Cluster Analysis Based on Fuzzy Quotient Space

Zhu, Ping; Cheng, Jia-Xing

doi:10.3724/sp.j.1001.2008.00861

Cited by 11 publications

(3 citation statements)

References 8 publications

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“…The method, with the nature of the distance metric spaces, merged the individual particles in information synthesis way for clustering results. Cluster analysis method [22] based on fuzzy similarity relations and normalized distance is proposed to solve data structure analysis of complex systems. The conclusion is suitable for the complicated systems.…”

Section: Introductionmentioning

confidence: 99%

Detecting overlapping protein complexes in weighted PPI network based on overlay network chain in quotient space

Zhao

Lei

2019

BMC Bioinformatics

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Background: Protein complexes are the cornerstones of many biological processes and gather them to form various types of molecular machinery that perform a vast array of biological functions. In fact, a protein may belong to multiple protein complexes. Most existing protein complex detection algorithms cannot reflect overlapping protein complexes. To solve this problem, a novel overlapping protein complexes identification algorithm is proposed. Results: In this paper, a new clustering algorithm based on overlay network chain in quotient space, marked as ONCQS, was proposed to detect overlapping protein complexes in weighted PPI networks. In the quotient space, a multilevel overlay network is constructed by using the maximal complete subgraph to mine overlapping protein complexes. The GO annotation data is used to weight the PPI network. According to the compatibility relation, the overlay network chain in quotient space was calculated. The protein complexes are contained in the last level of the overlay network. The experiments were carried out on four PPI databases, and compared ONCQS with five other state-of-the-art methods in the identification of protein complexes. Conclusions: We have applied ONCQS to four PPI databases DIP, Gavin, Krogan and MIPS, the results show that it is superior to other five existing algorithms MCODE, MCL, CORE, ClusterONE and COACH in detecting overlapping protein complexes.

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Section: Introductionmentioning

confidence: 99%

Detecting overlapping protein complexes in weighted PPI network based on overlay network chain in quotient space

Zhao

Lei

2019

BMC Bioinformatics

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“…Pedrycz and Reformat 15 presented a hierarchical fuzzy C-means FCM method in a stepwise discovery of structure in data. Tang et al 16 discussed the sufficient condition of isomorphism between fuzzy similarity relations and uncovered the relationships between fuzzy similarity relation and fuzzy equivalence relation. Although each person has his/her own membership function for the same concept, and he/she may get the different fuzzy similarity relations, he/she may finally obtain the same or isomorphic fuzzy equivalent relation which can produce the same hierarchical quotient space structure and classification of objects in the domain X.…”

Section: Introductionmentioning

confidence: 99%

The Uncertainty Measure of Hierarchical Quotient Space Structure

Zhang

Wang

2011

Mathematical Problems in Engineering

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In the application of fuzzy reasoning, researchers usually choose the membership function optionally in some degree. Even though the membership functions may be different for the same concept, they can generally get the same or approximate results. The robustness of the membership function optionally chosen has brought many researchers' attention. At present, many researchers pay attention to the structural interpretation definition of a fuzzy concept, and find that a hierarchical quotient space structure may be a better tool than a fuzzy set for characterizing the essential of fuzzy concept in some degree. In this paper, first the uncertainty of a hierarchical quotient space structure is defined, the information entropy sequence of a hierarchical quotient space structure is proposed, the concept of isomorphism between two hierarchical quotient space structures is defined, and the sufficient condition of isomorphism between two hierarchical quotient space structures is discovered and proved also. Then, the relationships among information entropy sequence, hierarchical quotient space structure, fuzzy equivalence relation, and fuzzy similarity relation are analyzed. Finally, a fast method for constructing a hierarchical quotient space structure is presented.2 for all x, y ∈ X, R x, y R y, x , then R is called a fuzzy similarity relation on X. Definition 2.2 see 6 . Let R be a fuzzy relation on X. If it satisfies, 1 for all x ∈ X, R x, x 1, 2 for all x, y ∈ X, R x, y R y, x , 3 for all x, y, z ∈ X, R x, z ≥ sup y∈X min R x, y , R y, z , the R is called a fuzzy equivalence relation on X and is denoted by R. Proposition 2.3 see 17 . Let R be a fuzzy similarity relation on X, and let R denote the transitive closure of R. Then, for all m ≥ n, R R m .According to Proposition 2.3, a fuzzy equivalence relation can be induced from a fuzzy similarity relation by R → R 2 → R 2 2 → · · · → R 2 k R. Where k ≥ log 2 n. Proposition 2.4 see 17 . Let R be a fuzzy equivalence relation on X, and R λ { x, y | R x, y ≥ λ} 0 ≤ λ ≤ 1 , then R λ is a crisp equivalence relation on X, R λ is called cut-relation of R.

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“…The theory and the method of quotient space in precise granularity are extended to fuzzy granular computing. The researchers apply fuzzy quotient space theory to clustering (Feng et al 2004;Tang et al 2008). The fuzziness of quotient space can be obtained from the following three aspects: (1) the universe is introduced into fuzzy sets.…”

Section: Fuzzy Quotient Spacementioning

confidence: 99%

Survey on granularity clustering

Ding

Zhu

2015

Cogn Neurodyn

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With the rapid development of uncertain artificial intelligent and the arrival of big data era, conventional clustering analysis and granular computing fail to satisfy the requirements of intelligent information processing in this new case. There is the essential relationship between granular computing and clustering analysis, so some researchers try to combine granular computing with clustering analysis. In the idea of granularity, the researchers expand the researches in clustering analysis and look for the best clustering results with the help of the basic theories and methods of granular computing. Granularity clustering method which is proposed and studied has attracted more and more attention. This paper firstly summarizes the background of granularity clustering and the intrinsic connection between granular computing and clustering analysis, and then mainly reviews the research status and various methods of granularity clustering. Finally, we analyze existing problem and propose further research.

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Cluster Analysis Based on Fuzzy Quotient Space

Cited by 11 publications

References 8 publications

Detecting overlapping protein complexes in weighted PPI network based on overlay network chain in quotient space

Detecting overlapping protein complexes in weighted PPI network based on overlay network chain in quotient space

The Uncertainty Measure of Hierarchical Quotient Space Structure

Survey on granularity clustering

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