You can use Naive Baye's classifier and adopt it as I explain below:
The classifier is based on the Bayesian Theorem which is a probabilistic theory and hence, the classifier becomes a probabilistic classifier. We can demonstrate the simple statement of the Bayesian theorem in Equation below:
$$
P(A|B) = \frac{P(B|A)P(A)}{P(B)}
$$
By re-writing this Equation, we can then obtain equation below:
$$
P(doc_{i}|Keyword) = \frac{P(Keyword|doc_{i})P(doc_{i})}{P(Keyword)}
$$
where $doc_i$ ($1 \leq i \leq n$) has a prior probability $P(doc_i)$ ,
$P(doc_i|Keyword)$ is $doc_i$'s posterior probability given Keyword $Keyword$, and $P(Keyword|doc_i)$ is the conditional probability of $Keyword$ being seen in $doc_i$. This can be said that the Posterior for Keyword is equal to a fraction of likelihood multiplied by prior divided by evidence. Since in practice the evidence is a constant. This is same as if we say in Equation of Bayesian theorem for text extraction, as the denominator $P(Keyword)$ is independent of $doc_i$, and $P(doc_i)$ remains the same for
all keywords, the likelihood that a search Keyword appears in $doc_i$, $P(Keyword|doc_i)$,
dominates the posterior probability $P(doc_i|Keyword)$. so we just need to calculate the prior and likelihood to find the probability of $doc_i$ being chosen regarded to the Keyword. This can be done by using the Naive Bayesian Classifier. With $mean_i=\mu_i$ and $variant_i=\sigma_i$ of all the words' tf*idf values in $doc_i$ ,
$P(Keyword|doc_i)$ in Equation of Bayesian theorem for text extraction can thus be approximately measured through a Normal Distribution ${\cal N}(\mu_i, \sigma_i^2)$:
$$
P(\text{Keyword}|\text{doc}_i)= \frac{1}{\sqrt{2\pi\sigma_i^{2}}}
\times e^{\frac{-(tf(\text{doc}_i,\text{Keyword})*idf(\text{doc}_i,\text{Keyword})-\mu_i)^{2}}{2\sigma_i^{2}}}
$$
To calculate the value for TFIDF, here we apply the stemmed tfidf principle. One way to calculate $tf(\text{doc}_i,\text{Keyword})*idf({doc}_i,{Keyword})$, is illustrated in the Equation below :
$$
\log (1+\frac{N_{Keyword}}{N_{total}})*\log \frac{N_{D}}{N_{KD}}
$$
Where $N_{Keyword}$ is equal to the frequency of the keyword and $N_{total}$ is equal to the total frequency of all words, including the corresponding keyword, $N_D$ is equal to the total number of all documents and $N_{KD}$ is equal to the number of documents that the keyword occurrence happens there. On the other hand, $idf(doc_i,Keyword)$ is computed as the inverse of the total number of $Keyword$ appearing in all parts.
The reason for using the Normal distribution (Gaussian distribution) is for the fact that for the weighting factor for reflecting the importance of words in a page, we used the TFIDF principle which is fundamentally equal to $tf*idf$. To calculate tf, we can use the Equation above. On the other hand, this is shown in literature that the word frequency follows the Log-normal distribution. By considering the Equation above, we can see that for calculating the value of $tf(doc_i,Keyword)$, we apply the logarithm of the term frequency and hence, the conditional probability, $P(Keyword|doc_i)$, follows a normal distribution.
The above article is taken from following paper:
Mostafa Alli
SERP-level Disambiguation from Search Results.
DOI: 10.5220/0005628606270636
In Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management,
pages 627-636
ISBN: 978-989-758-158-8
Copyright
c 2015 by SCITEPRESS - Science and Technology Publications, Lda.
