isomap

Computes Isomap embedding using the algorithm of Tenenbaum, de Silva, and Langford (2000).

Input Arguments:

• D = N by N matrix of distances (where N is the number of data points). This can be obtained using pdist and then squareform.
• n_fcn = neighborhood function ('epsilon' or 'k')
• n_size = neighborhood size (value for epsilon or k)
  
• options.dims = (row) vector of embedding dimensionalities to use (1:10 = default)
• options.comp = which connected component to embed, if more than one. (1 = largest (default), 2 = second largest, ...)
• options.display = plot residual variance and 2-D embedding? (1 = yes (default), 0 = no)
• options.overlay = overlay graph on 2-D embedding? (1 = yes (default), 0 = no)
• options.verbose = display progress reports? (1 = yes (default), 0 = no)

Output Arguments:

• Y = Y.coords is a cell array, with coordinates for d-dimensional embeddings in Y.coords{d}. Y.index contains the indices of the points embedded.
• R = residual variances for embeddings in Y
• E = edge matrix for neighborhood graph

Synopsis

[Y, R, E] = isomap(D, n_fcn, n_size, options);

References:

Tenenbaum, J. B., V. de Silva, and J. C. Langford. 2000. “A global geometric framework for nonlinear dimensionality reduction,” Science, 290:2319-2323.

ISOMAP Homepage

Copyright Notice

Isomap code -- (c) 1998-2000 Josh Tenenbaum
This code is provided as is, with no guarantees except that bugs are almost surely present. Published reports of research using this code (or a modified version) should cite the article that describes the algorithm:

J. B. Tenenbaum, V. de Silva, J. C. Langford (2000). A global
geometric framework for nonlinear dimensionality reduction.
Science 290 (5500): 2319-2323, 22 December 2000.

Comments and bug reports are welcome. Email to jbt@psych.stanford.edu. I would also appreciate hearing about how you used this code, improvements that you have made to it, or translations into other languages.

You are free to modify, extend or distribute this code, as long as this copyright notice is included whole and unchanged.

NOTE: We think Josh Tenenbaum has moved to MIT. His email address is jbt@mit.edu and his homepage is here.