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Method for analyzing and recognizing complex network cluster structure based on markov process metastability

A complex network and structure analysis technology, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as unbiased, high recognition accuracy, and unsupervised

Inactive Publication Date: 2010-12-01
JILIN UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, for CNCS identification, the main disadvantage of the spectral method is that it needs to use prior knowledge to define the recursive termination condition, that is, the spectral method does not have the ability to automatically identify the total number of network clusters
[0009] First, theoretically, we have not objectively understood the essential meaning of the network cluster structure
So far we have not been able to answer fundamental questions like the following: How is the network cluster structure formed? How does it necessarily relate to other properties of the network? What intrinsic properties does it have to do with the network itself? Therefore, at this stage, we have to understand the concept of network clusters by observing the "external" phenomena displayed by the clustered network, and then use the "subjective" defined objective function or heuristic rules to describe and identify CNCS
[0010] Second, existing CNCS recognition algorithms have their own limitations, and cannot simultaneously meet the basic requirements of unbiasedness, fast calculation speed, high recognition accuracy, and unsupervised (ie, do not rely on prior knowledge and are insensitive to parameters)
Through qualitative and quantitative analysis and comparison of existing main algorithms, it is found that algorithms with high recognition accuracy often have high time complexity (higher than O(n2)), while fast recognition algorithms often sacrifice accuracy and require More parameters and prior knowledge

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  • Method for analyzing and recognizing complex network cluster structure based on markov process metastability
  • Method for analyzing and recognizing complex network cluster structure based on markov process metastability
  • Method for analyzing and recognizing complex network cluster structure based on markov process metastability

Examples

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Effect test

example 1

[0067] Example 1 Using the NAP method to analyze the number of real network clusters in the network

[0068] image 3 (a) represents an image including 4 characters. image 3 (b) represents the network corresponding to the image. The network modeling method adopts the full connection method, and the weight of the network connection is calculated using the Gaussian similarity formula. In this network, each character constitutes a natural network cluster, so the number of real network clusters in this network is 4. image 3 (c) represents each CQ calculated by NAP K value, where CQ 4 The smallest, so the total number of network clusters calculated by NAP is 4, which is consistent with the real total number of network clusters.

example 2

[0069] Example 2 Figure 4 The software interface for implementing the fast_NAP method is given. Using the fast_NAP method, the software can identify all network clusters and their hierarchical structures in the network, and visualize complex network clusters and their hierarchical structures by combining adjacency matrix and hierarchical tree. By rearranging the rows and columns of the original adjacency matrix and arranging the nodes of the same cluster together, a transformed adjacency matrix that can clearly represent the network cluster structure can be obtained. If the network has a clear cluster structure, the corresponding transformation matrix should be an approximate diagonal matrix, and each block sub-matrix of the main diagonal corresponds to exactly one network cluster. The non-zero elements distributed in the main diagonal area (corresponding to the inner edge of the cluster) are much more than the non-zero elements scattered outside the main diagonal area (corr...

example 3

[0070] Example 3 Using the fast_NAP method to analyze the American College Football League network

[0071] Figure 5 (a) The NCAA network for the 2000 season is given. The network contains 115 nodes and 613 edges. Each node in the network represents a college football team, and each edge represents a game between two teams. All teams are organized into 12 leagues based on geographic location. According to the rules of the game, there are far more games within the league than between leagues. Therefore, according to the relationship of the competition, 12 alliances correspond to 12 network clusters.

[0072] Figure 5 (b) The calculation results of the fast_NAP method are given, a diagonalized adjacency matrix and a network cluster hierarchy tree. After analysis and comparison, it is found that the 12 network clusters obtained by the fast_NAP algorithm are basically consistent with the 12 actual football leagues, and only 6 teams belonging to 3 relatively independent lea...

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Abstract

The invention relates to a method for analyzing and recognizing a complex network cluster structure based on markov process metastability, comprising the following main steps: configuring a markov process on a given complex network; calculating a transition probability matrix of the markov process; calculating the characteristic values of the matrix; calculating the number of network clusters through analyzing the characteristic values; calculating the first metastability of the markov process; and recognizing all the network clusters of the network and hierachical structures thereof according to the first metastability. The invention provides the new and high-efficient method for the analysis and recognition of the complex network clusters, and has the characteristics of unbiasedness (having optimization objects or heuristic rule which are not dependent of subjective definition), rapid calculation speed (having approximate linear calculation time complexity), high recognition precision (correctly recognizing the network clusters of the complex network in a real world and the hierachical structures thereof) and no monitoring ( needing no prior knowledge) as compared with the existing similar methods.

Description

technical field [0001] The invention belongs to the fields of pattern recognition and data mining, and in particular relates to the analysis of complex networks such as social networks, world wide networks and biological networks. Background technique [0002] Many systems in the real world exist in the form of networks, such as interpersonal networks, scientist collaboration networks, and epidemic transmission networks in social systems; neuron networks, gene regulation networks, and protein interaction networks in ecosystems; Electric grid, Internet and World Wide Web etc. These networks are called "complex networks" due to their high complexity. Juxtaposed with small-world and scale-free, complex network cluster structure (CNCS) is one of the most common and important topological properties of complex networks, which is characterized by close interconnection of nodes in the same cluster and sparse interconnection of nodes in different clusters. The CNCS identification m...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/30
Inventor 杨博刘大有
Owner JILIN UNIV