Plus: An Improved version of VF2 for Biological Graphs

Graph matching is essential in several fields that use structured information, such as biology, chemistry, social networks, knowledge management, document analysis and others. Except for special classes of graphs, graph matching has in the worst-case an exponential complexity; however, there are algorithms that show an acceptable execution time, as long as the graphs are not too large and not too dense. In this paper we introduce a novel subgraph isomorphism algorithm, VF3, particularly efficient in the challenging case of graphs with thousands of nodes and a high edge density. Its performance, both in terms of time and memory, has been assessed on a large dataset of 12,700 random graphs with a size up to 10,000 nodes, made publicly available. VF3 has been compared with four other state-of-the-art algorithms, and the huge experimentation required more than two years of processing time. The results confirm that VF3 definitely outperforms the other algorithms when the graphs become huge and dense, but also has a very good performance on smaller or sparser graphs.