Calculate the TF-IDF weight for tems of a given document

Find the TF-IDF of terms of a given document and a collection of documents, how to calculate tf-idf, the use of tf-idf in finding the importance of a term in a document, term frequency-inverse document frequency

Question:

Given a document X containing terms t1, t2 and t3 with frequencies (inside brackets) as follows;

t1(3), t2(2), t3(1)

Let us assume that the collection contains 10,000 documents and document frequencies of these terms are as follows;

t1(50), t2(1300), t3(250)

Then, find the TF-IDF weight of terms t1, t2, and t3 in the document X.

 

Solution:

TF-IDF (Term Frequency-Inverse Document Frequency) is a measure to calculate “how relevant a term is in a given document”.

TF_t,d counts the number of times a term t occurs in a document d. It can be calculated as follows;

For example, if the document D1 contains the term ‘quick’ 10 times, and it has 54 words in it, then the TF_{’quick’, D1} = 10/54 = 0.19.

DF_t refers to the number of documents in which t presents.

For example, if 120 documents consist of the word ‘quick’, then the DF_’quick’ = 120.

IDF_t is the inverse measure used to calculate the informativeness of the given term t. This means, how common or rare a word is in the entire document set. The closer it is to 0, the more common a word is. This can be calculated as follows;

Here, N is the number of documents in the given collection, and DF_t is the document frequency of term t.

The TF-IDF weight of a term is the product of its TF weight and its IDF weight.

TF-IDF for term t1;

TF_t1 = (number of times t1 occurs in X)/(number of words in X) = 3/3

IDF_t1 = log(No. of docs in the collection/No. of docs t1 appears) = log(10000/50) = 5.3

TF-IDF for t1 = 5.3

 

TF-IDF for term t2;

TF_t2 = 2/3

IDF_t2 = log (10000/1300) = 2.0

TF-IDF for t2 = 1.3

 

TF-IDF for term t3;

TF_t3 = 1/3

IDF_t3 = log (10000/250) = 3.7

TF-IDF for t3 = 1.23

 

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how to find term frequency? how to find inverse document frequency? how to calculate tf-idf weight? what is the importance of tf-idf weights? solved exercise in information retrieval, define term frequency, define document frequency, define inverse document frequency

Find the average precision of a retrieval system - Information retrieval exercise

Find average precision of a retrieval system, information retrieval system evaluation, how to find the average precision of a search engine, information retrieval systems solved exercises

Question:

An information retrieval system give us the following result (10 documents) where the green colored are relevant ones and the red colored are non-relevant. The numbers indicate the rank of the document. Find the average precision of the given system.

1

2

3

4

5

6

7

8

9

10

 

Solution:

Precision = Fraction of retrieved documents that are relevant.

Precision = No. of relevant items retrieved/No. of retrieved items

Precision@k = Fraction of retrieved documents that are relevant in the top k documents.

Precision@k = No. of relevant docs in the top 5 results / k

Precision@5 = 3/5 = 0.6

Precision values @k is calculated and shown in the table below for all documents.

Rank	1	2	3	4	5	6	7	8	9	10
Precision	1.0	0.5	0.33	0.5	0.6	0.5	0.43	0.5	0.44	0.5

 

We need to compute Precision@k for each of the k values in the ranked document list. Then we can calculate the average precision as follows;

Average precision = average of precision@k

Here, rel(k) is 1 if the document is relevant, otherwise 0. Hence, we can add the relevant documents precision@k and calculate the average precision as follows;

Average precision = (1.0 + 0.5 + 0.6 + 0.5 + 0.5)/5 = 0.62

Average precision for the retrieved documents = 0.62

 

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How to calculate the average precision of a search result?

What is average precision?

What is precision@k?

How to calculate precision@k? 

How to evaluate an information retrieval system?