Supervised Learning of Graph Structure

Torsello, Andrea; Rossi, Luca

doi:10.1007/978-3-642-24471-1_9

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…To these four datasets, we add a fifth set of 30 synthetically generated graphs, 10 for each class. The graphs belonging to each class were sampled from a generative model with size 12,14 and 16 respectively [19].…”

Section: Resultsmentioning

confidence: 99%

Manifold Learning and the Quantum Jensen-Shannon Divergence Kernel

Rossi

Torsello

Hancock

2013

Computer Analysis of Images and Patterns

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The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach.

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Section: Resultsmentioning

confidence: 99%

Manifold Learning and the Quantum Jensen-Shannon Divergence Kernel

Rossi

Torsello

Hancock

2013

Computer Analysis of Images and Patterns

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“…Here a generative model consists of a graph where each node and edge is labelled with the probability of observing that node and edge, respectively. Details concerning the generative model can be found in 44 .…”

Section: Shockmentioning

confidence: 99%

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

2015

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In this paper we propose a quantum algorithm to measure the similarity between a pair of unattributed graphs. We design an experiment where the two graphs are merged by establishing a complete set of connections between their nodes and the resulting structure is probed through the evolution of continuous-time quantum walks. In order to analyze the behavior of the walks without causing wave function collapse, we base our analysis on the recently introduced quantum Jensen-Shannon divergence. In particular, we show that the divergence between the evolution of two suitably initialized quantum walks over this structure is maximum when the original pair of graphs is isomorphic. We also prove that under special conditions the divergence is minimum when the sets of eigenvalues of the Hamiltonians associated with the two original graphs have an empty intersection.

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“…Given the prototypes, we sampled 20 observations from each class being careful to discard graphs that were disconnected. Details about the generative model used to sample the graphs can be found in [19]. Figure 2 shows the edit distance matrix of the dataset and the Multidimensional Scaling [20] of the graph distances.…”

Section: Synthetic Datamentioning

confidence: 99%

Attributed Graph Similarity from the Quantum Jensen-Shannon Divergence

Rossi

Torsello

Hancock

2013

Similarity-Based Pattern Recognition

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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.

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Supervised Learning of Graph Structure

Cited by 7 publications

References 19 publications

Manifold Learning and the Quantum Jensen-Shannon Divergence Kernel

Manifold Learning and the Quantum Jensen-Shannon Divergence Kernel

Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence

Attributed Graph Similarity from the Quantum Jensen-Shannon Divergence

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