Incremental ISOMAP

The information of incremental ISOMAP is in this page. Currently, this page is under construction.

See also the manifold learning page.

Papers

• M. H. Law, A. K. Jain. Incremental Nonlinear Dimensionality Reduction By Manifold Learning. Accepted by IEEE Transactions of Pattern Analysis and Machine Intelligence.
• M. H. Law, N. Zhang, A. K. Jain. Nonlinear Manifold Learning for Data Stream. Proceedings of SIAM Data Mining, pp. 33-44, Orlando, Florida, 2004.
• An expanded proof for the algorithm

Software

Currently, we are working towards a version of our software that can be released on the web. Before this happens, you are welcome to request a preliminary version of our incremental ISOMAP implementation. Please contact Martin Law for this.

Be warned, though, that the code in its current state is not well-documented. The current interface is designed for the ease of performing experiments. So, they will be clumsy to use.

The matlab code that I use to draw the neighborhood graph in the journal version of the paper is as follows:

[II, JJ, SS] = find(neighborhood_graph);    
% neighborhood graph is represented by the sparse adjacency matrix "neighborhood_graph"
plot3( X_cord, Y_cord, Z_cord, '.'); 
% X_cord is a column vector containing the X co-ordinate of the points.
hold on;
mygplot(II, JJ, SS, [X_cord, Y_cord, Z_cord] );
hold off;

The function "mygplot" is modified from the function "gplot" so that it can handle 3D graph plot.

Sample avi

• Swiss roll data set, basic ISOMAP
• S-curve data set, basic ISOMAP
• Swiss roll data set, landmark ISOMAP
• S-curve data set, landmark ISOMAP

There are four windows in these avi files. The top-left compares the co-ordinates estimated by the batch and the incremental version of ISOMAP. The top-right denotes the neighborhood graph. Points in the lower-left are colored according to the first dimension extracted by ISOMAP. Points in the lower-right are colored according to the second dimension extracted by ISOMAP.

This page is maintained by Martin Law.