Naive_Bayes_Classification in detail with exzmaple

naive bayes

1. Naïve Bayes Theorem in Data Mining Theory • Formula • Example • Applications

2. Introduction

3. What is Naïve Bayes? • Naïve Bayes is a probabilistic classifier based on Bayes’ Theorem. • Assumes independence among predictors. • Simple, fast, and effective for large datasets. • Commonly used for text classification, spam filtering, sentiment analysis.

4. Bayes Theorem

5. Formula Bayes’ Theorem: P(A|B) = [ P(B|A) * P(A) ] / P(B) Where: • P(A|B): Probability of hypothesis A given evidence B • P(B|A): Probability of evidence B given hypothesis A • P(A): Prior probability of A • P(B): Probability of evidence B

6. Naïve Bayes Classifier

7. Classifier Formula Naïve Bayes Classifier Formula: P(C|X) = [ P(x1|C) * P(x2|C) * ... * P(xn|C) * P(C) ] / P(X) Where: • C = Class • X = Feature vector (x1, x2, …, xn) • Assumes independence among features xi

8. Example

9. Worked Example Example: Spam Email Classification Suppose we want to classify whether an email is Spam or Not Spam based on words like 'offer', 'win', 'buy'. Steps: 1. Calculate prior probabilities P(Spam) and P(Not Spam). 2. Calculate likelihoods P(word|Spam) and P(word|Not Spam). 3. Apply Naïve Bayes formula. 4. Choose the class with higher probability.

10. Applications

11. Where is Naïve Bayes Used? • Text Classification • Spam Email Filtering • Sentiment Analysis • Medical Diagnosis • Document Categorization • Recommendation Systems

12. Advantages & Limitations

13. Pros and Cons Advantages: • Simple and easy to implement • Works well with large datasets • Effective for text and categorical data Limitations: • Assumes independence among features (rare in reality) • Zero probability issue • Not suitable for numerical data without preprocessing

14. Summary

15. Key Takeaways • Naïve Bayes is based on Bayes’ Theorem with independence assumption. • Formula: P(C|X) = P(C) * Π P(xi|C) / P(X) • Useful for classification tasks like spam filtering and sentiment analysis. • Pros: Simple, fast, scalable. • Cons: Strong independence assumption, zero probability issue.