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# Information Retrieval

Information Retrieval and Related Applications. TF/IDF, Cosine Similarity.

## TF/IDF

### Term Frequency (TF)

TF: number of times term t occurs in document (or alternative: number of terms divided by length of document)
$TF(t, d)=Count(times\ of\ term\ t\ appearing\ in\ d)$

### Inverse Document Frequency (IDF)

IDF: logarithm of number of documents (in corpus) divided by number of documents containing term t
$IDF(t)=\log{{Count(documents\ in\ total)}\over{Count(documents\ containing\ term\ t)}}$

### TF-IDF

$TF\_IDF(t, d)=TF(t, d) * IDF(t)$

## Cosine Similarity

Cosine of the Angle Between the Vectors. Range is [0, 1]. The higher the value, the more similar the vectors.
$Cosine(v1, v2) = \frac{v_1 \cdot v_2}{\sqrt{{v_1}^2} \cdot \sqrt{{v_2}^2}}$

### Example

$v1 = [0, 5, 0, 5, 0]$
$v2 = [0, 7, 0, 9, 0]$
$Cosine(v1, v2) = {{0*0+5*7+0*0+5*9+0*0}\over{\sqrt{0^2+5^2+0^2+5^2+0^2}+\sqrt{0^2+7^2+0^2+9^2+0^2}}} = 0.992$