Optimized ISOMAP algorithm using similarity matrix

Dimension reduction techniques are used to obtain a reduced representation of the data that maintains the integrity of the original data. ISOMAP (Isometric Feature Mapping) is one of the dimension reduction techniques, which is a nonlinear generalization of Classical MDS (Multi-Dimensional Scaling) and works well both for real world and artificial data. It uses k-nearest neighbors concept for creating the neighborhood graph. In this paper, we have considered the similarity among data points as another approach for constructing the neighborhood graph, instead of using the concept of k-nearest neighbors.

[1]  Kap Luk Chan,et al.  An extended Isomap algorithm for learning multi-class manifold , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).

[2]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[3]  Ming-Hsuan Yang,et al.  Extended isomap for pattern classification , 2002, AAAI/IAAI.

[4]  Miguel Á. Carreira-Perpiñán,et al.  Continuous latent variable models for dimensionality reduction and sequential data reconstruction , 2001 .

[5]  Joydeep Ghosh,et al.  Improved Nonlinear Manifold Learning for Land Cover Classification via Intelligent Landmark Selection , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.