[SOLVED] Isye 6740, homework 3

The objective of this question is to reproduce the ISOMAP algorithm results that we have seen discussed in lecture as an excercise. The file isomap.mat (or isomap.dat) contains 698 images, corresponding to different poses of the same face. Each image is given as a 64 × 64 luminosity map, hence represented as a vector in R⁴⁰⁹⁶. This vector is stored as a row in the file. [This is one of the datasets used in the original paper for ISOMAP, J.B. Tenenbaum, V. de Silva, and J.C. Langford, Science 290 (2000) 2319-2323.]1The data set n90pol.csv contains information on 90 university students who participated in a psychological experiment designed to look for relationships between the size of different regions of the brain and political views. The variables amygdala and acc indicate the volume of two particular brain regions known to be involved in emotions and decision-making, the amygdala and the anterior cingulate cortex; more exactly, these are residuals from the predicted volume, after adjusting for height, sex, and similar body-type variables. The variable orientation gives the students’ locations on a five-point scale from 1 (very conservative) to 5 (very liberal).,where x₁ and x₂ are the two dimensions respectively.Recall in this case, the kernel density estimator (KDE) for a density is given by,where xⁱ are two-dimensional vectors, h > 0 is the kernel bandwidth. Set an appropriate h so you can see the shape of the distribution clearly. Plot of contour plot (like the ones in slides) for your estimated density.2