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 notes:bayesian_classification [2013/03/15 13:36]andy [Combining words] notes:bayesian_classification [2013/03/15 14:11]andy [Combining words] Both sides previous revision Previous revision 2013/03/15 14:13 andy 2013/03/15 14:11 andy [Combining words] 2013/03/15 14:06 andy [Combining words] 2013/03/15 13:37 andy [Combining words] 2013/03/15 13:36 andy [Combining words] 2013/03/15 13:12 andy [Combining words] 2013/03/15 12:18 andy 2013/03/15 11:43 andy [Combining words] 2013/03/15 10:29 andy [Classification based on a word] 2013/03/14 16:33 andy [Combining words] 2013/03/14 16:16 andy 2013/03/14 15:21 andy 2013/03/14 11:56 andy created Next revision Previous revision 2013/03/15 14:13 andy 2013/03/15 14:11 andy [Combining words] 2013/03/15 14:06 andy [Combining words] 2013/03/15 13:37 andy [Combining words] 2013/03/15 13:36 andy [Combining words] 2013/03/15 13:12 andy [Combining words] 2013/03/15 12:18 andy 2013/03/15 11:43 andy [Combining words] 2013/03/15 10:29 andy [Classification based on a word] 2013/03/14 16:33 andy [Combining words] 2013/03/14 16:16 andy 2013/03/14 15:21 andy 2013/03/14 11:56 andy created Last revision Both sides next revision Line 94: Line 94: \begin{equation*} P(C_i|W_a \cap W_b \cap ... \cap W_z) = \frac{\frac{1}{N}N_{C_i}\prod\limits_{j=a}^z{\frac{N_{C_i}(W_j)}{N_{C_i}}}}{\frac{1}{N}\sum\limits_{k=1}^n{N_{C_k}\prod\limits_{j=a}^z{\frac{N_{C_k}(W_j)}{N_{C_k}}}}} \end{equation*} \begin{equation*} P(C_i|W_a \cap W_b \cap ... \cap W_z) = \frac{\frac{1}{N}N_{C_i}\prod\limits_{j=a}^z{\frac{N_{C_i}(W_j)}{N_{C_i}}}}{\frac{1}{N}\sum\limits_{k=1}^n{N_{C_k}\prod\limits_{j=a}^z{\frac{N_{C_k}(W_j)}{N_{C_k}}}}} \end{equation*} - \begin{equation*} P(C_i|W_a \cap W_b \cap ... \cap W_z) = \frac{\prod\limits_{j=a}^z{N_{C_i}(W_j)}}{N_{C_i}^{x-1}\sum\limits_{k=1}^n{\frac{1}{N_{C_k}^{x-1}}\prod\limits_{j=a}^z{N_{C_k}(W_j)}}} \end{equation*} + ​\Rightarrow ​P(C_i|W_a \cap W_b \cap ... \cap W_z) = \frac{\prod\limits_{j=a}^z{N_{C_i}(W_j)}}{N_{C_i}^{x-1}\sum\limits_{k=1}^n{\frac{1}{N_{C_k}^{x-1}}\prod\limits_{j=a}^z{N_{C_k}(W_j)}}} - Where $x$ is the total number of words. + Where $x$ is the total number of words. This version may help avoid underflow, but may instead be susceptible to overflow due to the exponentiation involved. ==== Two-category case ==== ==== Two-category case ====
notes/bayesian_classification.txt ยท Last modified: 2013/03/15 14:13 by andy