CS365 Assignment 2

Submitted by Kritika Singh(Y9288) and Khushdeep Singh(10351)

Part A

1. 2-D isomap for MNIST training set using Euclidean distance

Residual Variance vs Dimensionality
(a) Digits 1 and 7

(b) Digits 4 and 9

2-D isomap for MNIST training set using Tangent distance

Residual Variance vs Dimensionality
(a) Digits 1 and 7

(b) Digits 4 and 9

Part B

1. Isomap for Nao

Residual error curve(using Euclidean distance)

Residual error curve(using Tangent distance)
The most likely dimensionality is 2.
This is because of the motion of the two links of the left arm which gives it two degrees of freedom.

2. Isomap for armed robotic agents

Residual error curve(using Euclidean distance)

Residual error curve(using Tangent distance)
The most likely dimensionality is 4
This is because of the motion of the two links of the left and the right arm which gives it four degrees of freedom defined by the angles theta1, theta2, theta3 and theta4. The residual variance curve using tangent distance clearly shows this.

3. Robotic agents holding a box

The values of theta1, theta2, theta3 and theta4 are 144.11 , 228.23 , 81.45 , 109.44 respectively.

4. Isomap for armed robotic agents holding a box

Residual variance vs Isomap dimensionality
The most likely dimensionality is 1
This is because for each position of the box theta1, theta2, theta3 and theta4 are fixed values and are not anymore independent. If we know one of the angles, the other three can be easily determined. The residual variance curve verifies this as the minima of the curve occurs at 1.
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