Homework 3

Part A. Residual Variance v/s k


After performing dimensionality reduction through nonlinear isomap algorithm we get this graph.

Part B


Part C

As observed from the 2d embedding figure the angles are measured clockwise, we can deduce that for a particular theta1,theta2 goes from 0 to +-180 than while in 3-d the values of theta2 vary along a ring on the toroid from(o to 360).

Part D


The topology is S1*S1 It looks like torus

Part E

Part F


Part G


For the source code click here