Assignment
1. Consider the following two-dimensional training data corresponding to
a two-class problem:
X1 = (0.5, 1,X)t; X2 = ((1, 1,X)t; X3 = (0.5, 0.5,X)t; X4 = (1, 0.5,X)t;
X5 = (2, 2.5,X)t; X6 = (2, 2,X)2; X7 = (4, 1.25,O)t; X8 = (5, 1.25,O)t;
X9 = (4, 0.5,O)t; X10 = (5, 0.5,O)t;
If different classifiers are formed using different subsets of the training
set,for the test pattern P = (3, 2)t, what is the class assigned by NNC
if either or both training patterns X5 and X6 are in the subset. What
happens if majority of the subsets (classifiers) do not have both X5 and
X6?
2. Consider the following training set :
X1 = (1, 1,X)t; X2 = (2, 1,X)t; X3 = (3.3, 1,X)t; X4 = (1, 2,X)t;
X5 = (2, 2,X)t; X6 = (5, 1,O)t; X7 = (6, 1,O)t; X8 = (5, 2,O)t;
X9 = (6, 2,O)t; X10 = (5, 3,O)t
We have the disjoint subsets, S1 = {1,2}, S2 = {4,5}, S3 = {3}, S4 =
{6,7}, S5 = {8,10}, S6 = {9}.
Consider classifiers obtained by leaving out (a) S1 and S4, (b) S1 and
S5, and (c) S1 and S6. What is the class label assigned to the test
pattern (4,2) if NNC is used as the classifier in all the three cases?
3. Consider the data provided in problem 2. How do you learn the
AdaBoost classifier using the following weak learners in that order?
Classifier1: if x < 3 then class X, else O
Classifier2: if x >5 then class X, else O
Classifier3: if x + y · 3.5 then class X, else O.
How do you classify the test pattern (4,2) using the AdaBoost classifier?
4. Consider the dataset given in problem 2 and the test pattern P =
(4, 2). Classifier 1 : This method finds the centroid of the two classes.
The distance from the test pattern P is found from the two centroids.
Let this be d(P,C1) and d(P,C2). Then the probability that P belongs
to class 1 will be
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