The Hierarchical Isometric Self-Organizing Map for Manifold Representation

We present an algorithm, Hierarchical ISOmetric SelfOrganizing Map (H-ISOSOM), for a concise, organized manifold representation of complex, non-linear, large scale, high-dimensional input data in a low dimensional space. The main contribution of our algorithm is threefold. First, we modify the previous ISOSOM algorithm by a local linear interpolation (LLI) technique, which maps the data samples from low dimensional space back to high dimensional space and makes the complete mapping pseudo-invertible. The modified-ISOSOM (M-ISOSOM) follows the global geometric structure of the data, and also preserves local geometric relations to reduce the nonlinear mapping distortion and make the learning more accurate. Second, we propose the H-ISOSOM algorithm for the computational complexity problem of Isomap, SOM and LLI and the nonlinear complexity problem of the highly twisted manifold. H-ISOSOM learns an organized structure of a non-convex, large scale manifold and represents it by a set of hie...

• Type: Conference
• Year: 2007
• Where: CVPR
• Authors: Haiying Guan, Matthew Turk
• Keywords: Coarse Global Structure, Computer Vision, CVPR 2007, Hierarchical Organized Maps, Large Scale Manifold, Low Dimensional Space, Nonlinear Complexity Problem