CS579 Machine Learning: Assignment #4.

Due: at the beginning of the lecture on Thursday, March 17.

Problem 1 Find the distance (positive or negative values) between a plane in a 3D space, described by the equation:

2x + 3y - z = 4

and the following points P1=(0,1,3), P2=(-2,-1,4), P3=(2,-2,2). Are these points on the same side of this plane?

Problem 2 A hypothetical SVM model has the following values of alpha and support vectors:

alpha	support vector	label (r)
1	(1,-1,1)	+1
0.5	(0,2,-1)	-1
0.5	(-1,0,2)	-1

Suppose that the linear kernel is used. Compute the output of this SM model when the input feature vector is (0.3,0.8,0.6). (Take w0 to be an average of w0 computed for each support vector as described on p.221.) (Note: this is NOT a real svm model, so values of w0 may be different for different support vectors.)

Problem 3 In this problem you will learn how to use the SVM tool called Libsvm, which is available at http://www.csie.ntu.edu.tw/~cjlin/libsvm. Install the software. Data sets are available at http://www.csie.ntu.edu.tw/~cjlin/papers/guide/data/. I recommend you to read A practical guide to support vector classification first. (It gives examples on how to use the software.) Use train data 3 to train the SVM. Use test data 3 to test the model accuracy. Run the program using different kernel functions: radial, linear, and 3rd degree polynomial. Try it with scaling and without scaling. For each kernel function report accuracy (for classification problem) with and without scaling. Total 6 numbers. Which model is the best for these data?