PLEASE READ: Submit printouts of well commented codes on February 13th 2018. You are encouraged to discuss in groups (two people for each group), but please complete your programming and writeup individually. Indicate the name of your collaborator in your writeup.
1. Multidimensional Scaling: Recall the concept of Multidimensional scaling that we discussed in class. Given, a dissimilarity or distance matrix of n points in RD, the task is to ﬁnd n points in Rd, d < D, such that the new distance matrix M’ is as close as possible to M. • Consider the MNIST dataset of handwritten digits. Sample 10,000 images (X) from the train dataset such that each class has equal number of images(1000). We now have 10000 data points in 784-dimensional space. • Construct the distance matrix D for all the pairs of points. D should be of dimension 10000×10000, where Di,j represents the Euclidean distance between the data points Xi and Xj. • Project these data points into 2-dimensional space, such that the new distance matrix M0 closely approximates M, i.e ﬁnd new points (x1,x2,...,xn) such that min x1,x2,...,xnX i