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Volumn 39, Issue 11, 2017, Pages 2227-2241

Principal Graph and Structure Learning Based on Reversed Graph Embedding

Author keywords

Principal curve; principal graph; structure learning

Indexed keywords

GRAPHIC METHODS; LEARNING ALGORITHMS;

EID: 85032304080     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2016.2635657     Document Type: Article
Times cited : (58)

References (59)
  • 4
    • 0036794475 scopus 로고    scopus 로고
    • Principal curves with bounded turn
    • Oct.
    • S. Sandilya and S. R. Kulkami, "Principal curves with bounded turn," IEEE Trans. Inf. Theory, vol. 48, no. 10, pp. 2789-2793, Oct. 2002.
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.10 , pp. 2789-2793
    • Sandilya, S.1    Kulkami, S.R.2
  • 6
    • 33846255123 scopus 로고
    • Principal curves revisited
    • R. Tibshirani, "Principal curves revisited," Statist. Comput., vol. 2, pp. 183-190, 1992.
    • (1992) Statist. Comput. , vol.2 , pp. 183-190
    • Tibshirani, R.1
  • 7
    • 0347963789 scopus 로고    scopus 로고
    • GTM: The generative topographic mapping
    • C. M. Bishop, M. Svensén, and C. K. I. Williams, "GTM: The generative topographic mapping," Neural Comput., vol. 10, no. 1, pp. 215-234, 1998.
    • (1998) Neural Comput. , vol.10 , Issue.1 , pp. 215-234
    • Bishop, C.M.1    Svensén, M.2    Williams, C.K.I.3
  • 8
    • 0008864273 scopus 로고    scopus 로고
    • Ph.D. dissertation, Dept. Comput. Sci., Concordia Univ., Montreal, Quebec, Canada
    • B. Kégl, "Principal curve: Learning, design, and applications," Ph.D. dissertation, Dept. Comput. Sci., Concordia Univ., Montreal, Quebec, Canada, 1999.
    • (1999) Principal Curve: Learning, Design, and Applications
    • Kégl, B.1
  • 10
    • 24644477028 scopus 로고    scopus 로고
    • Elastic principal graphs and manifold and their practical applications
    • A. Gorban and A. Y. Zinovyev, "Elastic principal graphs and manifold and their practical applications," Computing, vol. 75, no. 4, pp. 359-379, 2006.
    • (2006) Computing , vol.75 , Issue.4 , pp. 359-379
    • Gorban, A.1    Zinovyev, A.Y.2
  • 12
    • 0026436795 scopus 로고
    • Self-organizing maps: Ordering, convergence properties and energy functions
    • E. Erwin, K. Obermayer, and K. Schulten, "Self-organizing maps: Ordering, convergence properties and energy functions," Biol. Cybern., vol. 67, pp. 47-55, 1992.
    • (1992) Biol. Cybern. , vol.67 , pp. 47-55
    • Erwin, E.1    Obermayer, K.2    Schulten, K.3
  • 13
    • 79955813270 scopus 로고    scopus 로고
    • Locally defined principal curves and surfaces
    • U. Ozertem and D. Erdogmus, "Locally defined principal curves and surfaces," J. Mach. Learn. Res., vol. 12, pp. 1249-1286, 2011.
    • (2011) J. Mach. Learn. Res. , vol.12 , pp. 1249-1286
    • Ozertem, U.1    Erdogmus, D.2
  • 14
    • 0036223199 scopus 로고    scopus 로고
    • Piecewise linear skeletonization using principal curves
    • Jan.
    • B. Kégl and A. Kryzak, "Piecewise linear skeletonization using principal curves," IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 1, pp. 59-74, Jan. 2002.
    • (2002) IEEE Trans. Pattern Anal. Mach. Intell. , vol.24 , Issue.1 , pp. 59-74
    • Kégl, B.1    Kryzak, A.2
  • 15
    • 35148855702 scopus 로고    scopus 로고
    • Fingerprint minutiae extraction based on principal curves
    • D. Miao, Q. Tang, and W. Fu, "Fingerprint minutiae extraction based on principal curves," Pattern Recognit. Lett., vol. 28, no. 16, pp. 2184-2189, 2007.
    • (2007) Pattern Recognit. Lett. , vol.28 , Issue.16 , pp. 2184-2189
    • Miao, D.1    Tang, Q.2    Fu, W.3
  • 16
    • 33751217172 scopus 로고    scopus 로고
    • Topological grammars for data approximation
    • A. Gorban, N. Sumner, and A. Zinovyev, "Topological grammars for data approximation," Appl. Math. Lett., vol. 20, no. 4, pp. 382-386, 2007.
    • (2007) Appl. Math. Lett. , vol.20 , Issue.4 , pp. 382-386
    • Gorban, A.1    Sumner, N.2    Zinovyev, A.3
  • 17
    • 0016900245 scopus 로고
    • Formal languages of labelled graphs
    • M. Nagl, "Formal languages of labelled graphs," Computing, vol. 16, no. 1/2, pp. 113-137, 1976.
    • (1976) Computing , vol.16 , Issue.1-2 , pp. 113-137
    • Nagl, M.1
  • 18
    • 0027558267 scopus 로고
    • Algebraic approach to single-pushout graph transformation
    • M. Löwe, "Algebraic approach to single-pushout graph transformation," Theoretical Comput. Sci., vol. 109, no. 1/2, pp. 181-224, 1993.
    • (1993) Theoretical Comput. Sci. , vol.109 , Issue.1-2 , pp. 181-224
    • Löwe, M.1
  • 19
    • 77953697253 scopus 로고    scopus 로고
    • Principal manifolds and graphs in practice: From molecular biology to dynamical systems
    • A. N. Gorban and A. Zinovyev, "Principal manifolds and graphs in practice: From molecular biology to dynamical systems," Int. J. Neural Syst., vol. 20, no. 3, pp. 219-232, 2010.
    • (2010) Int. J. Neural Syst. , vol.20 , Issue.3 , pp. 219-232
    • Gorban, A.N.1    Zinovyev, A.2
  • 20
    • 70049091784 scopus 로고    scopus 로고
    • Topology and data
    • G. Carlsson, "Topology and data," Bulletin Amer. Math. Soc., vol. 46, no. 2, pp. 255-308, 2009.
    • (2009) Bulletin Amer. Math. Soc. , vol.46 , Issue.2 , pp. 255-308
    • Carlsson, G.1
  • 22
    • 84872330038 scopus 로고    scopus 로고
    • Reeb graphs: Approximation and persistence
    • T. K. Dey and Y. Wang, "Reeb graphs: Approximation and persistence," Discr. Comput. Geom., vol. 49, no. 1, pp. 46-73, 2013.
    • (2013) Discr. Comput. Geom. , vol.49 , Issue.1 , pp. 46-73
    • Dey, T.K.1    Wang, Y.2
  • 24
    • 79955561607 scopus 로고    scopus 로고
    • Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival
    • M. Nicolau, A. J. Levine, and G. Carlsson, "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival," Proc. Nat. Academy Sci. United States America, vol. 108, no. 17, pp. 7265-7270, 2011.
    • (2011) Proc. Nat. Academy Sci. United States America , vol.108 , Issue.17 , pp. 7265-7270
    • Nicolau, M.1    Levine, A.J.2    Carlsson, G.3
  • 32
    • 85030460212 scopus 로고    scopus 로고
    • A unified probabilistic framework for robust manifold learning and embedding
    • Q. Mao, L. Wang, and I. W. Tsang, "A unified probabilistic framework for robust manifold learning and embedding," Mach. Learn., 2016.
    • (2016) Mach. Learn.
    • Mao, Q.1    Wang, L.2    Tsang, I.W.3
  • 36
    • 33750743381 scopus 로고    scopus 로고
    • An introduction to nonlinear dimensionality reduction by maximum variance unfolding
    • K. Q. Weinberger and L. K. Saul, "An introduction to nonlinear dimensionality reduction by maximum variance unfolding," in Proc. 21st Nat. Conf. Artif. Intell.-Vol. 2, 2006, pp. 1683-1686.
    • (2006) Proc. 21st Nat. Conf. Artif. Intell.-Vol. 2 , pp. 1683-1686
    • Weinberger, K.Q.1    Saul, L.K.2
  • 38
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • J. B. Tenenbaum, V. de Silva, and J. C. Landford, "A global geometric framework for nonlinear dimensionality reduction," Science, vol. 290, pp. 2319-2323, 2000.
    • (2000) Science , vol.290 , pp. 2319-2323
    • Tenenbaum, J.B.1    De Silva, V.2    Landford, J.C.3
  • 39
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • S. T. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science, vol. 290, no. 5500, pp. 2323-2326, 2000.
    • (2000) Science , vol.290 , Issue.5500 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 40
    • 84856013431 scopus 로고    scopus 로고
    • Clonal evolution in cancer
    • M. Greaves and C. C. Maley, "Clonal evolution in cancer," Nature, vol. 481, no. 7381, pp. 306-313, 2012.
    • (2012) Nature , vol.481 , Issue.7381 , pp. 306-313
    • Greaves, M.1    Maley, C.C.2
  • 41
    • 84964315153 scopus 로고    scopus 로고
    • Cancer progression modeling using static sample data
    • Y. Sun, J. Yao, N. Nowak, and S. Goodison, "Cancer progression modeling using static sample data," Genome Biol., vol. 15, no. 8, 2014, Art. no. 440.
    • (2014) Genome Biol. , vol.15 , Issue.8
    • Sun, Y.1    Yao, J.2    Nowak, N.3    Goodison, S.4
  • 42
    • 0029357425 scopus 로고
    • Mean shift, mode seeking, and clustering
    • Aug.
    • Y. Cheng, "Mean shift, mode seeking, and clustering," IEEE Trans. Pattern Anal. Mach. Intell., vol. 17, no. 8, pp. 790-799, Aug. 1995.
    • (1995) IEEE Trans. Pattern Anal. Mach. Intell. , vol.17 , Issue.8 , pp. 790-799
    • Cheng, Y.1
  • 43
    • 70350674995 scopus 로고
    • On the shortest spanning subtree of a graph and the traveling salesman problem
    • J. B. Kruskal, "On the shortest spanning subtree of a graph and the traveling salesman problem," Proc. Amer. Math. Soc., vol. 7, pp. 48-50, 1958.
    • (1958) Proc. Amer. Math. Soc. , vol.7 , pp. 48-50
    • Kruskal, J.B.1
  • 44
    • 84954160188 scopus 로고    scopus 로고
    • [Online]
    • M. Cheung, "Minimum-cost spanning trees," (2008). [Online]. Available: http://people.orie.cornell.edu/dpw/orie6300/fall2008/Recitations/rec09.pdf
    • (2008) Minimum-cost Spanning Trees
    • Cheung, M.1
  • 46
    • 36348960733 scopus 로고    scopus 로고
    • Biconvex sets and optimization with biconvex functions-A survey and extensions
    • J. Gorski, F. Pfeuffer, and K. Klamroth, "Biconvex sets and optimization with biconvex functions-A survey and extensions," Math. Methods Operations Res., vol. 66, pp. 373-407, 2007.
    • (2007) Math. Methods Operations Res. , vol.66 , pp. 373-407
    • Gorski, J.1    Pfeuffer, F.2    Klamroth, K.3
  • 47
    • 0001614864 scopus 로고    scopus 로고
    • The mosek interior point optimizer for linear programming: An implementation of the homogeneous algorithm
    • Berlin, Germany: Springer
    • E. D. Andersen and K. D. Andersen, "The mosek interior point optimizer for linear programming: An implementation of the homogeneous algorithm," in High Performance Optimization. Berlin, Germany: Springer, 2000, pp. 197-232.
    • (2000) High Performance Optimization , pp. 197-232
    • Andersen, E.D.1    Andersen, K.D.2
  • 50
    • 79955830804 scopus 로고    scopus 로고
    • A family of simple nonparametric kernel learning algorithms
    • J. Zhuang, I. W. Tsang, and S. C. Hoi, "A family of simple nonparametric kernel learning algorithms," J. Mach. Learn. Res., vol. 12, pp. 1313-1347, 2011.
    • (2011) J. Mach. Learn. Res. , vol.12 , pp. 1313-1347
    • Zhuang, J.1    Tsang, I.W.2    Hoi, S.C.3
  • 52
    • 80055037608 scopus 로고    scopus 로고
    • Large scale spectral clustering with landmark-based representation
    • X. Chen and D. Cai, "Large scale spectral clustering with landmark-based representation," in Proc. 25th AAAI Conf. Artif. Intell., 2011, pp. 313-318.
    • (2011) Proc. 25th AAAI Conf. Artif. Intell. , pp. 313-318
    • Chen, X.1    Cai, D.2
  • 54
    • 84860672647 scopus 로고    scopus 로고
    • Sampling method for the Nyström method
    • S. Kumar, M. Mohri, and A. Talwalkar, "Sampling method for the Nyström method," J. Mach. Learn. Res., vol. 13, pp. 981-1006, 2012.
    • (2012) J. Mach. Learn. Res. , vol.13 , pp. 981-1006
    • Kumar, S.1    Mohri, M.2    Talwalkar, A.3
  • 56
    • 77954603019 scopus 로고    scopus 로고
    • A framework for feature selection in clustering
    • D. M. Witten and R. Tibshirani, "A framework for feature selection in clustering," J. Royal Statistical Soc., vol. 105, no. 490, pp. 713-726, 2010.
    • (2010) J. Royal Statistical Soc. , vol.105 , Issue.490 , pp. 713-726
    • Witten, D.M.1    Tibshirani, R.2
  • 57
    • 84861527388 scopus 로고    scopus 로고
    • The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups
    • C. Curtis, et al., "The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups," Nature, vol. 486, no. 7403, pp. 346-352, 2012.
    • (2012) Nature , vol.486 , Issue.7403 , pp. 346-352
    • Curtis, C.1
  • 58
    • 62449131093 scopus 로고    scopus 로고
    • Supervised risk predictor of breast cancer based on intrinsic subtypes
    • J. Parker, et al., "Supervised risk predictor of breast cancer based on intrinsic subtypes," J. Clinical Oncology, vol. 27, no. 8, pp. 1160-1167, 2009.
    • (2009) J. Clinical Oncology , vol.27 , Issue.8 , pp. 1160-1167
    • Parker, J.1
  • 59
    • 84866756366 scopus 로고    scopus 로고
    • The molecular profile of luminal B breast cancer
    • C. J. Creighton, et al., "The molecular profile of luminal B breast cancer," Biologics, vol. 6, no. 2, pp. 289-297, 2012.
    • (2012) Biologics , vol.6 , Issue.2 , pp. 289-297
    • Creighton, C.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.