rule based classifier problems

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Instructions

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20% WILL BE IF YOU DO NOT SHOW YOUR CALCULATIONS FOR EACH ANSWER.

You must make your own calculations and you must show your calculations in the answer document.Insufficient calculation steps will result in reduced points earned.

1. Consider a binary classification problem with the following set of attributes and attribute values:

• Air Conditioner = {Working, Broken}

• Engine = {Good, Bad}

• Mileage = {High, Medium, Low}

• Rust = {Yes, No}

Suppose a rule-based classifier produces the following rule set:

(a) Are the rules mutually exclusive?

Answer:

(b) Is the rule set exhaustive?

Answer:

(c) Is ordering needed for this set of rules?

Answer:

(d) Do you need a default class for the rule set?

Answer:

2. Consider a training set that contains 100 positive examples and 400 negative examples. For each of the following candidate rules.

R1: A -→ + (covers 4 positive and 1 negative examples)

R2: B -→ + (covers 30 positive and 10 negative examples)

R3: C -→ + (covers 100 positive and 90 negative examples)

Note:The rules do not cover the entire training set.This is not an exhaustive rule set.

a.Determine which is the best and worst candidate rule according to Rule accuracy.

Answer:

b. Determine which is the best and worst candidate rule according to FOIL’s information gain.

Review of FOIL’s Information Gain

R0:{} => class(initial rule)

R1:{A} => class (rule after adding conjunct)

Gain(R0, R1) = t [log (p1/(p1+n1)) – log (p0/(p0 + n0)) ]

where…
t(total) number of positive instances covered by both R0 and R1

p0number of positive instances covered by R0

n0number of negative instances covered by R0

p1number of positive instances covered by R1

n1number of negative instances covered by R1

Answer:

3. Consider the one-dimensional data set shown below.

Data set for Exercise 3.

x	0.5	3.0	4.5	4.6	4.9	5.2	5.3	5.5	7.0	9.5
y – 1st
y – 2nd
y – 3rd
y – 4th

a. Place the indicated symbol ( +or- ) into each cell for the purpose of classifying the data point x =5.0 according to its 1-, 3-, 5-, and 9-nearest neighbors (using majority vote).

Answer:

Number of data points symbol to be used/inserted into y row

1^stRow 1-nearest neighbor +

2^nd Row 3-nearest neighbor –

3^rd Row 5-nearest neighbor+

4^th Row 9-nearest neighbor-

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