Tutorial 8
Q1. An SVM classifier is employed to classify the following points: 1 1
Class1:x1= 1 ,x2= −1 . −1 −1
Class2:x3= 1 ,x4= −1 .
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a. Determine the best kernel function for this classification problem. b. Design an SVM classifier to correctly classify all given points.
c. Identify the support vectors.
Q2. An SVM classifier is employed to classify the following points:
3 3 7 8
Class1:x1= 1 ,x2= −1 ,x3= 1 ,x4= 0 . 1 0 −1 −2
Class2:x5= 0 ,x6= 1 ,x7= 0 ,x8= 0 .
a. Determine if the dataset is linearly separable.
b. Identify the support vectors by inspection.
c. Design an SVM classifier to correctly classify all given points. What is the margin?
d. Classify the point x = 0.5 using the designed SVM classifier.
Q3. An SVM classifier is employed to classify the following points:
2 2 −2 −2
Class1:x1= 2 ,x2= −2 ,x3= −2 ,x4= 2 . 1 1 −1 −1
Class2:x5= 1 ,x6= −1 ,x7= −1 ,x8= 1 .
a. Determine if the dataset is linearly separable.
if ∥x∥ > 2
to the dataset where x = x . Determine if the dataset is linearly separable
2 b. Apply the feature mapping function Φ(x) =
in the new feature space.
x2 4− +|x1−x2|
4− +|x−x|
c. Identify the support vectors by inspection.
d. Design a nonlinear SVM classifier to correctly classify all given points. What is the margin? Which data points can be removed without changing the size of the margin?
e. Classify the point x = 0.5 using the designed SVM classifier.
Q4. Compare and discuss the four multi-class approaches (namely one against one, one against all, binary decision tree and binary coded approach) their advantages and disadvantages.
Q5. Given the class assignments in Table 1 for a multi-class SVM classifier using binary coded approach, list the binary codes for all classes in a table. What is the main disadvantage?
SVM Number SVM 1 SVM 2 SVM 3 SVM 4
Class assignment (+1| − 1) 12345|6789 12567|3489 14578|2369 1368|24579
Table 1: Class assignments.
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