An improved Isomap method for manifold learning
International Journal of Intelligent Computing and Cybernetics
ISSN: 1756-378X
Article publication date: 13 March 2017
Abstract
Purpose
Isometric feature mapping (Isomap) is a very popular manifold learning method and is widely used in dimensionality reduction and data visualization. The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph. The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths. The purpose of this paper is to speed up Isomap.
Design/methodology/approach
Through theoretical analysis, it is found that the neighbourhood graph in Isomap is sparse. In this case, the Dijkstra’s algorithm with Fibonacci heap (Fib-Dij) is faster than Floyd’s algorithm. In this paper, an improved Isomap method based on Fib-Dij is proposed. By using Fib-Dij to replace Floyd’s algorithm, an improved Isomap method is presented in this paper.
Findings
Using the S-curve, the Swiss-roll, the Frey face database, the mixed national institute of standards and technology database of handwritten digits and a face image database, the performance of the proposed method is compared with C-Isomap, showing the consistency with C-Isomap and marked improvements in terms of the high speed. Simulations also demonstrate that Fib-Dij reduces the computation time of the shortest paths from O(N3) to O(N2lgN).
Research limitations/implications
Due to the limitations of the computer, the sizes of the data sets in this paper are all smaller than 3,000. Therefore, researchers are encouraged to test the proposed algorithm on larger data sets.
Originality/value
The new method based on Fib-Dij can greatly improve the speed of Isomap.
Keywords
Acknowledgements
This work is supported by the National Natural Science Foundation of China under Grant Nos 91220301, 61273314 and 61175064.
Citation
Qu, T. and Cai, Z. (2017), "An improved Isomap method for manifold learning", International Journal of Intelligent Computing and Cybernetics, Vol. 10 No. 1, pp. 30-40. https://doi.org/10.1108/IJICC-03-2016-0014
Publisher
:Emerald Publishing Limited
Copyright © 2017, Emerald Publishing Limited