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| − | Question 1: In the Parametric Method section of the course, we learned how to draw a separation hyperplane between two classes by obtaining w0, the argmax of the cost function J(w)= | + | Question 1: In the Parametric Method section of the course, we learned how to draw a separation hyperplane between two classes by obtaining w0, the argmax of the cost function <math>J(w)=w^TS_Bw / w^TS_ww</math>. The solution was found to be<math>w_0= S_w^{-1}(m_1-m_2)</math>, where <math>m_1</math> and <math>m_2</math> are the sample means of each class, respectively. |
| − | Some students raised the question: can one simply use J(w)= | + | Some students raised the question: can one simply use <math>J(w)= w^TS_Bw</math> instead (i.e. setting <math>S_w</math> as the identity matrix in the solution <math>w_0</math>? Investigate this question by numerical experimentation. |
Revision as of 19:10, 10 March 2008
Hw assignment 2
Assignment Description
Due Tuesday April 1, 2008
Guidelines:
Write a short report to present your results. Be sure to include all the relevant graphs as well as a copy of your code. Teamwork is encouraged, but the write up of your report must be your own. Please write the names of ALL your collaborators on the cover page of your report.
Question 1: In the Parametric Method section of the course, we learned how to draw a separation hyperplane between two classes by obtaining w0, the argmax of the cost function $ J(w)=w^TS_Bw / w^TS_ww $. The solution was found to be$ w_0= S_w^{-1}(m_1-m_2) $, where $ m_1 $ and $ m_2 $ are the sample means of each class, respectively.
Some students raised the question: can one simply use $ J(w)= w^TS_Bw $ instead (i.e. setting $ S_w $ as the identity matrix in the solution $ w_0 $? Investigate this question by numerical experimentation.
Question 2: Obtain a set of training data. Divide the training data into two sets. Use the first set as training data and the second set as test data.
a) Experiment with designing a classifier using the neural network approach.
b) Experiment with designing a classifier using the support vector machine approach.
c) Compare the two approaches.
Note: you may use code downloaded from the web, but if you do so, please be sure to explain what the code does in your report and give the reference.
Question 3: Using the same data as for question 2 (perhaps projected to one or two dimensions for better visualization),
a) Design a classifier using the Parzen window technique.
b) Design a classifier using the K-nearest neighbor technique
c) Design a classifier using the nearest neighbor technique.
d) Compare the three approaches.
Data
Publicly available data sources are listed here.
