Assignment#3

Part A: Scree plot

Dimensionality of this manifold is 2 because we can see clearly that error goes down suddenly for k=2 after that there is not much significant increase or decrease in error rate

PartB: Lower dimensional 2-D embedding

Part C:

On the 2D isomap variation of theta2 for a particular theta1 is along a straight line.In 3D isomap emnbedding for a particular theta1 the variation of theta2 is in a ring of toroid

Variation of theta2

Part D: Embedding in 3-D space

Part F: Shortest Path(2D)

The red part shows the shortest path between source and goal

Part G: Shortest Path(3D)

The blue part shows the shortest path between source and goal