[ammai] week 13 A global geometric framework for nonlinear dimensionality reduction

Paper:
J.B. Tenenbaum, "A global geometric framework for nonlinear dimensionality reduction," Science, 2000 (ISOMAP)

This work (ISOMAP) aims to reduce the high-dimensional data to low dimension.The most difference between ISOMAP and others reduction algorithms (ex: PCA , MDS) is that it is capable of discovering the nonlinear degrees of freedom that underline complex natural observations.

The following are the steps that how it works:

It measures the distance in two ways. With near neighbors,it use Euclidean distance while measuring the distance to non-neighbors in shortest path found from Step 1 to represent the distance. After the distance is determined,ISOMAP applies the MDS to find the meaningful dimension. 

ISOMAP's global coordinates provide a simple way to analyze and manipulate high-dimensional observations in terms of their intrinsic nonlinear degrees of freedom.