ML -- A3

VU Machine Learning - Homework 3

Individual Effort:: No team participation is really encouraged in the case of the homeworks or the labs.

Late Submission:: Late Submissions are possible, yet they will be penalized.
One day late: 15% penalty
Two days late: 30% penalty
Three days late: 50% penalty
Four or more days late: 100% penalty.

Academic Misconduct

(10p) Given are two classes with three points each:
C1: x1 = (1,1), x2 = (-1,3), x3 = (2,6);
C2: x1 = (-1,-2), x2 = (1,-3), x3 = (-5,-7);
Compute the best decision boundary as well as the support vectors.

(25p) Given are two classes with three points each:
C1: x1 = (1,1), x2 = (3,7), x3 = (5,9);
C2: x1 = (-1,-2), x2 = (1,6), x3 = (2,-1);
Show that there is no linear decision boundary separating these two classes. Instead, use a soft-margin classifier SVM using a (a) linear, as well as (b) a Gaussian kernel.

(25p) Consider the following XOR-Problem:
class C1: 20 2D points from a normal distribution N((3,0), 0.5I) as well as 20 2D points from a normal distribution N((-3,0), 0.5I).
class C2: 20 2D points from a normal distribution N((0,3), 0.5I) as well as 20 2D points from a normal distribution N((0,-3), 0.5I).
You can find a data set in the file XOR.txt. Find a decision boundary for linear, Gaussian, as well as polynomial kernel SVMs. Report your observations (and results).

(40p) There is a file temperature.txt containing 100 data points of a temperature sensor that spits out 12 temperatures in an interval of 10 minutes. These are temperatures in a storage facility. Using the 'group' label, the data is separated into two classes 'normal' and 'except'. Using an SVM, learn a classifier for these two groups. Determine the quality of the classifier using cross-validation. Is there an easy interpretation of the classifier? Now find a decision boundary through a visual analysis. I.e. plot the functions and reason about the two classes visually.

To hand in: