IDS575_PS1_Q4
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School
University of Illinois, Chicago *
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Course
575
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by maabba
4 Points
-NN performs efficiently when there are only a few prediction queries.
Q4 k-Nearest Neighborhood
36 Points
Consider a binary classification problem with two real valued features and . Figures 1 and 2 illustrate two different training sets and . White circles indicate the positively-labeled examples, whereas black squares indicate the negatively-labeled examples. To classify a new instance point, we will use (unweighted) -Nearest Neighbors with Euclidean distance and different values. Thus the label for a new point will be predicted by the majority class (i.e., positive or negative) among the k closest examples around the query point.
Q4.1
8 Points
Draw the decision boundaries of and when .
Q4.1.pdf
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k
True
False
x
1
x
2
S
1
S
2
k
k
S
1
S
2
k
= 1
1
of 1
Q4.2
5 Points
Which label would you predict for the query points (3, 2) and (4, 2) given the decision boundary of in Q4.1? Ties must be broken toward predicting the positive class. (Auto: Your answer must be look like "negative, negative")
negative, positive
S
1
Q4.3
5 Points
Which label would you predict for the query points (4.5, 4) and (4, 2) given the decision boundary of in Q4.1? Ties must be broken toward predicting the positive class. (Auto: Your answer must be look like "negative, negative")
positive, positive
Q4.4
10 Points
When , a partition of spaces like the above is called the -th order Voronoi Diagram or Voronoi Tesselation. Try to draw the decision boundaries of when . (Hint: Try to draw every bisector between all pairs of positive and negative examples)
Q4.4.pdf
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S
2
k
> 1
k
S
1
k
= 3
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1
of 1
Q4.5
8 Points
If the -coordinate of four example points in are multiplied by 5, what would happen to its decision boundary when ? Could this effect cause problems when working with real data? Describe your idea: how to alleviate it. (Free Response)
Multiplying only x2 coordinates with any scalar value (>1), significance of x2 coordinates will have larger impact as compare x
2
S
1
k
= 1
to x1 coordinates. And so distribution of nearest point will change accordingly which will result in change in decision boundary. To eliminate it, we can standardize or bring all attributes on same scale which makes more sense in terms of end result on real data.
GRADED
Problem Set (PS) #01
STUDENT
Urvashiben Patel
TOTAL POINTS
93 / 100 pts
QUESTION 1
Instance-based Learning
30
/ 30 pts
1.1
(no title)
5
/ 5 pts
1.2
(no title)
5
/ 5 pts
1.3
(no title)
5
/ 5 pts
1.4
(no title)
5
/ 5 pts
1.5
(no title)
5
/ 5 pts
1.6
(no title)
5
/ 5 pts
QUESTION 2
Mathematical Function
10
/ 10 pts
2.1
(no title)
5
/ 5 pts
2.2
(no title)
5
/ 5 pts
QUESTION 3
k-Nearest Neighborhood Basic
24
/ 24 pts
3.1
Basic
5
/ 5 pts