A graph distance metric based on the maximal common subgraph

Bunke, Horst; Shearer, Kim

doi:10.1016/s0167-8655(97)00179-7

Cited by 615 publications

(390 citation statements)

References 20 publications

Supporting

Mentioning

382

Contrasting

Unclassified

Order By: Relevance

“…known models stored in a database, transforming a difficult recognition problem into a more tractable graph matching problem [2]. The broad literature available on graph distance metrics has been successfully transitioned to areas as diverse as text data mining [4] and detection of change in computer networks [5,6,19].…”

Section: C452mentioning

confidence: 99%

“…The graph distances between sequential graphs are calculated using ten commonly used graph distance metrics: weight [19], Maximum Common Subgraph weight, mcs vertex, mcs edge [19,6], edit [2], median edit [5], spectral, modality [13], diameter [8] and entropy distances. This radically reduces the amount of information that needs to be stored, as only the number representing the distance from the last graph to the present one and the graphs needed to calculate the next graph distance need be retained.…”

Section: C452mentioning

confidence: 99%

See 1 more Smart Citation

Detecting changes in time series of network graphs using minimum mean squared error and cumulative summation

Pincombe¹

2007

ANZIAMJ

View full text Add to dashboard Cite

Through characterising a computer network as a time series of graphs, with ip addresses on the vertices and edges weighted by the number of packets transmitted, we apply graph distance metrics to arrive at a measure of the distance between the network at different times. Two computationally simple methods of detecting change points in a one dimensional time series of this distance data are proposed. These techniques are cumulative summation and minimum mean squared error. This offers a very space efficient method of detecting change points as only the time series of graph distances and the network graph for the last time slice need be kept. The two techniques are compared on a dataset containing 102 consecutive working days See

show abstract

Section: C452mentioning

confidence: 99%

Section: C452mentioning

confidence: 99%

Detecting changes in time series of network graphs using minimum mean squared error and cumulative summation

Pincombe¹

2007

ANZIAMJ

View full text Add to dashboard Cite

show abstract

“…There exist several similarity measures for general graphs in the literature [7][8][9]. All of them either suffer from a high computational complexity or are limited to special graph types.…”

Section: Structural Similaritymentioning

confidence: 99%

Efficient Similarity Search for Hierarchical Data in Large Databases

Kailing

Kriegel

Schönauer

et al. 2004

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. Structured and semi-structured object representations are getting more and more important for modern database applications. Examples for such data are hierarchical structures including chemical compounds, XML data or image data. As a key feature, database systems have to support the search for similar objects where it is important to take into account both the structure and the content features of the objects. A successful approach is to use the edit distance for tree structured data. As the computation of this measure is NP-complete, constrained edit distances have been successfully applied to trees. While yielding good results, they are still computationally complex and, therefore, of limited benefit for searching in large databases. In this paper, we propose a filter and refinement architecture to overcome this problem. We present a set of new filter methods for structural and for content-based information in tree-structured data as well as ways to flexibly combine different filter criteria. The efficiency of our methods, resulting from the good selectivity of the filters is demonstrated in extensive experiments with real-world applications.

show abstract

“…Grewenig, Zimmer and Weickert [31] studied the rotationally invariant similarity measures for non-local image denoising. Besides these studies, many other similarity measuring approaches are proposed in references [32][33][34][35][36][37][38][39], in this paper's.Taking the relational information of directly-linked patterns and indirectly-linked patterns into account, here we propose a random walk-based similarity measure method for patterns in complex object. Here, the "random walk" refers to the linking route between any two patterns, and the "complex object" refers to the data that it contains not only the attribute information of patterns but also the relational information between patterns.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Random walk-based similarity measure method for patterns in complex object

Liu

Chen

2017

Open Physics

View full text Add to dashboard Cite

This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the speci city of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can nd that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated. Introductory comments and Problem statementSimilarity measurement, as a tool to determine the similar between two patterns, is given special attention from its wide application in many elds, such as pattern recog [24]. Besides these, many similarity measure methods are applied, such as the cosine method, correlation coe cient method and the max-min method, amongst others.No matter which representation the data has or what similarity measurement method is used, all the data are vector-based attribute information, to some extent. But, in practical problem solving, this is not enough. For example, if we want to detect the community structure, the research should be aimed at network data [25]. Therefore, the data takes not only the attribute information of patterns but also the relational information between patterns.In view of the similarity problem of such data, a lot of studies have been done. For example, Rossi et al. [26] proposed a quantum algorithm to measure the similarity between a pair of unattributed graphs, and in which the theory of quantum Jensen-Shannon divergence constitutes the basis of theoretical analysis. Moreover, Rossi et al. [27] discussed the similarity between attributed graphs by means of the evolution of a continuous-time quantum walk. In [28], Cason et al. computed the low approximation of the graph similarity matrix. Brandes and Lerner [29] introduced the concept of structural similarity by relaxation of equitable partitions. Kpodjedo et al.[30] investigated heuristics for approximate graph matching. Maggini et al. [2] presented a neural networks model that could be used to learn a similarity measure for pairs of patterns. Grewenig, Zimmer and Weickert [31] studied the rotationally invariant similarity measures for non-local image denoising. Besides these studies, many other similarity measuring approaches are proposed in references [32][33][34][35][36][37][38][39], in this paper's.Taking the relational information of directly-linked patterns and indirectly-linked patterns into account, here we propose a random walk-based similarity measure method for patterns in complex object. Here, the "random walk" refers to ...

show abstract

A graph distance metric based on the maximal common subgraph

Cited by 615 publications

References 20 publications

Detecting changes in time series of network graphs using minimum mean squared error and cumulative summation

Detecting changes in time series of network graphs using minimum mean squared error and cumulative summation

Efficient Similarity Search for Hierarchical Data in Large Databases

Random walk-based similarity measure method for patterns in complex object

Contact Info

Product

Resources

About