The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
Gi Hyun Park - One of the best experts on this subject based on the ideXlab platform.
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the structure of gauge invariant ideals of Labelled Graph c algebras
Journal of Functional Analysis, 2012Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:Abstract In this paper we consider the gauge-invariant ideal structure of a C ⁎ -algebra C ⁎ ( E , L , B ) associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space ( E , L , B ) , where L is a labelling map assigning an alphabet to each edge of the directed Graph E with no sinks. It is obtained that if an accommodating set B is closed under relative complements, there is a one-to-one correspondence between the set of all hereditary saturated subsets of B and the gauge-invariant ideals of C ⁎ ( E , L , B ) . For this, we introduce a quotient Labelled space ( E , L , [ B ] R ) arising from an equivalence relation ∼ R on B and show the existence of the C ⁎ -algebra C ⁎ ( E , L , [ B ] R ) generated by a universal representation of ( E , L , [ B ] R ) . Finally we give necessary and sufficient conditions for simplicity of certain Labelled Graph C ⁎ -algebras.
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the structure of gauge invariant ideals of Labelled Graph c algebras
arXiv: Operator Algebras, 2011Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed Graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient Labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple Labelled Graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged Labelled Graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share.
Ja A Jeong - One of the best experts on this subject based on the ideXlab platform.
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the structure of gauge invariant ideals of Labelled Graph c algebras
Journal of Functional Analysis, 2012Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:Abstract In this paper we consider the gauge-invariant ideal structure of a C ⁎ -algebra C ⁎ ( E , L , B ) associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space ( E , L , B ) , where L is a labelling map assigning an alphabet to each edge of the directed Graph E with no sinks. It is obtained that if an accommodating set B is closed under relative complements, there is a one-to-one correspondence between the set of all hereditary saturated subsets of B and the gauge-invariant ideals of C ⁎ ( E , L , B ) . For this, we introduce a quotient Labelled space ( E , L , [ B ] R ) arising from an equivalence relation ∼ R on B and show the existence of the C ⁎ -algebra C ⁎ ( E , L , [ B ] R ) generated by a universal representation of ( E , L , [ B ] R ) . Finally we give necessary and sufficient conditions for simplicity of certain Labelled Graph C ⁎ -algebras.
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the structure of gauge invariant ideals of Labelled Graph c algebras
arXiv: Operator Algebras, 2011Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed Graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient Labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple Labelled Graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged Labelled Graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share.
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on simple Labelled Graph c algebras
arXiv: Operator Algebras, 2011Co-Authors: Ja A Jeong, Sun Ho KimAbstract:We consider the simplicity of the $C^*$-algebra associated to a Labelled space $(E,\CL,\bE)$, where $(E,\CL)$ is a Labelled Graph and $\bE$ is the smallest accommodating set containing all generalized vertices. We prove that if $C^*(E, \CL, \bE)$ is simple, then $(E, \CL, \bE)$ is strongly cofinal, and if, in addition, $\{v\}\in \bE$ for every vertex $v$, then $(E, \CL, \bE)$ is disagreeable. It is observed that $C^*(E, \CL, \bE)$ is simple whenever $(E, \CL, \bE)$ is strongly cofinal and disagreeable, which is recently known for the $C^*$-algebra $C^*(E, \CL, \CEa)$ associated to a Labelled space $(E, \CL, \CEa)$ of the smallest accommodating set $\CEa$.
Sun Ho Kim - One of the best experts on this subject based on the ideXlab platform.
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the structure of gauge invariant ideals of Labelled Graph c algebras
Journal of Functional Analysis, 2012Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:Abstract In this paper we consider the gauge-invariant ideal structure of a C ⁎ -algebra C ⁎ ( E , L , B ) associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space ( E , L , B ) , where L is a labelling map assigning an alphabet to each edge of the directed Graph E with no sinks. It is obtained that if an accommodating set B is closed under relative complements, there is a one-to-one correspondence between the set of all hereditary saturated subsets of B and the gauge-invariant ideals of C ⁎ ( E , L , B ) . For this, we introduce a quotient Labelled space ( E , L , [ B ] R ) arising from an equivalence relation ∼ R on B and show the existence of the C ⁎ -algebra C ⁎ ( E , L , [ B ] R ) generated by a universal representation of ( E , L , [ B ] R ) . Finally we give necessary and sufficient conditions for simplicity of certain Labelled Graph C ⁎ -algebras.
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the structure of gauge invariant ideals of Labelled Graph c algebras
arXiv: Operator Algebras, 2011Co-Authors: Ja A Jeong, Sun Ho Kim, Gi Hyun ParkAbstract:In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving Labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed Graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient Labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple Labelled Graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged Labelled Graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share.
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on simple Labelled Graph c algebras
arXiv: Operator Algebras, 2011Co-Authors: Ja A Jeong, Sun Ho KimAbstract:We consider the simplicity of the $C^*$-algebra associated to a Labelled space $(E,\CL,\bE)$, where $(E,\CL)$ is a Labelled Graph and $\bE$ is the smallest accommodating set containing all generalized vertices. We prove that if $C^*(E, \CL, \bE)$ is simple, then $(E, \CL, \bE)$ is strongly cofinal, and if, in addition, $\{v\}\in \bE$ for every vertex $v$, then $(E, \CL, \bE)$ is disagreeable. It is observed that $C^*(E, \CL, \bE)$ is simple whenever $(E, \CL, \bE)$ is strongly cofinal and disagreeable, which is recently known for the $C^*$-algebra $C^*(E, \CL, \CEa)$ associated to a Labelled space $(E, \CL, \CEa)$ of the smallest accommodating set $\CEa$.
Robert P W Duin - One of the best experts on this subject based on the ideXlab platform.
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selecting structural base classifiers for Graph based multiple classifier systems
International Conference on Multiple Classifier Systems, 2010Co-Authors: Wanjui Lee, Robert P W Duin, Horst BunkeAbstract:Selecting a set of good and diverse base classifiers is essential for building multiple classifier systems. However, almost all commonly used procedures for selecting such base classifiers cannot be directly applied to select structural base classifiers. The main reason is that structural data cannot be represented in a vector space. For Graph-based multiple classifier systems, only using subGraphs for building structural base classifiers has been considered so far. However, in theory, a full Graph preserves more information than its subGraphs. Therefore, in this work, we propose a different procedure which can transform a Labelled Graph into a new set of unLabelled Graphs and preserve all the linkages at the same time. By embedding the label information into edges, we can further ignore the labels. By assigning weights to the edges according to the labels of their linked nodes, the strengths of the connections are altered, but the topology of the Graph as a whole is preserved. Since it is very difficult to embed Graphs into a vector space, Graphs are usually classified based on pairwise Graph distances. We adopt the dissimilarity representation and build the structural base classifiers based on labels in the dissimilarity space. By combining these structural base classifiers, we can solve the Labelled Graph classification problem with a multiple classifier system. The performance of using the subGraphs and full Graphs to build multiple classifier systems is compared in a number of experiments.
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a Labelled Graph based multiple classifier system
Multiple Classifier Systems, 2009Co-Authors: Wanjui Lee, Robert P W DuinAbstract:In general, classifying Graphs with Labelled nodes (also known as Labelled Graphs) is a more difficult task than classifying Graphs with unLabelled nodes. In this work, we decompose the Labelled Graphs into unLabelled subGraphs with respect to the labels, and describe these decomposed subGraphs with the travelling matrices. By utilizing the travelling matrices to calculate the dissimilarity for all pairs of subGraphs with the JoEig approach [6], we can build a base classifier in the dissimilarity space for each label. By combining these label base classifiers with the global structure base classifiers built on dissimilarities of Graphs considering the full adjacency matrices and the full travelling matrices, respectively, we can solve the Labelled Graph classification problem with the multiple classifier system.
Rama Chellappa - One of the best experts on this subject based on the ideXlab platform.
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recursive tracking of image points using Labelled Graph matching
Systems Man and Cybernetics, 1991Co-Authors: S Chandrashekhar, C Von Der Malsburg, Rama ChellappaAbstract:The authors address the problem of obtaining the image-plane trajectories of feature points from a sequence of images. The matching of points between successive images in the sequence is treated as a labeled Graph matching problem, and solved by minimizing a weighted sum of three cost functions. The nodes in the Graph are the feature points to be matched, which are labeled using Gabor wavelets. Information gathered from the previous image frames is processed by a Kalman filter and used to predict the positions of the match points in the incoming image, and thereby initialize the Graph matching. Results on synthetic and real image sequences are presented. >
