The Experts below are selected from a list of 21117 Experts worldwide ranked by ideXlab platform
Ling Zhang - One of the best experts on this subject based on the ideXlab platform.
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the property of different granule and granular methods based on Quotient Space
2015Co-Authors: Yan Ping Zhang, Ling ZhangAbstract:Nowadays, we have entered the era of big data, and we have to deal with complex systems and massive data frequently. Facing complicated objects, how to describe or present objects is the base to solve questions frequently. So we suppose that a problem solving Space, or a problem Space for short, is described by a triplet (X, f, Γ), and assume that X is a domain, R is an equivalence relation on X, Г is a topology of X, [X] is a Quotient set under R. Regarding [X] as a new domain, we have a new world to analyse and to research this object, consequently we describe or present a question into different granule worlds, these granular worlds are called the Quotient Space. Further we are able to predigest and solve a question, i.e. we apply Quotient Space and granulate to represent an object. Comparing rough set and decision-making tree, the Quotient Space has the stronger representation. Not only it can represent vectors of the problem domain, different structures between vectors, but also it can define different attribute functions and operations etc. In this paper, we discuss the method how to represent and to partition an object in granular worlds, and educe the relationship of different granular worlds and confirm the degree of granule. We will prove three important theorems of different granules, i.e. to preserve false property theorem and to preserve true property theorem. To solve a problem in different granular worlds, the process procedure of Quotient approximate will be applied. We also supply an example of solving problem by different granule worlds—the shortest path of a complex network. The example indicates that to describe or present a complicated object is equal to construct Quotient Space. In Quotient set [X], the complexity to solve a problem is lower than X. We have a new solution method to analysis a big data based on the Quotient Space theory.
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Quotient Space based problem solving a theoretical foundation of granular computing
2014Co-Authors: Ling Zhang, Bo ZhangAbstract:Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing Describes a human-like, theoretical framework using Quotient Space theory, that will be of interest to researchers in artificial intelligence. Provides many applications and examples in the engineering and computer science area. Includes complete coverage of planning, heuristic search and coverage of strictly mathematical models.
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computing the point to point shortest path Quotient Space theory s application in complex network
Rough Sets and Knowledge Technology, 2010Co-Authors: Yan Ping Zhang, Shu Zhao, Ling ZhangAbstract:The Quotient Space theory can represent the world at different granularity sizes and deal with complicated problems hierarchically. We present significant improvement to point-to-point shortest path based on Quotient Space theory in complex large-scale network. We propose the shortest path algorithm that is a heuristic method, in which evaluation function is based on community and hierarchical granularity decomposition of Quotient Space theory. In preprocessing, we decompose large-scale network into some communities using hierarchical granularity decomposition of Quotient Space theory, compute and store the minimum spanning trees in the communities and the shortest distance among communities. The implementation works on the large-scale road network. From experimental results, we know the proposed algorithm is effective and efficient in the road network of US.
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a new algorithm for optimal path finding in complex networks based on the Quotient Space
Fundamenta Informaticae, 2009Co-Authors: Ling Zhang, Yan Ping Zhang, Shu ZhaoAbstract:The optimal path finding problem in weighted edge networks is an old and interesting one in many fields. There were many well-known algorithms to deal with that issue. But they were confronted with the high computational complexity while the network becoming larger. We present a hierarchical Quotient Space model based algorithm that reduces the computational complexity. The basic idea is the following. The nodes of a given network are partitioned with respect to the weights of their adjacent edges. We construct a variety of coarser versions of the given network with new nodes corresponding to the blocks of partitions at various levels of granularity. They are called the Quotient Spaces (networks) of the original network. The construction of the (sub- )optimal path is then done incrementally, throughout the hierarchy of Quotient networks. Since each version of the network is much simpler than the original one, especially of the coarsest Spaces, the computational complexity is reduced. In this paper, we present the basic principles of the algorithm and its experimental comparison to other well-known algorithms.
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advances in the Quotient Space theory and its applications
International Journal of Cognitive Informatics and Natural Intelligence, 2009Co-Authors: Liquan Zhao, Ling ZhangAbstract:Quotient Space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem Space or simply a Space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the Quotient Space’s model and its main principle. Then some basic operations on Quotient Space are introduced, and the significant properties of the fuzzy Quotient Space family are elaborated. Finally the main applications of Quotient Space theory are discussed.
Bo Zhang - One of the best experts on this subject based on the ideXlab platform.
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Quotient Space based problem solving a theoretical foundation of granular computing
2014Co-Authors: Ling Zhang, Bo ZhangAbstract:Quotient Space Based Problem Solving provides an in-depth treatment of hierarchical problem solving, computational complexity, and the principles and applications of multi-granular computing, including inference, information fusing, planning, and heuristic search. Explains the theory of hierarchical problem solving, its computational complexity, and discusses the principle and applications of multi-granular computing Describes a human-like, theoretical framework using Quotient Space theory, that will be of interest to researchers in artificial intelligence. Provides many applications and examples in the engineering and computer science area. Includes complete coverage of planning, heuristic search and coverage of strictly mathematical models.
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KSEM - Quotient Space based multi-granular analysis
Knowledge Science Engineering and Management, 2007Co-Authors: Ling Zhang, Bo ZhangAbstract:We presented a Quotient Space model that can represent a problem at different granularities; each model has three components: the universe X, property f and structure T. So a multi-granular analysis can be implemented based on the model. The basic properties among different Quotient Spaces such as the falsity preserving, the truth preserving properties are discussed. There are three Quotient-Space model construction approaches, i.e., the construction based on universe, based on property and based on structure. Four examples are given to show how a Quotient Space model can be constructed from a real problem and how benefit we can get from the multi-granular analysis. First, by adding statistical inference method to heuristic search, a statistical heuristic search approach is presented. Due to the hierarchical and multi-granular problem solving strategy, the computational complexity of the new search algorithm is reduced greatly. Second, in the collision-free paths planning in robotics, the topological model is constructed from geometrical one. By using the truth preserving property between these two models, the paths planning can be implemented in the coarser and simpler topological Space so that the computational cost is saved. Third, we discuss the Quotient Space approximation and the multi-resolution signal analysis. And the second-generation wavelet analysis can be obtained from QuotientSpace based function approximation. It shows the equivalence relation between the Quotient Space model based analysis and wavelet transform. Fourth, in the automatic assembly sequence planning of mechanical product, we mainly show how a Quotient structure can be constructed from the original one. By using the simpler Quotient structure, the assembly sequence planning can be simplified greatly. In conclusion, the QuotientSpace model enables us to implement a multi-granular analysis. And we can get great benefit from the analysis.
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Quotient Space based multi granular analysis
Knowledge Science Engineering and Management, 2007Co-Authors: Ling Zhang, Bo ZhangAbstract:We presented a Quotient Space model that can represent a problem at different granularities; each model has three components: the universe X, property f and structure T. So a multi-granular analysis can be implemented based on the model. The basic properties among different Quotient Spaces such as the falsity preserving, the truth preserving properties are discussed. There are three Quotient-Space model construction approaches, i.e., the construction based on universe, based on property and based on structure. Four examples are given to show how a Quotient Space model can be constructed from a real problem and how benefit we can get from the multi-granular analysis. First, by adding statistical inference method to heuristic search, a statistical heuristic search approach is presented. Due to the hierarchical and multi-granular problem solving strategy, the computational complexity of the new search algorithm is reduced greatly. Second, in the collision-free paths planning in robotics, the topological model is constructed from geometrical one. By using the truth preserving property between these two models, the paths planning can be implemented in the coarser and simpler topological Space so that the computational cost is saved. Third, we discuss the Quotient Space approximation and the multi-resolution signal analysis. And the second-generation wavelet analysis can be obtained from QuotientSpace based function approximation. It shows the equivalence relation between the Quotient Space model based analysis and wavelet transform. Fourth, in the automatic assembly sequence planning of mechanical product, we mainly show how a Quotient structure can be constructed from the original one. By using the simpler Quotient structure, the assembly sequence planning can be simplified greatly. In conclusion, the QuotientSpace model enables us to implement a multi-granular analysis. And we can get great benefit from the analysis.
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granular analysis of time sequence based on Quotient Space
Computational Intelligence for Modelling Control and Automation, 2006Co-Authors: Liquan Zhao, Ling Zhang, Bo ZhangAbstract:This paper aims to carry out granular analysis of time sequence based on Quotient Space. Granular methods have long before been adopted to analyze time sequence, but the granularity was based on time, for example, day mean, month mean, year mean and so on in finance forecast. In this paper, the granularity is based on Space and some significant results are obtained: we can, in certain circumstances, get characteristics of time sequence in an original Space when carrying out granular analysis of it in its coarser-grain Space; granular analysis of a Markov chain is equivalent to an hidden Markov model (HMM), contrarily, any HMM is equivalent to granular analysis of a Markov chain. These results deepened our understanding of HMM from the perspective of granular analysis. We can not only use the methods of HMM to study time sequence, but also use the methods of granular analysis based on Quotient Space theory to solve the problems of HMM.
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Quotient Space model of hierarchical query-by-humming system
2005 IEEE International Conference on Granular Computing, 2005Co-Authors: Zhi Wang, Bo ZhangAbstract:In this paper, we put ideas of granular computing into the application of query-by-humming. Leading by Quotient Space theory of problem solving, we present a Quotient Space model of hierarchical query-by-humming system, which do search in two stages. The first is searching in the Quotient Space to obtain high recall rate and a narrowed possible region with accepted speed. The second step is doing accurate but relatively slow search in the small original Space to achieve high precision. In addition, we improve the previous dynamic programming techniques for melody matching, which tolerate the input error more reasonably. We also compare our hierarchical method with the previous flat note-based algorithm and frame-based algorithm on MIDI-encoded database of Chinese music and obtain promising results both in efficiency and accuracy.
Xavier Pennec - One of the best experts on this subject based on the ideXlab platform.
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Bias on estimation in Quotient Space and correction methods: Applications to statistics on organ shapes
2020Co-Authors: Nina Miolane, Loïc Devilliers, Xavier PennecAbstract:Riemannian geometry and the theory of Quotient Spaces facilitate the analysis of medical imaging algorithms dealing with organ shapes. These algorithms often start with the computation of a template organ shape that serves as a reference for normalizing the measurements of each individual data into a common Space. The template represents the organ's “prototype” for further analysis. The template is modeled as a parameter of a generative model that is estimated from the observed data, that is, from noisy images of organs. A usual procedure for template estimation is the computation of the Fréchet mean of the observed data projected in a Quotient Space. In this chapter we introduce the geometry of Quotient Spaces and use it to show that the usual template estimation procedure is biased. Riemannian geometry allows us to explain the origin of the bias and to design bias correction methods to improve statistical analysis on organ shapes.
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bias on estimation in Quotient Space and correction methods applications to statistics on organ shapes
2020Co-Authors: Nina Miolane, Loïc Devilliers, Xavier PennecAbstract:Riemannian geometry and the theory of Quotient Spaces facilitate the analysis of medical imaging algorithms dealing with organ shapes. These algorithms often start with the computation of a template organ shape that serves as a reference for normalizing the measurements of each individual data into a common Space. The template represents the organ's “prototype” for further analysis. The template is modeled as a parameter of a generative model that is estimated from the observed data, that is, from noisy images of organs. A usual procedure for template estimation is the computation of the Frechet mean of the observed data projected in a Quotient Space. In this chapter we introduce the geometry of Quotient Spaces and use it to show that the usual template estimation procedure is biased. Riemannian geometry allows us to explain the origin of the bias and to design bias correction methods to improve statistical analysis on organ shapes.
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Inconsistency of Template Estimation with the Fréchet mean in Quotient Space
2017Co-Authors: Loïc Devilliers, Xavier Pennec, Stéphanie AllassonnièreAbstract:We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fréchet mean in Quotient Space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In this article we establish an asymptotic behavior of the consistency bias with respect to the noise level. This behavior is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is large enough. In practice, the template estimation with a finite sample is often done with an algorithm called max-max. We show the convergence of this algorithm to an empirical Karcher mean. Finally, our numerical experiments show that the bias observed in practice cannot be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency.
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inconsistency of template estimation with the frechet mean in Quotient Space
Information Processing in Medical Imaging, 2017Co-Authors: Loïc Devilliers, Xavier Pennec, Stéphanie AllassonnièreAbstract:We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Frechet mean in Quotient Space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In this article we establish an asymptotic behavior of the consistency bias with respect to the noise level. This behavior is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is large enough. In practice, the template estimation with a finite sample is often done with an algorithm called max-max. We show the convergence of this algorithm to an empirical Karcher mean. Finally, our numerical experiments show that the bias observed in practice cannot be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency.
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Inconsistency of template estimation by minimizing of the variance/pre-variance in the Quotient Space
Entropy, 2017Co-Authors: Loïc Devilliers, Stéphanie Allassonnière, Alain Trouvé, Xavier PennecAbstract:We tackle the problem of template estimation when data have been randomly deformed under a group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fréchet mean in the Quotient Space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In the first part, we restrict ourselves to isometric group action, in this case the Hilbertian distance is invariant under the group action. We establish an asymptotic behavior of the consistency bias which is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is enough. In practice, template estimation with a finite sample is often done with an algorithm called "max-max". In the second part, also in the case of isometric group finite, we show the convergence of this algorithm to an empirical Karcher mean. Our numerical experiments show that the bias observed in practice can not be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency. In a third part, we also present some insights of the case of a non invariant distance with respect to the group action. We will see that the inconsistency still holds as soon as the noise level is large enough. Moreover we prove the inconsistency even when a regularization term is added.
Shuiguang Deng - One of the best experts on this subject based on the ideXlab platform.
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alliance aware service composition based on Quotient Space
International Conference on Web Services, 2016Co-Authors: Yiwen Zhangy, Guangming Cuiy, Shuiguang DengAbstract:Along with the progress of the enterprise globalization, alliance and cooperation have become an important means for enterprises to improve their competitiveness in the market. Yet, most current methods for Service Composition Optimization (SCO) fail to address the Alliance Relation (AR) between services and assume that services are independent of each other. To address this issue, this paper presents an alliance-aware service composition method. Firstly, the fundamental properties of the AR are given based on a multi-granularity service composition model. Secondly, alliance relation granularity is coarsened into a relation granulation Quotient Space and the domain elements are matched reversely with service compositions, thereby reducing the complexity of query and computation of the AR. Finally, a Relation Granularity-aware Particle Swarm Optimization Algorithm (RG-PSO) is proposed based on relation granulation Quotient Space to solve the alliance-aware SCO prolem. Substantial experimental results show that the proposed model and algorithm are effective and efficient.
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ICWS - Alliance-Aware Service Composition Based on Quotient Space
2016 IEEE International Conference on Web Services (ICWS), 2016Co-Authors: Yiwen Zhangy, Guangming Cuiy, Shuiguang DengAbstract:Along with the progress of the enterprise globalization, alliance and cooperation have become an important means for enterprises to improve their competitiveness in the market. Yet, most current methods for Service Composition Optimization (SCO) fail to address the Alliance Relation (AR) between services and assume that services are independent of each other. To address this issue, this paper presents an alliance-aware service composition method. Firstly, the fundamental properties of the AR are given based on a multi-granularity service composition model. Secondly, alliance relation granularity is coarsened into a relation granulation Quotient Space and the domain elements are matched reversely with service compositions, thereby reducing the complexity of query and computation of the AR. Finally, a Relation Granularity-aware Particle Swarm Optimization Algorithm (RG-PSO) is proposed based on relation granulation Quotient Space to solve the alliance-aware SCO prolem. Substantial experimental results show that the proposed model and algorithm are effective and efficient.
Zhang Ling - One of the best experts on this subject based on the ideXlab platform.
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Quotient Space model based hierarchical machine learning
International Conference on Neural Networks and Brain, 2005Co-Authors: Zhang LingAbstract:We proposed a Quotient Space based model that can represent the world at different granularities and can be used to handle problems hierarchically. The model can be used in two different ways: top-down deduction and bottom-up induction. In this paper, we will discuss the Quotient Space model based bottom-up induction, i.e., hierarchical learning. Some approaches for learning the structural knowledge from data are presented. The main advantage of hierarchical induction is its efficiency, that is, the whole structure of data can be abstracted at once.
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algorithm of hierarchical competitive covering networks based on Quotient Space
Microcomputer Development, 2005Co-Authors: Mao Junjun, Wu Tao, Zheng Tingting, Zhang LingAbstract:In this paper,the algorithm of a kind of hierarchical competitive covering networks for the classification problems is proposed based on the introduction of Quotient Space theory,which defines granularity according to Huffman coding and Huffman coding algorithm.Instances show that this kind of network can improve the sorting ability of covering networks.
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an analysis of uneven granules clustering based on Quotient Space
Computer Engineering, 2005Co-Authors: Zhang LingAbstract:The fuzzy granules clustering based on the Quotient Space is discussed by the metric Space. The cluster is a combination of information obtained from different granules in information fusion. Clustering with uneven granules in this way represents samples sets. By this means, a fuzzy clustering (FCluster) is proposed. In the clustering, the distance measure function, which is defined with Gaussian function between samples, is employed other than membership functions, fuzzy matrix, and the Gaussian width parameters are ignored. As the experiment showed, the approach advantage is: (1) the cluster is observed in different viewpoints; (2) the computational and special cost is saved; (3) it is efficient for the large number of observations; (4) Gaussian distance is able to achieve better accuracy to the synthetic control chart time series data sets.
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to compare the theory of Quotient Space with rough set
Microcomputer Development, 2004Co-Authors: Zhang Yanping, Zhang Ling, Xia YingAbstract:The relationship between rough set and Quotient Space is discussed by comparing in the paper.After analyzing basic algorithms and complexity and expansibility in theory about rough set and Quotient Space,think that the same point of them is to represent granule by using equivalence relation and to depict concept by using granule.But the emphasis of both discussions is difference.The theory of Quotient Space researches transformed and depended relations between different granules mainly.It is the theory to represent Space relationship.For granular computing today such as rough set,it studies to represent and depict granule and relation between granule and concept primarily.The greatest difference is that there is topological relation among domain elements in the theory of Quotient Space,i.e.the domain is a topological Space.Whereas the domain of rough set is only simple point set,there is no topological relation among elements.So the theory of Quotient Space applies to not only data mining and knowledge discovery,but also restriction problem such as route layout and Space state distributing etc.
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theory of fuzzy Quotient Space methods of fuzzy granular computing
Journal of Software, 2003Co-Authors: Zhang LingAbstract:In this paper, the Quotient Space model is extended to the fuzzy granular world and two main conclusions are given. First, the following four statements are equivalent: (1) a fuzzy equivalence relation given in universe X, (2) a normalized isosceles distance given in Quotient Space [X], (3) a hierarchical structure given in X, (4) a fuzzy knowledge base given in X. Second, the whole world with different fuzzy granularities composes a complete semi-order lattice. The results provide a powerful mathematical model and tool for granule computing.
