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Graph (abstract data type)

About: Graph (abstract data type) is a(n) research topic. Over the lifetime, 69988 publication(s) have been published within this topic receiving 1218314 citation(s). The topic is also known as: graph.

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Papers
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Open accessJournal ArticleDOI: 10.1109/34.868688
Jianbo Shi1, Jitendra Malik2Institutions (2)
Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.

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  • Fig. 1. A case where minimum cut gives a bad partition.
    Fig. 1. A case where minimum cut gives a bad partition.
  • Fig. 2. A gray level image of a baseball game.
    Fig. 2. A gray level image of a baseball game.
  • Fig. 3. Subplot (a) plots the smallest eigenvectors of the generalized eigenvalue system (11). Subplots (b)-(i) show the eigenvectors corresponding the second smallest to the ninth smallest eigenvalues of the system. The eigenvectors are reshaped to be the size of the image.
    Fig. 3. Subplot (a) plots the smallest eigenvectors of the generalized eigenvalue system (11). Subplots (b)-(i) show the eigenvectors corresponding the second smallest to the ninth smallest eigenvalues of the system. The eigenvectors are reshaped to be the size of the image.
  • Fig. 4. (a) shows the original image of size 80 100. Image intensity is normalized to lie within 0 and 1. Subplots (b)-(h) show the components of the partition with Ncut value less than 0.04. Parameter setting: I 0:1, X 4:0, r 5.
    Fig. 4. (a) shows the original image of size 80 100. Image intensity is normalized to lie within 0 and 1. Subplots (b)-(h) show the components of the partition with Ncut value less than 0.04. Parameter setting: I 0:1, X 4:0, r 5.
  • Fig. 5. (a) Point set generated by two Poisson processes, with densities of 2.5 and 1.0 on the left and right clusters respectively, (b)4 and indicate the partition of point set in (a). Parameter settings: X 5, r 3.
    Fig. 5. (a) Point set generated by two Poisson processes, with densities of 2.5 and 1.0 on the left and right clusters respectively, (b)4 and indicate the partition of point set in (a). Parameter settings: X 5, r 3.
  • + 13

13,025 Citations


Open accessJournal ArticleDOI: 10.1088/1742-5468/2008/10/P10008
Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

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Topics: Modularity (networks) (67%), Clique percolation method (62%), Girvan–Newman algorithm (57%) ...read more

11,078 Citations


Open accessProceedings ArticleDOI: 10.1109/CVPR.1997.609407
Jianbo Shi1, Jitendra Malik1Institutions (1)
17 Jun 1997-
Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

...read more

  • Fig. 1. A case where minimum cut gives a bad partition.
    Fig. 1. A case where minimum cut gives a bad partition.
  • Fig. 2. A gray level image of a baseball game.
    Fig. 2. A gray level image of a baseball game.
  • Fig. 3. Subplot (a) plots the smallest eigenvectors of the generalized eigenvalue system (11). Subplots (b)-(i) show the eigenvectors corresponding the second smallest to the ninth smallest eigenvalues of the system. The eigenvectors are reshaped to be the size of the image.
    Fig. 3. Subplot (a) plots the smallest eigenvectors of the generalized eigenvalue system (11). Subplots (b)-(i) show the eigenvectors corresponding the second smallest to the ninth smallest eigenvalues of the system. The eigenvectors are reshaped to be the size of the image.
  • Fig. 4. (a) shows the original image of size 80 100. Image intensity is normalized to lie within 0 and 1. Subplots (b)-(h) show the components of the partition with Ncut value less than 0.04. Parameter setting: I 0:1, X 4:0, r 5.
    Fig. 4. (a) shows the original image of size 80 100. Image intensity is normalized to lie within 0 and 1. Subplots (b)-(h) show the components of the partition with Ncut value less than 0.04. Parameter setting: I 0:1, X 4:0, r 5.
  • Fig. 5. (a) Point set generated by two Poisson processes, with densities of 2.5 and 1.0 on the left and right clusters respectively, (b)4 and indicate the partition of point set in (a). Parameter settings: X 5, r 3.
    Fig. 5. (a) Point set generated by two Poisson processes, with densities of 2.5 and 1.0 on the left and right clusters respectively, (b)4 and indicate the partition of point set in (a). Parameter settings: X 5, r 3.
  • + 13

Topics: Image segmentation (61%), Graph partition (54%), Graph (abstract data type) (53%) ...read more

10,996 Citations


Open accessJournal ArticleDOI: 10.1088/1742-5468/2008/10/P10008
Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .

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10,260 Citations


Journal ArticleDOI: 10.1109/TSSC.1968.300136
Abstract: Although the problem of determining the minimum cost path through a graph arises naturally in a number of interesting applications, there has been no underlying theory to guide the development of efficient search procedures. Moreover, there is no adequate conceptual framework within which the various ad hoc search strategies proposed to date can be compared. This paper describes how heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching and demonstrates an optimality property of a class of search strategies.

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Topics: Beam search (63%), Incremental heuristic search (60%), Bidirectional search (60%) ...read more

8,780 Citations


Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2022158
20217,346
20207,228
20195,990
20184,812
20174,094

Top Attributes

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Topic's top 5 most impactful authors

Feiping Nie

77 papers, 1.9K citations

Philip S. Yu

70 papers, 1.9K citations

Edwin R. Hancock

44 papers, 683 citations

Alejandro Ribeiro

40 papers, 1.3K citations

Hartmut Ehrig

40 papers, 2.1K citations

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