Supervised Learning

1. The goal of Support Vector Machine is to fine a hyperplane, i.e., a decision boundary that linearly separates the points into different classes.

Given the hyperplane defined by y = x1 - 2x2.

i. How do you find the projection of a point , to the specified hyperplane?

ii. What are the distances of the following points from the hyperplane

x = [-1,2]

x = [1,0]

x = [1,1]

Unsupervised Learning

1. The figure below contains twelve points that live in 2-dimensional Euclidean space, and each of the point is named by its (x, y) coordinates.

Perform hierarchical clustering of the points in figure below.

The distance between two clusters is defined to be the minimum of the distances between any two points, one chosen from each cluster.

State clearly the steps that you have taken to merge the different clusters, along with the distance matrices.

State the result of the clustering using a tree representation or a dendrogram.

(4.10 7.10) 4.8) (6.8) (12.0 10.5] (11.4) 3.4] 19.3) (12.3) 2.2) 6.2)