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