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8

x2

15

16

Elliptical blobs (objects)

Objects, Feature Vectors, PointsX(15)

X(1)

X(7)

X(16)

X(3)

X(8)

X(25)

X(12)

X(13)

X(6)

X(9)

X(10)

X(4)

X(11)

X(14)

x2

Nearest NeighboursX(j)=(x1(j), x2(j), …,xn(j))

X(i)=(x1(i), x2(i), …,xn(i))

G53MLE Machine Learning Dr Guoping Qiu

Nearest Neighbour Algorithm

- Given training data (X(1),D(1)), (X(2),D(2)), …, (X(N),D(N))
- Define a distance metric between points in inputs space. Common measures are:

Euclidean Distance

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

Given test point X

- Find the K nearest training inputs to X
- Denote these points as

(X(1),D(1)), (X(2), D(2)), …, (X(k), D(k))

x

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

Classification

- The class identification of X

Y = most common class in set {D(1), D(2), …, D(k)}

x

x

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Example : Classify whether a customer will respond to a survey question using a 3-Nearest Neighbor classifier

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Example : 3-Nearest Neighbors

15.16

15

152.23

122

15.74

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Example : 3-Nearest Neighbors

15.16

15

152.23

122

15.74

Three nearest ones to David are: No, Yes, Yes

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Example : 3-Nearest Neighbors

15.16

15

152.23

122

15.74

Yes

Three nearest ones to David are: No, Yes, Yes

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Picking K
- Use N fold cross validation – Pick K to minimize the cross validation error
- For each of N training example
- Find its K nearest neighbours
- Make a classification based on these K neighbours
- Calculate classification error
- Output average error over all examples
- Use the K that gives lowest average error over the N training examples

G53MLE Machine Learning Dr Guoping Qiu

K-Nearest Neighbour Model

- Example: For the example we saw earlier, pick the best K from the set {1, 2, 3} to build a K-NN classifier

G53MLE Machine Learning Dr Guoping Qiu

Further Readings

- T. M. Mitchell, Machine Learning, McGraw-Hill International Edition, 1997

Chapter 8

G53MLE Machine Learning Dr Guoping Qiu

Tutorial/Exercise Questions

- K nearest neighbor classifier has to store all training data creating high requirement on storage. Can you think of ways to reduce the storage requirement without affecting the performance? (hint: search the Internet, you will find many approximation methods).

G53MLE Machine Learning Dr Guoping Qiu

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