## Description

Problem 1

Given data-points {{1, 3}, {2, 5}, {3, 4}, {4, 3}, {5, 2}, {5, 1}}.

1. Please scatter-plot each data point within one figure (you can use Matlab, Python or any

other programming language).

2. Now if we want to reduce the dimension from 2 to 1 by PCA, please determine the projection

line which crosses the origin (please plot the line based on the scatter-plot figure above).

3. Assume the first 4 data points belong to one class, while the rest 2 belong to the other. Now

if we want to reduce the dimension from 2 to 1 by LDA, please determine the projection line

which crosses the origin (you are expected to plot the line based on the scatter-plot figure).

Problem 2

Given positive data-set {{1, 1}, {2, 2}, {2, 3}}, as well as negative data-set {{3, 2}, {3, 3}, {4, 4}},

please determine the decision boundary when leveraging k-NN where k = 1 and k = 3 respectively.

Problem 3

Given X, Y, Z, now please follow the idea/method used in LDA/PCA to find the best solution to:

arg max

| {z }

a,b

a

TZb

s.t. aT Xa = 1, bT Y b = 1

(1)