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%matplotlib inline
In many cases, normalizing the tfidf weights for each term favors weight of terms of the documents with shorter length. The pivoted document length normalization scheme counters the effect of this bias for short documents by making tfidf independent of the document length.
This is achieved by tilting the normalization curve along the pivot point defined by user with some slope.
Roughly following the equation:
pivoted_norm = (1 - slope) * pivot + slope * old_norm
This scheme is proposed in the paper Pivoted Document Length Normalization <http://singhal.info/pivoted-dln.pdf>_ by Singhal, Buckley and Mitra.
Overall this approach can increase the accuracy of the model where the document lengths are hugely varying in the entire corpus.
This guide demonstrates how to perform pivoted document length normalization.
We will train a logistic regression to distinguish between text from two different newsgroups.
Our results will show that using pivoted document length normalization yields a better model (higher classification accuracy).
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#
# Download our dataset
#
import gensim.downloader as api
nws = api.load("20-newsgroups")
#
# Pick texts from relevant newsgroups, split into training and test set.
#
cat1, cat2 = ('sci.electronics', 'sci.space')
#
# X_* contain the actual texts as strings.
# Y_* contain labels, 0 for cat1 (sci.electronics) and 1 for cat2 (sci.space)
#
X_train = []
X_test = []
y_train = []
y_test = []
for i in nws:
if i["set"] == "train" and i["topic"] == cat1:
X_train.append(i["data"])
y_train.append(0)
elif i["set"] == "train" and i["topic"] == cat2:
X_train.append(i["data"])
y_train.append(1)
elif i["set"] == "test" and i["topic"] == cat1:
X_test.append(i["data"])
y_test.append(0)
elif i["set"] == "test" and i["topic"] == cat2:
X_test.append(i["data"])
y_test.append(1)
Preprocess the data
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from gensim.parsing.preprocessing import preprocess_string
from gensim.corpora import Dictionary
id2word = Dictionary([preprocess_string(doc) for doc in X_train])
train_corpus = [id2word.doc2bow(preprocess_string(doc)) for doc in X_train]
test_corpus = [id2word.doc2bow(preprocess_string(doc)) for doc in X_test]
print(len(X_train), len(X_test))
# We perform our analysis on top k documents which is almost top 10% most scored documents
k = len(X_test) // 10
Prepare our evaluation function
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from gensim.sklearn_api.tfidf import TfIdfTransformer
from sklearn.linear_model import LogisticRegression
from gensim.matutils import corpus2csc
# This function returns the model accuracy and indivitual document prob values using
# gensim's TfIdfTransformer and sklearn's LogisticRegression
def get_tfidf_scores(kwargs):
tfidf_transformer = TfIdfTransformer(**kwargs).fit(train_corpus)
X_train_tfidf = corpus2csc(tfidf_transformer.transform(train_corpus), num_terms=len(id2word)).T
X_test_tfidf = corpus2csc(tfidf_transformer.transform(test_corpus), num_terms=len(id2word)).T
clf = LogisticRegression().fit(X_train_tfidf, y_train)
model_accuracy = clf.score(X_test_tfidf, y_test)
doc_scores = clf.decision_function(X_test_tfidf)
return model_accuracy, doc_scores
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params = {}
model_accuracy, doc_scores = get_tfidf_scores(params)
print(model_accuracy)
Examine the bias towards shorter documents
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import numpy as np
# Sort the document scores by their scores and return a sorted list
# of document score and corresponding document lengths.
def sort_length_by_score(doc_scores, X_test):
doc_scores = sorted(enumerate(doc_scores), key=lambda x: x[1])
doc_leng = np.empty(len(doc_scores))
ds = np.empty(len(doc_scores))
for i, _ in enumerate(doc_scores):
doc_leng[i] = len(X_test[_[0]])
ds[i] = _[1]
return ds, doc_leng
print(
"Normal cosine normalisation favors short documents as our top {} "
"docs have a smaller mean doc length of {:.3f} compared to the corpus mean doc length of {:.3f}"
.format(
k, sort_length_by_score(doc_scores, X_test)[1][:k].mean(),
sort_length_by_score(doc_scores, X_test)[1].mean()
)
)
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best_model_accuracy = 0
optimum_slope = 0
for slope in np.arange(0, 1.1, 0.1):
params = {"pivot": 10, "slope": slope}
model_accuracy, doc_scores = get_tfidf_scores(params)
if model_accuracy > best_model_accuracy:
best_model_accuracy = model_accuracy
optimum_slope = slope
print("Score for slope {} is {}".format(slope, model_accuracy))
print("We get best score of {} at slope {}".format(best_model_accuracy, optimum_slope))
Evaluate the model with optimum slope
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params = {"pivot": 10, "slope": optimum_slope}
model_accuracy, doc_scores = get_tfidf_scores(params)
print(model_accuracy)
print(
"With pivoted normalisation top {} docs have mean length of {:.3f} "
"which is much closer to the corpus mean doc length of {:.3f}"
.format(
k, sort_length_by_score(doc_scores, X_test)[1][:k].mean(),
sort_length_by_score(doc_scores, X_test)[1].mean()
)
)
Since cosine normalization favors retrieval of short documents from the plot we can see that when slope was 1 (when pivoted normalisation was not applied) short documents with length of around 500 had very good score hence the bias for short documents can be seen. As we varied the value of slope from 1 to 0 we introdcued a new bias for long documents to counter the bias caused by cosine normalisation. Therefore at a certain point we got an optimum value of slope which is 0.5 where the overall accuracy of the model is increased.
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import matplotlib.pyplot as py
best_model_accuracy = 0
optimum_slope = 0
w = 2
h = 2
f, axarr = py.subplots(h, w, figsize=(15, 7))
it = 0
for slope in [1, 0.2]:
params = {"pivot": 10, "slope": slope}
model_accuracy, doc_scores = get_tfidf_scores(params)
if model_accuracy > best_model_accuracy:
best_model_accuracy = model_accuracy
optimum_slope = slope
doc_scores, doc_leng = sort_length_by_score(doc_scores, X_test)
y = abs(doc_scores[:k, np.newaxis])
x = doc_leng[:k, np.newaxis]
py.subplot(1, 2, it+1).bar(x, y, width=20, linewidth=0)
py.title("slope = " + str(slope) + " Model accuracy = " + str(model_accuracy))
py.ylim([0, 4.5])
py.xlim([0, 3200])
py.xlabel("document length")
py.ylabel("confidence score")
it += 1
py.tight_layout()
py.show()
The above histogram plot helps us visualize the effect of slope. For top
k documents we have document length on the x axis and their respective scores
of belonging to a specific class on y axis.
As we decrease the slope the density of bins is shifted from low document
length (around ~250-500) to over ~500 document length. This suggests that the
positive biasness which was seen at slope=1 (or when regular tfidf was
used) for short documents is now reduced. We get the optimum slope or the max
model accuracy when slope is 0.2.
Using pivoted document normalization improved the classification accuracy significantly: