Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model
In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated fro...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Wang, Wenqi [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017transfer abstract |
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| Umfang: |
6 |
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| Übergeordnetes Werk: |
Enthalten in: Thermal structure optimization of a supercondcuting cavity vertical test cryostat - Jin, Shufeng ELSEVIER, 2019, an official publ. of the International Association for Pattern Recognition, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:100 ; year:2017 ; day:1 ; month:12 ; pages:104-109 ; extent:6 |
| Links: |
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| DOI / URN: |
10.1016/j.patrec.2017.10.003 |
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| Katalog-ID: |
ELV041147251 |
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| 520 | |a In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. | ||
| 520 | |a In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. | ||
| 700 | 1 | |a Aggarwal, Vaneet |4 oth | |
| 700 | 1 | |a Aeron, Shuchin |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n Elsevier |a Jin, Shufeng ELSEVIER |t Thermal structure optimization of a supercondcuting cavity vertical test cryostat |d 2019 |d an official publ. of the International Association for Pattern Recognition |g Amsterdam [u.a.] |w (DE-627)ELV003173968 |
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10.1016/j.patrec.2017.10.003 doi GBV00000000000043A.pica (DE-627)ELV041147251 (ELSEVIER)S0167-8655(17)30365-3 DE-627 ger DE-627 rakwb eng 004 004 DE-600 660 VZ 52.43 bkl 33.09 bkl Wang, Wenqi verfasserin aut Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model 2017transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. Aggarwal, Vaneet oth Aeron, Shuchin oth Enthalten in Elsevier Jin, Shufeng ELSEVIER Thermal structure optimization of a supercondcuting cavity vertical test cryostat 2019 an official publ. of the International Association for Pattern Recognition Amsterdam [u.a.] (DE-627)ELV003173968 volume:100 year:2017 day:1 month:12 pages:104-109 extent:6 https://doi.org/10.1016/j.patrec.2017.10.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 52.43 Kältetechnik VZ 33.09 Physik unter besonderen Bedingungen VZ AR 100 2017 1 1201 104-109 6 045F 004 |
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10.1016/j.patrec.2017.10.003 doi GBV00000000000043A.pica (DE-627)ELV041147251 (ELSEVIER)S0167-8655(17)30365-3 DE-627 ger DE-627 rakwb eng 004 004 DE-600 660 VZ 52.43 bkl 33.09 bkl Wang, Wenqi verfasserin aut Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model 2017transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. Aggarwal, Vaneet oth Aeron, Shuchin oth Enthalten in Elsevier Jin, Shufeng ELSEVIER Thermal structure optimization of a supercondcuting cavity vertical test cryostat 2019 an official publ. of the International Association for Pattern Recognition Amsterdam [u.a.] (DE-627)ELV003173968 volume:100 year:2017 day:1 month:12 pages:104-109 extent:6 https://doi.org/10.1016/j.patrec.2017.10.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 52.43 Kältetechnik VZ 33.09 Physik unter besonderen Bedingungen VZ AR 100 2017 1 1201 104-109 6 045F 004 |
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10.1016/j.patrec.2017.10.003 doi GBV00000000000043A.pica (DE-627)ELV041147251 (ELSEVIER)S0167-8655(17)30365-3 DE-627 ger DE-627 rakwb eng 004 004 DE-600 660 VZ 52.43 bkl 33.09 bkl Wang, Wenqi verfasserin aut Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model 2017transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. Aggarwal, Vaneet oth Aeron, Shuchin oth Enthalten in Elsevier Jin, Shufeng ELSEVIER Thermal structure optimization of a supercondcuting cavity vertical test cryostat 2019 an official publ. of the International Association for Pattern Recognition Amsterdam [u.a.] (DE-627)ELV003173968 volume:100 year:2017 day:1 month:12 pages:104-109 extent:6 https://doi.org/10.1016/j.patrec.2017.10.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 52.43 Kältetechnik VZ 33.09 Physik unter besonderen Bedingungen VZ AR 100 2017 1 1201 104-109 6 045F 004 |
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10.1016/j.patrec.2017.10.003 doi GBV00000000000043A.pica (DE-627)ELV041147251 (ELSEVIER)S0167-8655(17)30365-3 DE-627 ger DE-627 rakwb eng 004 004 DE-600 660 VZ 52.43 bkl 33.09 bkl Wang, Wenqi verfasserin aut Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model 2017transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. Aggarwal, Vaneet oth Aeron, Shuchin oth Enthalten in Elsevier Jin, Shufeng ELSEVIER Thermal structure optimization of a supercondcuting cavity vertical test cryostat 2019 an official publ. of the International Association for Pattern Recognition Amsterdam [u.a.] (DE-627)ELV003173968 volume:100 year:2017 day:1 month:12 pages:104-109 extent:6 https://doi.org/10.1016/j.patrec.2017.10.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 52.43 Kältetechnik VZ 33.09 Physik unter besonderen Bedingungen VZ AR 100 2017 1 1201 104-109 6 045F 004 |
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10.1016/j.patrec.2017.10.003 doi GBV00000000000043A.pica (DE-627)ELV041147251 (ELSEVIER)S0167-8655(17)30365-3 DE-627 ger DE-627 rakwb eng 004 004 DE-600 660 VZ 52.43 bkl 33.09 bkl Wang, Wenqi verfasserin aut Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model 2017transfer abstract 6 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. Aggarwal, Vaneet oth Aeron, Shuchin oth Enthalten in Elsevier Jin, Shufeng ELSEVIER Thermal structure optimization of a supercondcuting cavity vertical test cryostat 2019 an official publ. of the International Association for Pattern Recognition Amsterdam [u.a.] (DE-627)ELV003173968 volume:100 year:2017 day:1 month:12 pages:104-109 extent:6 https://doi.org/10.1016/j.patrec.2017.10.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 52.43 Kältetechnik VZ 33.09 Physik unter besonderen Bedingungen VZ AR 100 2017 1 1201 104-109 6 045F 004 |
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Unsupervised clustering under the Union of Polyhedral Cones (UOPC) model |
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In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. |
| abstractGer |
In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. |
| abstract_unstemmed |
In this paper, we consider clustering data that is assumed to come from a union of finitely many pointed convex polyhedral cones. This model is referred to as the Union of Polyhedral Cones (UOPC) model. Similar to the Union of Subspaces (UOS) model where each data from each subspace is generated from a (unknown) basis, in the UOPC model each data from each cone is assumed to be generated from a finite number of (unknown) extreme rays. To cluster data under this model, we first build an affinity graph with the different edge weights where the edge weights are derived using a K-nearest neighbor (KNN) algorithm. Subsequently, spectral clustering is applied to obtain the clusters, and the proposed algorithm is denoted as KNN-SC. We show that on average KNN-SC outperforms Sparse Subspace Clustering by Non-negative constraints Lasso (NCL), Least squares approximation (LSA), Sparse Subspace Clustering (SSC), robust Subspace Clustering via Thresholding (TSC), and Mutual KNN based Spectral Clustering (KNNM-SC), and we provide deterministic conditions for correct clustering using KNN-SC. We show that on average KNN-SC outperforms NCL, LSA, SSC, TSC, and KNNM-SC, and we provide deterministic conditions for correct clustering using KNN-SC. For an affinity measure between the cones it is shown that as long as the cones are not very coherent and as long as the density of data within each cone exceeds a threshold, KNN-SC leads to accurate clustering. Finally, simulation results on real datasets (MNIST and CMU Motion datasets) depict that the proposed algorithm works well on real data indicating the utility of the UOPC model and the proposed algorithm. |
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