Incremental isometric embedding of high-dimensional data using connected neighborhood graphs

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 31, Issue 1, 2009, Pages 86-98

  Zhao, Dongfang ^a   Yang, Li ^b  

^a Distribution and Marketing Inc   (United States)

^b Parkview Campus   (United States)

Author keywords

Data mining; Database applications; Database management; Design methodology; Discrete mathematics; Feature evaluation and selection; Geometric; Graph algorithms; Graph theory; Models; Pattern recognition; Statistical

Indexed keywords

ADMINISTRATIVE DATA PROCESSING; CLUSTERING ALGORITHMS; DATA MINING; DATABASE SYSTEMS; DECISION SUPPORT SYSTEMS; FEATURE EXTRACTION; GRAPH THEORY; INFORMATION MANAGEMENT; MANAGEMENT INFORMATION SYSTEMS; PATTERN RECOGNITION; TOPOLOGY;

DATABASE APPLICATIONS; DATABASE MANAGEMENT; DESIGN METHODOLOGY; DISCRETE MATHEMATICS; FEATURE EVALUATION AND SELECTION; GEOMETRIC; GRAPH ALGORITHMS; STATISTICAL;

TREES (MATHEMATICS);

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER SIMULATION; METHODOLOGY; THEORETICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; MODELS, THEORETICAL; PATTERN RECOGNITION, AUTOMATED;

EID: 57149123782     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2008.34     Document Type: Article

References (28)

1. G. Ausiello, G.F. Italiano, A.M. Spaccamela, and U. Nanni, "On-Line Computation of Minimal and Maximal Length Paths," Theoretical Computer Science, vol. 95, no. 2, pp. 245-261, Mar. 1992.
2. J.A. Blakeley, P.-A. Larson, and F.W. Tompa, "Efficiently Updating Materialized Views," Proc. ACM SIGMOD '86, pp. 61-71, May 1986.
3. A.L. Buchsbaum, P.C. Kanellakis, and J.S. Vitter, "A Data Structure for Arc Insertion and Regular Path Finding," Proc. First Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 22-31, 1990.
4. F. Chin and D. Houck, "Algorithms for Updating Minimal Spanning Trees," J. Computer and System Sciences, vol. 16, no. 3, pp. 333-344, 1978.
5. T.F. Cox and M.A.A. Cox, Multidimensional Scaling, second ed. Chapman Hall, 2001.
6. P. Demartines and J. Herault, "Curvilinear Component Analysis: A Self-Organizing Neural Network for Nonlinear Mapping of Data Sets," IEEE Trans. Neural Networks, vol. 8, no. 1, pp. 148-154, Jan. 1997.
7. G. Dong and R. Topor, "Incremental Evaluation of Datalog Queries," Proc. Fourth Int'l Conf. Database Theory, pp. 282-296, Oct. 1992.
8. S. Even and H. Gazit, "Updating Distances in Dynamic Graphs," Methods of Operations Research, vol. 49, pp. 371-387, 1985.
9. L.R. Ford and D.R. Fulkerson, Flows in Networks. Princeton Univ. Press, 1962.
10. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, 1979.
11. G.H. Golub and C.F.V. Loan, Matrix Computations. Johns Hopkins Univ. Press, 1996.
12. J.V. Harrison and S.W. Dietrich, "Maintenance of Materialized Views in a Deductive Database: An Update Propagation Approach," Proc. JICSLP Workshop Deductive Databases, pp. 56-65, 1992.
13. J. Kruskal, "Multidimensional Scaling by Optimizing Goodnessof-Fit to a Nonmetric Hypothesis," Psychometrika, vol. 29, pp. 1-27, 1964.
14. J. Kruskal, "Comments on a Nonlinear Mapping for Data Structure Analysis," IEEE Trans. Computers, vol. 20, no. 12, p. 1614, Dec. 1971.
15. M.H.C. Law and A.K. Jain, "Incremental Nonlinear Dimensionality Reduction by Manifold Learning," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 3, pp. 377-391, Mar. 2006.
16. J.A. Lee, A. Lendasse, N. Donckers, and M. Verleysen, "A Robust Nonlinear Projection Method," Proc. Eighth European Symp. Artificial Neural Networks, pp. 13-20, Apr. 2000.
17. D. Matula, "k-Blocks and Ultrablocks in Graphs," J. Combinatorial Theory B, vol. 24, no. 1, pp. 1-13, Feb. 1978.
18. C. Pang, G. Dong, and K. Ramamohanarao, "Incremental Maintenance of Shortest Distance and Transitive Closure in First-Order Logic and SQL," ACM Trans. Database Systems, vol. 30, no. 3, pp. 698-721, Sept. 2005.
19. S.T. Roweis and L.K. Saul, "Nonlinear Dimensionality Reduction by Locally Linear Embedding," Science, vol. 290, pp. 2323-2326, Dec. 2000.
20. J.J.W. Sammon, "A Nonlinear Mapping for Data Structure Analysis," IEEE Trans. Computers, vol. 18, no. 5, pp. 401-409, May 1969.
21. O. Shmueli and A. Itai, "Maintenance of Views," Proc. ACM SIGMOD '84, pp. 240-255, June 1984.
22. P.M. Spira and A. Pan, "On Finding and Updating Spanning Trees and Shortest Paths," SIAM J. Computing, vol. 4, no. 3, pp. 2015-2021, Sept. 1975.
23. R.R. Tarjan, "Testing Graph Connectivity," Proc. Sixth Ann. ACM Symp. Theory of Computing, pp. 185-193, 1974.
24. J.B. Tenenbaum, V. de Silva, and J.C. Langford, "A Global Geometric Framework for Nonlinear Dimensionality Reduction," Science, vol. 290, pp. 2319-2323, Dec. 2000.
25. L. Yang, "k-Edge Connected Neighborhood Graph for Geodesic Distance Estimation and Nonlinear Data Projection," Proc. 17th Int'l Conf. Pattern Recognition, vol. 1, pp. 196-199, Aug. 2004.
26. L. Yang, "Building k-Edge-Connected Neighborhood Graphs for Distance-Based Data Projection," Pattern Recognition Letters, vol. 26, no. 13, pp. 2015-2021, Oct. 2005.
27. L. Yang, "Building k Edge-Disjoint Spanning Trees of Minimum Total Length for Isometric Data Embedding," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 10, pp. 1680-1683, Oct. 2005.
28. L. Yang, "Building k-Connected Neighborhood Graphs for Isometric Data Embedding," IEEE Trans. Pattern Analysis and Machine Intelligence vol. 28, no. 5, pp. 827-831, May 2006.