Abstract The traditional Isomap algorithm emphasizes analyzing the manifold structure of the existing dataset. It can not provide fast and direct mapping of a new sample from high dimensional space to low dimensional space, so the traditional Isomap algorithm can not be used for feature extraction and high-dimensional data retrieval. In this paper, a fast mapping Isomap algorithm is proposed, by which the low-dimensional coordinates of a new sample can be calculated with relatively low computational complexity, and the most similar sample of the query sample can be retrieved based on such low-dimensional coordinates. Experimental results on typical benchmark datasets demonstrate that the proposed algorithm accomplishes the task of fast mapping with well preserving of the neighborhood relationship.
[1] Tenenbaum J B, vin de Silva, Langford J C. A Global Geometric Framework for Nonlinear Dimension Reduction. Science, 2000, 290(5500): 2319-2323 [2] Borg I, Groenen P. Modern Multidimensional Scaling: Theory and Application. New York, USA: Springer, 1997 [3] vin de Silva, Tenenbaum J B. Global versus Local Methods in Nonlinear Dimensionality Reduction // Becker S, Thrun S, Obermayer K, eds. Advances in Neural Information Processing Systems. Cambridge, USA: MIT Press, 2003, 15: 705-712 [4] Li Chunguang, Guo Jun, Nie Xiangfei. Learning Geodesic Metric for Out-of-Sample Extension of Isometric Embedding // Proc of the International Conference on Computational Intelligence and Security. Guangzhou, China, 2006: 449-452 [5] Law M H C, Jain A K. Incremental Nonlinear Dimensionality Reduction by Manifold Learning. IEEE Trans on Pattern Analysis and Machine Intelligence, 2006, 28(3): 377-391 [6] Shi Lukui, He Pilian, Liu Enhai. An Incremental Nonlinear Dimensionality Reduction Algorithm Based on Isomap // Proc of the 18th Australian Conference on Artificial Intelligence. Sydney, Australia, 2005: 892- 895 [7] vin de Silva, Tenenbaum J B. Sparse Multidimensional Scaling Using Landmark Points. Technical Report, Stanford, USA: Stanford University. Department of Mathematics, 2004 [8] Su K, Qi T, Qing X, et al. Neighborhood Issue in Single-Frame Image Super-Resolution // Proc of the IEEE International Conference on Multimedia and Exposition. Amsterdam, Netherlands, 2005: 1122-1125
2009, Vol. 22 
