The Experts below are selected from a list of 123 Experts worldwide ranked by ideXlab platform
Jörg Sander - One of the best experts on this subject based on the ideXlab platform.
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Semi-supervised density-based Clustering
Proceedings - IEEE International Conference on Data Mining, ICDM, 2009Co-Authors: Levi Lelis, Jörg SanderAbstract:Most of the effort in the semi-supervised Clustering liter- ature was devoted to variations of the K-means algorithm. In this paper we show how background knowledge can be used to bias a partitional density-based Clustering algo- rithm. Our work describes how labeled objects can be used to help the algorithm detecting suitable density parameters for the algorithm to extract density-based Clusters in spe- cific parts of the feature space. Considering the set of con- straints established by the labeled dataset we show that our algorithm, called SSDBSCAN, automatically finds density parameters for each Natural Cluster in a dataset. Four of the most interesting characteristics of SSDBSCAN are that (1) it only requires a single, robust input parameter, (2) it does not need any user intervention, (3) it automatically finds the noise objects according to the density of the nat- ural Clusters and (4) it is able to find the Natural Cluster structure even when the density among Clusters vary widely. The algorithm presented in this paper is evaluated with arti- ficial and real-world datasets, demonstrating better results when compared to other unsupervised and semi-supervised density-based approaches.
Levi Lelis - One of the best experts on this subject based on the ideXlab platform.
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ICDM - Semi-supervised Density-Based Clustering
2009 Ninth IEEE International Conference on Data Mining, 2009Co-Authors: Levi Lelis, Jörg SanderAbstract:Most of the effort in the semi-supervised Clustering literature was devoted to variations of the K-means algorithm. In this paper we show how background knowledge can be used to bias a partitional density-based Clustering algorithm. Our work describes how labeled objects can be used to help the algorithm detecting suitable density parameters for the algorithm to extract density-based Clusters in specific parts of the feature space. Considering the set of constraints estabilished by the labeled dataset we show that our algorithm, called SSDBSCAN, automatically finds density parameters for each Natural Cluster in a dataset. Four of the most interesting characteristics of SSDBSCAN are that (1) it only requires a single, robust input parameter, (2) it does not need any user intervention, (3) it automaticaly finds the noise objects according to the density of the Natural Clusters and (4) it is able to find the Natural Cluster structure even when the density among Clusters vary widely. The algorithm presented in this paper is evaluated with artificial and real-world datasets, demonstrating better results when compared to other unsupervised and semi-supervised density-based approaches.
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Semi-supervised density-based Clustering
Proceedings - IEEE International Conference on Data Mining, ICDM, 2009Co-Authors: Levi Lelis, Jörg SanderAbstract:Most of the effort in the semi-supervised Clustering liter- ature was devoted to variations of the K-means algorithm. In this paper we show how background knowledge can be used to bias a partitional density-based Clustering algo- rithm. Our work describes how labeled objects can be used to help the algorithm detecting suitable density parameters for the algorithm to extract density-based Clusters in spe- cific parts of the feature space. Considering the set of con- straints established by the labeled dataset we show that our algorithm, called SSDBSCAN, automatically finds density parameters for each Natural Cluster in a dataset. Four of the most interesting characteristics of SSDBSCAN are that (1) it only requires a single, robust input parameter, (2) it does not need any user intervention, (3) it automatically finds the noise objects according to the density of the nat- ural Clusters and (4) it is able to find the Natural Cluster structure even when the density among Clusters vary widely. The algorithm presented in this paper is evaluated with arti- ficial and real-world datasets, demonstrating better results when compared to other unsupervised and semi-supervised density-based approaches.
Alek Vainshtein - One of the best experts on this subject based on the ideXlab platform.
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Cluster STRUCTURES ON SIMPLE COMPLEX LIE GROUPS AND BELAVIN-DRINFELD CLASSIFICATION
Moscow Mathematical Journal, 2020Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We study Natural Cluster structures in the rings of regular func- tions on simple complex Lie groups and Poisson-Lie structures compatible with these Cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on G corresponds to a Cluster structure in O(G). We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for SLn, n < 5, and for any G in the case of the standard Poisson- Lie structure. Since the invention of Cluster algebras in 2001, a large part of research in the field has been devoted to uncovering Cluster structures in rings of regular functions on various algebraic varieties arising in algebraic geometry, representation theory, and mathematical physics. Once the existence of such a structure was established, abstract features of Cluster algebras were used to study geometric properties of underlying objects. Research in this direction led to many exciting results (SSVZ, FoGo1, FoGo2). It also created an impression that, given an algebraic variety, there is a unique (if at all) Natural Cluster structure associated with it. The main goal of the current paper is to establish the following phenomenon: in certain situations, the same ring may have multiple Natural Cluster structures. More exactly, we engage into a systematic study of multiple Cluster structures in the rings of regular functions on simple Lie groups (in what follows we will shorten that to Cluster structures on simple Lie groups). Consistent with the philosophy advocated in (GSV1, GSV2, GSV3, GSV4, GSV5, GSV6), we will focus on compatible Poisson structures on the Lie groups, that is, on compatible Poisson-Lie structures. The notion of a Poisson bracket compatible with a Cluster structure was intro- duced in (GSV1). It was used there to interpret Cluster transformations and matrix mutations from a viewpoint of Poisson geometry. In addition, it was shown that if a Poisson algebraic variety (M,f�,ŧ ) possesses a coordinate chart that consists of regular functions whose logarithms have pairwise constant Poisson brackets, then one can use this chart to define a Cluster structure CM compatible with f�,ŧ . Al- gebraic structures corresponding to CM (the Cluster algebra and the upper Cluster algebra) are closely related to the ring O(M) of regular functions on M. More pre- cisely, under certain rather mild conditions, O(M) can be obtained by tensoring one of these algebras by C.
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Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification
arXiv: Quantum Algebra, 2010Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We study Natural Cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these Cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\G$ corresponds to a Cluster structure in $\O(\G)$. We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for $SL_n$, $n
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Poisson geometry of directed networks in a disk
Selecta Mathematica, 2009Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grassmannian is viewed as a Poisson homogeneous space of the general linear group equipped with an appropriate R-matrix Poisson–Lie structure. We also prove that the Poisson brackets on the Grassmannian arising in this way are compatible with the Natural Cluster algebra structure.
Michael Gekhtman - One of the best experts on this subject based on the ideXlab platform.
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Cluster STRUCTURES ON SIMPLE COMPLEX LIE GROUPS AND BELAVIN-DRINFELD CLASSIFICATION
Moscow Mathematical Journal, 2020Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We study Natural Cluster structures in the rings of regular func- tions on simple complex Lie groups and Poisson-Lie structures compatible with these Cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on G corresponds to a Cluster structure in O(G). We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for SLn, n < 5, and for any G in the case of the standard Poisson- Lie structure. Since the invention of Cluster algebras in 2001, a large part of research in the field has been devoted to uncovering Cluster structures in rings of regular functions on various algebraic varieties arising in algebraic geometry, representation theory, and mathematical physics. Once the existence of such a structure was established, abstract features of Cluster algebras were used to study geometric properties of underlying objects. Research in this direction led to many exciting results (SSVZ, FoGo1, FoGo2). It also created an impression that, given an algebraic variety, there is a unique (if at all) Natural Cluster structure associated with it. The main goal of the current paper is to establish the following phenomenon: in certain situations, the same ring may have multiple Natural Cluster structures. More exactly, we engage into a systematic study of multiple Cluster structures in the rings of regular functions on simple Lie groups (in what follows we will shorten that to Cluster structures on simple Lie groups). Consistent with the philosophy advocated in (GSV1, GSV2, GSV3, GSV4, GSV5, GSV6), we will focus on compatible Poisson structures on the Lie groups, that is, on compatible Poisson-Lie structures. The notion of a Poisson bracket compatible with a Cluster structure was intro- duced in (GSV1). It was used there to interpret Cluster transformations and matrix mutations from a viewpoint of Poisson geometry. In addition, it was shown that if a Poisson algebraic variety (M,f�,ŧ ) possesses a coordinate chart that consists of regular functions whose logarithms have pairwise constant Poisson brackets, then one can use this chart to define a Cluster structure CM compatible with f�,ŧ . Al- gebraic structures corresponding to CM (the Cluster algebra and the upper Cluster algebra) are closely related to the ring O(M) of regular functions on M. More pre- cisely, under certain rather mild conditions, O(M) can be obtained by tensoring one of these algebras by C.
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Cluster structures on simple complex Lie groups and the Belavin-Drinfeld classification
arXiv: Quantum Algebra, 2010Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We study Natural Cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structures compatible with these Cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on $\G$ corresponds to a Cluster structure in $\O(\G)$. We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for $SL_n$, $n
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Poisson geometry of directed networks in a disk
Selecta Mathematica, 2009Co-Authors: Michael Gekhtman, Michael Shapiro, Alek VainshteinAbstract:We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grassmannian is viewed as a Poisson homogeneous space of the general linear group equipped with an appropriate R-matrix Poisson–Lie structure. We also prove that the Poisson brackets on the Grassmannian arising in this way are compatible with the Natural Cluster algebra structure.
Espen Villanger - One of the best experts on this subject based on the ideXlab platform.
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Active Private Sector Development Policies Revisited: Impacts of the Ethiopian Industrial Cluster Policy
Journal of Development Studies, 2018Co-Authors: Tigabu Degu Getahun, Espen VillangerAbstract:© 2018 Informa UK Limited, trading as Taylor & Francis Group We analyse impacts of a Cluster policy aiming to increase firm growth through maximising agglomeration benefits and improving production facilities. Firms located in a Natural Cluster were incentivised to move to a new government-created Cluster. A limited number of firms were allowed to move, and many similar firms, also eager to move but could not, formed our comparison group. Controlling for selection, and employing difference in-difference estimation, we find large negative effects on job-creation and firm performance. The policy hampered the firms’ business and knowledge networks, reduced trust among firms, increased transaction costs and curbed market information.