메뉴 건너뛰기




Volumn 4, Issue 4, 2008, Pages

Ordinal embeddings of minimum relaxation: General properties, trees, and ultrametrics

Author keywords

Distortion; Metrics; Ordinal embedding; Relaxation

Indexed keywords

DISTORTION; METRICS; ORDINAL EMBEDDING; RELAXATION; ULTRAMETRICS;

EID: 50849083491     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1383369.1383377     Document Type: Article
Times cited : (24)

References (35)
  • 1
    • 0032256591 scopus 로고    scopus 로고
    • On the approximability of numerical taxonomy (fitting distances by tree metrics)
    • AGARWALA. R., BAFNA, V., FARACH, M., PATERSON, M., AND THORUP, M. 1999. On the approximability of numerical taxonomy (fitting distances by tree metrics). SIAM J. Comput. 283, 1073-1085.
    • (1999) SIAM J. Comput , vol.28 , Issue.3 , pp. 1073-1085
    • AGARWALA, R.1    BAFNA, V.2    FARACH, M.3    PATERSON, M.4    THORUP, M.5
  • 2
    • 0003359872 scopus 로고
    • Tools from higher algebra
    • R. L. Graham, M. Grötschel, and L. Lovász, Eds. MIT Press, Chap. 32, 1995
    • ALON, N. 1995. Tools from higher algebra. In Handbook of Combinatorics, R. L. Graham, M. Grötschel, and L. Lovász, Eds. Vol. 2. MIT Press, Chap. 32. 1749-1783.
    • (1749) Handbook of Combinatorics , vol.2
    • ALON, N.1
  • 4
    • 85137969404 scopus 로고    scopus 로고
    • BABILON, R., MATOUŠEK, J., MAXOVÁ , J., AND VALTR, P. 2003. Low-distortion embeddings of trees. J. Graph Algor. Appl. 7, 4, 399-409.
    • BABILON, R., MATOUŠEK, J., MAXOVÁ , J., AND VALTR, P. 2003. Low-distortion embeddings of trees. J. Graph Algor. Appl. 7, 4, 399-409.
  • 8
    • 20744455736 scopus 로고    scopus 로고
    • Monotone maps, sphericity and bounded second eigenvalue
    • arXiv:math.CO/0401293
    • BILU, Y., AND LINIAL, N. 2004. Monotone maps, sphericity and bounded second eigenvalue. arXiv:math.CO/0401293.
    • (2004)
    • BILU, Y.1    LINIAL, N.2
  • 9
    • 51249178997 scopus 로고
    • On Lipschitz embedding of finite metric spaces in Hilbert space
    • BOURGAIN, J. 1985. On Lipschitz embedding of finite metric spaces in Hilbert space. Israel J. Math. 52, 1-2, 46-52.
    • (1985) Israel J. Math , vol.52 , Issue.1-2 , pp. 46-52
    • BOURGAIN, J.1
  • 13
    • 0003593943 scopus 로고    scopus 로고
    • A geometric approach to betweennes
    • CHOR. B., AND SUDAN, M. 1998. A geometric approach to betweennes. SIAM J. Discrete Math. 114, 511-523.
    • (1998) SIAM J. Discrete Math , vol.11 , Issue.4 , pp. 511-523
    • CHOR, B.1    SUDAN, M.2
  • 14
    • 0008917762 scopus 로고
    • Monotone mapping of similarities into a general metric space
    • CUNNINGHAM, J. P., AND SHEPARD, R. N. 1974. Monotone mapping of similarities into a general metric space. J. Math. Psych. 11, 335-364.
    • (1974) J. Math. Psych , vol.11 , pp. 335-364
    • CUNNINGHAM, J.P.1    SHEPARD, R.N.2
  • 15
    • 50849097799 scopus 로고    scopus 로고
    • ERDOS, P., AND SACHS. H. 1963. Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl. Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 12, 251-257.
    • ERDOS, P., AND SACHS. H. 1963. Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl. Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 12, 251-257.
  • 16
    • 0000161374 scopus 로고    scopus 로고
    • Efficient algorithms for inverting evolution
    • FARACH, M., AND KANNAN, S. 1999. Efficient algorithms for inverting evolution. J. ACM 46, 4, 437-449.
    • (1999) J. ACM , vol.46 , Issue.4 , pp. 437-449
    • FARACH, M.1    KANNAN, S.2
  • 17
    • 0029192324 scopus 로고
    • A robust model for finding optimal evolutionary trees
    • FARACH, M., KANNAN, S., AND WARNOW, T. 1995. A robust model for finding optimal evolutionary trees. Algorithmica 13, 1-2, 155-179.
    • (1995) Algorithmica , vol.13 , Issue.1-2 , pp. 155-179
    • FARACH, M.1    KANNAN, S.2    WARNOW, T.3
  • 18
    • 0034389097 scopus 로고    scopus 로고
    • Embedding tree metrics into low-dimensional Euclidean spaces
    • GUPTA, A. 2000. Embedding tree metrics into low-dimensional Euclidean spaces. Discrete Comput. Geom. 24, 1, 105-116.
    • (2000) Discrete Comput. Geom , vol.24 , Issue.1 , pp. 105-116
    • GUPTA, A.1
  • 19
    • 84974054501 scopus 로고
    • The number of partitions of a set of Npoints in kdimensions induced by hyperplanes
    • Series II
    • HARDING. E. F. 1966/1967. The number of partitions of a set of Npoints in kdimensions induced by hyperplanes. Proceedings of the Edinburgh Mathematical Society, Series II 15285-289.
    • (1966) Proceedings of the Edinburgh Mathematical Society , vol.15 , pp. 285-289
    • HARDING, E.F.1
  • 20
    • 10744229030 scopus 로고    scopus 로고
    • Fitting points on the real line and its application to RH mapping
    • HÅSTAD, J., IVANSSON, L., AND LAGERGREN, J. 2003. Fitting points on the real line and its application to RH mapping. J. Algor. 49, 62, 42-62.
    • (2003) J. Algor , vol.49 , Issue.62 , pp. 42-62
    • HÅSTAD, J.1    IVANSSON, L.2    LAGERGREN, J.3
  • 21
    • 0039419498 scopus 로고
    • The relation between hierarchical and euclidean models for psychological distances
    • HOLMAN, W. 1972. The relation between hierarchical and euclidean models for psychological distances. Psychometrika 37, 4, 417-423.
    • (1972) Psychometrika , vol.37 , Issue.4 , pp. 417-423
    • HOLMAN, W.1
  • 22
    • 4544370554 scopus 로고    scopus 로고
    • Low-distortion embeddings of finite metric spaces
    • 2nd Ed, J. E. Goodman and J. O'Rourke, Eds. CRC Press, Chap. 8, 177-196
    • INDYK, P., AND MATOUŠEK, J. 2004. Low-distortion embeddings of finite metric spaces. In Handbook of Discrete and Computational Geometry, 2nd Ed., J. E. Goodman and J. O'Rourke, Eds. CRC Press, Chap. 8, 177-196.
    • (2004) Handbook of Discrete and Computational Geometry
    • INDYK, P.1    MATOUŠEK, J.2
  • 23
    • 0038776464 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Numerical Analysis and Computer Science, Royal Institute of Technology
    • IVANSSON, L. 2000. Computational aspects of radiation hybrid. Ph.D. thesis, Department of Numerical Analysis and Computer Science, Royal Institute of Technology.
    • (2000) Computational aspects of radiation hybrid
    • IVANSSON, L.1
  • 24
    • 0001654702 scopus 로고
    • Extensions of lipshitz mapping into hilbert space
    • JOHNSON, W. B., AND LINDENSTRAUSS, J. 1984. Extensions of lipshitz mapping into hilbert space. Contemp. Math. 26, 189-206.
    • (1984) Contemp. Math , vol.26 , pp. 189-206
    • JOHNSON, W.B.1    LINDENSTRAUSS, J.2
  • 25
    • 0041654220 scopus 로고
    • Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
    • KRUSKAL, J. B. 1964a. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika 29, 1-28.
    • (1964) Psychometrika , vol.29 , pp. 1-28
    • KRUSKAL, J.B.1
  • 26
    • 24944533365 scopus 로고
    • Non-metric multidimensional scaling
    • KRUSKAL, J. B. 1964b. Non-metric multidimensional scaling. Psychometrika 29, 115-129.
    • (1964) Psychometrika , vol.29 , pp. 115-129
    • KRUSKAL, J.B.1
  • 28
    • 0000652415 scopus 로고
    • The geometry of graphs and some of its algorithmic applications
    • LINIAL, N., LONDON, E., AND RABINOVICH, Y. 1995. The geometry of graphs and some of its algorithmic applications. Combinatorica 15, 2, 215-245.
    • (1995) Combinatorica , vol.15 , Issue.2 , pp. 215-245
    • LINIAL, N.1    LONDON, E.2    RABINOVICH, Y.3
  • 29
    • 0001438129 scopus 로고
    • Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
    • MATOUŠEK, J. 1990. Bi-Lipschitz embeddings into low-dimensional Euclidean spaces. Commentationes Mathematicae Universitatis Carolinae 31, 3, 589-600.
    • (1990) Commentationes Mathematicae Universitatis Carolinae , vol.31 , Issue.3 , pp. 589-600
    • MATOUŠEK, J.1
  • 31
    • 0342765582 scopus 로고
    • Total ordering problem
    • OPATRNY, J. 1979. Total ordering problem. SIAM J. Comput. 8, 111-114.
    • (1979) SIAM J. Comput , vol.8 , pp. 111-114
    • OPATRNY, J.1
  • 32
    • 20744443876 scopus 로고    scopus 로고
    • On the complexity of ordinal clustering
    • To appear
    • SHAH, R., AND FARACH-COLTON, M. 2004. On the complexity of ordinal clustering. J. Classification, To appear.
    • (2004) J. Classification
    • SHAH, R.1    FARACH-COLTON, M.2
  • 33
    • 34250926052 scopus 로고
    • Multidimensional scaling with unknown distance function I
    • SHEPARD. R. N. 1962. Multidimensional scaling with unknown distance function I. Psychometrika 27125-140.
    • (1962) Psychometrika , vol.27 , pp. 125-140
    • SHEPARD, R.N.1
  • 34
    • 84950351930 scopus 로고
    • Multidimensional scaling I: Theory and method
    • TORGERSON, W. S. 1952. Multidimensional scaling I: Theory and method. Psychometrika 17, 4, 401-414.
    • (1952) Psychometrika , vol.17 , Issue.4 , pp. 401-414
    • TORGERSON, W.S.1
  • 35
    • 84968495010 scopus 로고
    • Lower bounds for approximation by nonlinear manifolds
    • WARREN, H. E. 1968. Lower bounds for approximation by nonlinear manifolds. Trans. Amer. Math. Soc. 133, 167-178.
    • (1968) Trans. Amer. Math. Soc , vol.133 , pp. 167-178
    • WARREN, H.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.