What does tf-idf mean?
Tf-idf stands for term frequency-inverse document frequency, and the tf-idf weight is a weight often used in information retrieval and text mining. This weight is a statistical measure used to evaluate how important a word is to a document in a collection or corpus. The importance increases proportionally to the number of times a word appears in the document but is offset by the frequency of the word in the corpus. Variations of the tf-idf weighting scheme are often used by search engines as a central tool in scoring and ranking a document's relevance given a user query.
One of the simplest ranking functions is computed by summing the tf-idf for each query term; many more sophisticated ranking functions are variants of this simple model.
Tf-idf can be successfully used for stop-words filtering in various subject fields including text summarization and classification.
Typically, the tf-idf weight is composed by two terms: the first computes the normalized Term Frequency (TF), aka. the number of times a word appears in a document, divided by the total number of words in that document; the second term is the Inverse Document Frequency (IDF), computed as the logarithm of the number of the documents in the corpus divided by the number of documents where the specific term appears.
TF: Term Frequency, which measures how frequently a term occurs in a document. Since every document is different in length, it is possible that a term would appear much more times in long documents than shorter ones. Thus, the term frequency is often divided by the document length (aka. the total number of terms in the document) as a way of normalization:
𝑇𝐹(𝑡)=(Number of times term t appears in a document)/(Total number of terms in the document)
IDF:Inverse Document Frequency, which measures how important a term is. While computing TF, all terms are considered equally important. However it is known that certain terms, such as "is", "of", and "that", may appear a lot of times but have little importance. Thus we need to weigh down the frequent terms while scale up the rare ones, by computing the following:
𝐼𝐷𝐹(𝑡)=log𝑒(Total number of documents)/(Number of documents with term t in it)
for numerical stabiltiy we will be changing this formula little bit
𝐼𝐷𝐹(𝑡)=log𝑒(Total number of documents)/(Number of documents with term t in it+1.)
Example
Consider a document containing 100 words wherein the word cat appears 3 times. The term frequency (i.e., tf) for cat is then (3 / 100) = 0.03. Now, assume we have 10 million documents and the word cat appears in one thousand of these. Then, the inverse document frequency (i.e., idf) is calculated as log(10,000,000 / 1,000) = 4. Thus, the Tf-idf weight is the product of these quantities: 0.03 * 4 = 0.12.
Task-1
Build a TFIDF Vectorizer & compare its results with Sklearn
As a part of this task you will be implementing TFIDF vectorizer on a collection of text documents.
You should compare the results of your own implementation of TFIDF vectorizer with that of sklearns implemenation TFIDF vectorizer.
Sklearn does few more tweaks in the implementation of its version of TFIDF vectorizer, so to replicate the exact results you would need to add following things to your custom implementation of tfidf vectorizer:
Sklearn has its vocabulary generated from idf sroted in alphabetical order
Sklearn formula of idf is different from the standard textbook formula. Here the constant "1" is added to the numerator and denominator of the idf as if an extra document was seen containing every term in the collection exactly once, which prevents zero divisions.𝐼𝐷𝐹(𝑡)=1+log𝑒1 + Total number of documents in collection1+Number of documents with term t in it. IDF(t)=1+loge(1 + Total number of documents in collection)/(1+Number of documents with term t in it.)
Sklearn applies L2-normalization on its output matrix.
The final output of sklearn tfidf vectorizer is a sparse matrix
Practical Example:
## SkLearn# Collection of string documents
#Read corpus corpus = [ 'this is the first document', 'this document is the second document', 'and this is the third one', 'is this the first document', ]
SkLearn Implementation
from sklearn.feature_extraction.text import TfidfVectorizer vectorizer = TfidfVectorizer() vectorizer.fit(corpus) skl_output = vectorizer.transform(corpus)
# sklearn feature names, they are sorted in alphabetic order by default. print(vectorizer.get_feature_names())
# Here we will print the sklearn tfidf vectorizer idf values after applying the fit method print(vectorizer.idf_)
# shape of sklearn tfidf vectorizer output after applying transform method. skl_output.shape
# sklearn tfidf values for first line of the above corpus. # Here the output is a sparse matrix print(skl_output[0])
# sklearn tfidf values for first line of the above corpus. # To understand the output better, here we are converting the sparse output matrix to dense matrix and printing it. # Notice that this output is normalized using L2 normalization. sklearn does this by default. print(skl_output[0].toarray())
From Scratch(Your custom implementation):
#import libraries
from collections import Counter from tqdm import tqdm from scipy.sparse import csr_matrix import math import operator from sklearn.preprocessing import normalize import numpy
#read dataset corpus
import sys dataset = ['this is the first document', 'this document is the second document', 'and this is the third one', 'is this the first document',]
#From the corpus we will take the bag of words of each document and assign it to the correspoding bag of word document #print("feature names, they are sorted in alphabetic order") bagOfWordsDoc1 = dataset[0].split(" ") bagOfWordsDoc2 = dataset[1].split(" ") bagOfWordsDoc3 = dataset[2].split(" ") bagOfWordsDoc4 = dataset[3].split(" ")#join them to remove common duplicate words total= set(bagOfWordsDoc1).union(set(bagOfWordsDoc2)).union(set(bagOfWordsDoc3)).union(set(bagOfWordsDoc4)) print(total)
#Now we will create a dictionary of words and their occurence for each document in the corpus(collection of documents) noOfWordsinDoc1 = dict.fromkeys(total,0) #This will give us the unique words as key and values are assigned to 0 for word in bagOfWordsDoc1: noOfWordsinDoc1[word] += 1 #This will give us the key as unique words and the words which are present in doc1 (+1) will be assigned as per their occurence noOfWordsinDoc2 = dict.fromkeys(total,0) #This will give us the unique words as key and values are assigned to 0 for word in bagOfWordsDoc2: noOfWordsinDoc2[word] += 1 #This will give us the key as unique words and the words which are present in doc2 (+1) will be assigned as per their occurence noOfWordsinDoc3 = dict.fromkeys(total,0) #This will give us the unique words as key and values are assigned to 0 for word in bagOfWordsDoc3: noOfWordsinDoc3[word] += 1 #This will give us the key as unique words and the words which are present in doc3 (+1) will be assigned as per their occurence noOfWordsinDoc4 = dict.fromkeys(total,0) #This will give us the unique words as key and values are assigned to 0 for word in bagOfWordsDoc4: noOfWordsinDoc4[word] += 1 #This will give us the key as unique words and the words which are present in doc4 (+1) will be assigned as per their occurence
print(noOfWordsinDoc1)
Result:
{'this': 1, 'third': 0, 'one': 0, 'and': 0, 'first': 1, 'is': 1, 'document': 1, 'the': 1, 'second': 0}
#Term Frequency Function def computingTermFrequency(noOfWordsinDoc,bagOfWordsDoc): #this function will count TF termFreqDict = {} #empty dictionary which will contain {key = word : value = TF} for each doc n = len(bagOfWordsDoc) #counting the length of BoW #print(n) for word,count in noOfWordsinDoc.items(): #{Key:value word:count} in noOfWordsinDoc termFreqDict[word] = float(float(count)/float(n)) #TF = occurence of word t in doc(count)/len of doc(n) return termFreqDict
#computing Term Frequency #TF = no of times term t appear in the document/ total no of terms in the document termFrequencyOfDoc1 = computingTermFrequency(noOfWordsinDoc1,bagOfWordsDoc1) #This will contains TF of doc1 termFrequencyOfDoc2 = computingTermFrequency(noOfWordsinDoc2,bagOfWordsDoc2) #This will contains TF of doc2 termFrequencyOfDoc3 = computingTermFrequency(noOfWordsinDoc3,bagOfWordsDoc3) #This will contains TF of doc3 termFrequencyOfDoc4 = computingTermFrequency(noOfWordsinDoc4,bagOfWordsDoc4) #This will contains TF of doc4 tf = { 'dict1' : termFrequencyOfDoc1, 'dict2' : termFrequencyOfDoc2, 'dict3' : termFrequencyOfDoc3, 'dict4' : termFrequencyOfDoc4} #creating a dictionary which will contain tf-idf of the 4 docs for k, v in tf.items(): print("key = ",k) print("value = ",v)
Output:
key = dict1 value = {'this': 0.2, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.2, 'is': 0.2, 'document': 0.2, 'the': 0.2, 'second': 0.0} key = dict2 value = {'this': 0.16666666666666666, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.0, 'is': 0.16666666666666666, 'document': 0.3333333333333333, 'the': 0.16666666666666666, 'second': 0.16666666666666666} key = dict3 value = {'this': 0.16666666666666666, 'third': 0.16666666666666666, 'one': 0.16666666666666666, 'and': 0.16666666666666666, 'first': 0.0, 'is': 0.16666666666666666, 'document': 0.0, 'the': 0.16666666666666666, 'second': 0.0} key = dict4 value = {'this': 0.2, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.2, 'is': 0.2, 'document': 0.2, 'the': 0.2, 'second': 0.0}
#Inverse Document Fequency Function
def computingIDF(documents):
import math
N = len(documents) #N=4 as we have 4 documents in our corpus
#print(N)
inverseDocumentFreqDict = {} #empty dictionary which will contain {key = word : value = IDF}
inverseDocumentFreqDict = dict.fromkeys(documents[0].keys(),0) #intially the dictionary will contain document1 words (or unique words) with value assign to 0
for document in documents:
for word,value in document.items():
if value > 0:
inverseDocumentFreqDict[word] += 1 #after iterating through all the doc in corpus
#print(inverseDocumentFreqDict)
for word,value in inverseDocumentFreqDict.items(): #iterating through inverseDocumentFreqDict dictionary
inverseDocumentFreqDict[word] = float(1+math.log(float(1+N)/float(1+value))) #calculating IDF
return inverseDocumentFreqDict
idf = computingIDF([noOfWordsinDoc1,noOfWordsinDoc2,noOfWordsinDoc3,noOfWordsinDoc4]) #This will contains IDF of corpus
print("After using the fit function on the corpus the vocab has 9 words in it, and each has its idf value.")
print(list(idf.values()))
#return idf
Result:
After using the fit function on the corpus the vocab has 9 words in it, and each has its idf value. [1.0, 1.916290731874155, 1.916290731874155, 1.916290731874155, 1.5108256237659907, 1.0, 1.2231435513142097, 1.0, 1.916290731874155]
#TFIDF def computingTFIDF(termFrequencies,inverseDocumentFrequencies): TFIDF = {} #empty dictionary which will contain {key = word : value = TF-IDF} for each doc for word,value in termFrequencies.items(): #iterating through term frequencies TFIDF[word] = value * inverseDocumentFrequencies[word] #calculating TF-IDF = TF * IDF return TFIDF tfidf1 = computingTFIDF(termFrequencyOfDoc1,idf) #This will contains TFIDF of doc1 tfidf2 = computingTFIDF(termFrequencyOfDoc2,idf) #This will contains TFIDF of doc2 tfidf3 = computingTFIDF(termFrequencyOfDoc3,idf) #This will contains TFIDF of doc3 tfidf4 = computingTFIDF(termFrequencyOfDoc4,idf) #This will contains TFIDF of doc4 #print("tfidf1") tfidf = { 'dict1' : tfidf1, 'dict2' : tfidf2, 'dict3' : tfidf3, 'dict4' : tfidf4} #creating a dictionary which will contain tf-idf of the 4 docs for k, v in tfidf.items(): print("key = ",k) print("value = ",v) #return tfidf
Result:
key = dict1 value = {'this': 0.2, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.3021651247531982, 'is': 0.2, 'document': 0.24462871026284194, 'the': 0.2, 'second': 0.0} key = dict2 value = {'this': 0.16666666666666666, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.0, 'is': 0.16666666666666666, 'document': 0.40771451710473655, 'the': 0.16666666666666666, 'second': 0.3193817886456925} key = dict3 value = {'this': 0.16666666666666666, 'third': 0.3193817886456925, 'one': 0.3193817886456925, 'and': 0.3193817886456925, 'first': 0.0, 'is': 0.16666666666666666, 'document': 0.0, 'the': 0.16666666666666666, 'second': 0.0} key = dict4 value = {'this': 0.2, 'third': 0.0, 'one': 0.0, 'and': 0.0, 'first': 0.3021651247531982, 'is': 0.2, 'document': 0.24462871026284194, 'the': 0.2, 'second': 0.0}
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