Calculating IDF using TfidfVectorizer from sklearn.feature_extraction.text.TfidfVectorizer

Question

I think the function TfidfVectorizer is not calculating correctly the IDF factor. For example, copying the code from tf-idf feature weights using sklearn.feature_extraction.text.TfidfVectorizer:

from sklearn.feature_extraction.text import TfidfVectorizer
corpus = ["This is very strange",
          "This is very nice"]
vectorizer = TfidfVectorizer(
                        use_idf=True, # utiliza o idf como peso, fazendo tf*idf
                        norm=None, # normaliza os vetores
                        smooth_idf=False, #soma 1 ao N e ao ni => idf = ln(N+1 / ni+1)
                        sublinear_tf=False, #tf = 1+ln(tf)
                        binary=False,
                        min_df=1, max_df=1.0, max_features=None,
                        strip_accents='unicode', # retira os acentos
                        ngram_range=(1,1), preprocessor=None,              stop_words=None, tokenizer=None, vocabulary=None
             )
X = vectorizer.fit_transform(corpus)
idf = vectorizer.idf_
print dict(zip(vectorizer.get_feature_names(), idf))

The Output is:

{u'is': 1.0,
 u'nice': 1.6931471805599454,
 u'strange': 1.6931471805599454,
 u'this': 1.0,
 u'very': 1.0}`

But should be:

{u'is': 0.0,
 u'nice': 0.6931471805599454,
 u'strange': 0.6931471805599454,
 u'this': 0.0,
 u'very': 0.0}

Isn't it? What am I doing wrong?

Whereas the calculation of IDF, according to http://www.tfidf.com/, is:

IDF(t) = log_e(Total number of documents / Number of documents with term t in it)

Thus, as the terms 'this', 'is' and 'very' appear in two sentences, the IDF = log_e (2/2) = 0.

The terms 'strange' and 'nice' appear in only one of the two documents, so log_e(2/1) = 0,69314.

Answer 1

Two things are happening that you might not expect in the sklearn implimentation:

1. The TfidfTransformer has smooth_idf=True as a default param
2. It always adds 1 to the weight

So it is using:

idf = log( 1 + samples/documents) + 1

Here it is in the source:

https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/feature_extraction/text.py#L987-L992

EDIT: You could subclass the standard TfidfVectorizer class like this:

import scipy.sparse as sp
import numpy as np
from sklearn.feature_extraction.text import (TfidfVectorizer,
                                             _document_frequency)
class PriscillasTfidfVectorizer(TfidfVectorizer):

    def fit(self, X, y=None):
        """Learn the idf vector (global term weights)
        Parameters
        ----------
        X : sparse matrix, [n_samples, n_features]
            a matrix of term/token counts
        """
        if not sp.issparse(X):
            X = sp.csc_matrix(X)
        if self.use_idf:
            n_samples, n_features = X.shape
            df = _document_frequency(X)

            # perform idf smoothing if required
            df += int(self.smooth_idf)
            n_samples += int(self.smooth_idf)

            # log+1 instead of log makes sure terms with zero idf don't get
            # suppressed entirely.
            ####### + 1 is commented out ##########################
            idf = np.log(float(n_samples) / df) #+ 1.0  
            #######################################################
            self._idf_diag = sp.spdiags(idf,
                                        diags=0, m=n_features, n=n_features)

        return self

Answer 2

The actual formula they use in computing idf (when smooth_idf is True) is

idf = log( (1 + samples)/(documents + 1)) + 1

It's in the source but the web documentation is a little bit ambiguous about it I think.

https://github.com/scikit-learn/scikit-learn/blob/14031f6/sklearn/feature_extraction/text.py#L966-L969