LO 7.2.3.C

Learning Objective: Calculate the prior probabilities of two classes, given a training set categorized into two categories.

Review:

Determining the class.

Assume, we have five text documents and two classes: ‘+’/positive comment and ‘-’/negative comment. The class categorization of the five documents are described in the figure below.

The goal is to classify the text “predictable with no fun” either as ‘+’/positive comment or ‘-’/negative comment.

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mi>c</mi></mfenced><mo>=</mo><mfrac><mtext>Number of documents classified as class c</mtext><mtext>Number of documents</mtext></mfrac></math>$

Thus, the priori probabilities of the class ‘positive comment’ and ‘negative comment’ are given by

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mtext>class +</mtext></mfenced><mo>=</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math>$

$<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mfenced><mtext>class -</mtext></mfenced><mo>=</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math>$

Source: Assigned reading