Subject: Data Mining And Business Intelligence

Topic: Classification

Difficulty: High

The table below shows a sample dataset of whether a customer responds to a survey or not. “Outcome” is the class label.Construst a Naïve Bayes’ Classifier for the dataset. For a new example (Rural, Semideatached, low, No).What will be the predicted class label?

Naive Bayes Classifier Example

Here, we want to classify a Rural, Semideatached, Low, No, and predict the class label for this sample.

The above sample dataset does not contain the class label for this sample. Hence, by using Naïve Bayes Classifier we can find out the class table value for the given sample.

To do this we need to calculate the below probabilities:

First, calculates the Probabilities for $P(x|Nothing)$

$$P(Nothing) = \frac{5}{14} $$

$$ P(Rural│Nothing) = \frac{0}{5} = 0 $$

$$ P(Semi-detached│Nothing) = \frac{1}{5} $$

$$ P(Low│Nothing) = \frac{1}{5} $$

$$P(No│Nothing) = \frac{2}{5} $$

Second, calculates the Probabilities for $P(x|Responded)$

$$P(Responded) = \frac{9}{14}$$

$$P(Rural│Responded) = \frac{4}{9}$$

$$P(Semi-detached│Responded) = \frac{4}{9}$$

$$P(Low│Responded) = \frac{6}{9}$$

$$P(No│Responded) = \frac{6}{9}$$

According to Naïve Bayes Classifier

$$P(C│X)=P(x1│C) × P(x2│C) ×…………P(xn│C) × P(C)$$

Therefore, Probability for Class label Nothing we have

$$Nothing=P(X│Nothing) × P(Nothing)$$

$$Nothing=P(Rural│Nothing)×P(Semi-detached│Nothing)×P(Low│Nothing)×P(No│Nothing)×P(Nothing)$$

$$= 0 ×\frac{1}{5} × \frac{1}{5} × \frac{2}{5} × \frac{5}{14} = 0$$

If one of the conditional probabilities is zero, then the entire expression becomes zero. This can be seen in the above scenario.

Therefore, Probability for Class label Responded we have

$$Responded=P(X│Responded) × P(Responded)$$

$$Responded= P(Rural│Responded)× P(Sumi-detached│Responded)× P(Low│Responded)×P(No│Responded)×P(Responded)$$

$$= \frac{4}{9} × \frac{4}{9} × \frac{6}{9} × \frac{6}{9} × \frac{9}{14} = 0.056$$

As

$$P(X│Responded).P(Responded) \gt P(X│Nothing).P(Nothing)$$

$$because,\ 0.056 \gt 0$$

Therefore, this sample (Rural, Semideatached, Low, No) gets classified under Class label ’Responded’.