Question

Problem 4 (20 pt.)
Given the following dataset:

?	?	?	Class
2.5	1.5	3.5	-
0.5	1.0	1.5	+
0.5	0.5	1.0	+
2.0	2.5	2.5	+
1.0	2.0	3.0	-
2.0	3.0	1.5	-

Supposethatyouwanttoclassifyanobservation?=(?.?, ?.?, ?.?)using?-NearestNeighbors with Euclidean distance as the proximity metric. Answer the following questions:

1. (8 pts.) What is the distance between ? and every observation in the dataset?

2. (3 pts.) What is the predicted class label for ? if ? = ??

3. (3 pts.) What is the predicted class label for ? if ? = ??

4. (3 pts.) What is the predicted class label for ? if ? = ??

5. (3 pts.) What is the predicted class label for ? if ? = ??

Answer 1

1) Distance Between z and every observation in dataset:

(i) Point 1:

(ii) Point 2:

(iii) Point 3:

(iv) Point 4:

(v) Point 5:

(vi) Point 6:

2) For K = 1, closest point is V. So the predicted class label for z is '-'

3) For K = 2, closest points are IV and V, both has different class label. So the predicted class label for z is '-'

4) For K = 3, closest points are I, IV and V, most occuring label is '-'. So the predicted class label for z is '-'

5) For K = 4, closest points are I, IV, V, and VI, most occuring label is '-'. So the predicted class label for z is '-'

For question 3, it depends on implementation whether result will be '+' or '-'.