Characterizing graph symmetries through quantum Jensen-Shannon divergence

In this paper we investigate the connection between quantum walks and graph symmetries. We begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse. To achieve this, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the quantum Jensen-Shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries. Hence, we assign to each pair of nodes of the graph a value of the divergence, and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph. © 2013 American Physical Society.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

A stable graph-based representation for object recognition through high-order matching

Many Object recognition techniques perform some flavour of point pattern matching between a model and a scene. Such points are usually selected through a feature detection algorithm that is robust to a class of image transformations and a suitable descriptor is computed over them in order to get a reliable matching. Moreover, some approaches take an additional step by casting the correspondence problem into a matching between graphs defined over feature points. The motivation is that the relational model would add more discriminative power, however the overall effectiveness strongly depends on the ability to build a graph that is stable with respect to both changes in the object appearance and spatial distribution of interest points. In fact, widely used graph-based representations, have shown to suffer some limitations, especially with respect to changes in the Euclidean organization of the feature points. In this paper we introduce a technique to build relational structures over corner points that does not depend on the spatial distribution of the features. © 2012 ICPR Org Committee.

Supervised learning of graph structure

Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. In this paper we take a simple yet effective Bayesian approach to attributed graph learning. We present a naïve node-observation model, where we make the important assumption that the observation of each node and each edge is independent of the others, then we propose an EM-like approach to learn a mixture of these models and a Minimum Message Length criterion for components selection. Moreover, in order to avoid the bias that could arise with a single estimation of the node correspondences, we decide to estimate the sampling probability over all the possible matches. Finally we show the utility of the proposed approach on popular computer vision tasks such as 2D and 3D shape recognition. © 2011 Springer-Verlag.

Using knowledge management to give context to analytics and big data and reduce strategic risk

At the moment, the phrases “big data” and “analytics” are often being used as if they were magic incantations that will solve all an organization’s problems at a stroke. The reality is that data on its own, even with the application of analytics, will not solve any problems. The resources that analytics and big data can consume represent a significant strategic risk if applied ineffectively. Any analysis of data needs to be guided, and to lead to action. So while analytics may lead to knowledge and intelligence (in the military sense of that term), it also needs the input of knowledge and intelligence (in the human sense of that term). And somebody then has to do something new or different as a result of the new insights, or it won’t have been done to any purpose. Using an analytics example concerning accounts payable in the public sector in Canada, this paper reviews thinking from the domains of analytics, risk management and knowledge management, to show some of the pitfalls, and to present a holistic picture of how knowledge management might help tackle the challenges of big data and analytics.

Integration of a graph-based model indexer in commercial modelling tools

Softeam has over 20 years of experience providing UML-based modelling solutions, such as its Modelio modelling tool, and its Constellation enterprise model management and collaboration environment. Due to the increasing number and size of the models used by Softeam’s clients, Softeam joined the MONDO FP7 EU research project, which worked on solutions for these scalability challenges and produced the Hawk model indexer among other results. This paper presents the technical details and several case studies on the integration of Hawk into Softeam’s toolset. The first case study measured the performance of Hawk’s Modelio support using varying amounts of memory for the Neo4j backend. In another case study, Hawk was integrated into Constellation to provide scalable global querying of model repositories. Finally, the combination of Hawk and the Epsilon Generation Language was compared against Modelio for document generation: for the largest model, Hawk was two orders of magnitude faster.