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