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In this project, we used 3 different metrics (Information Gain, Mutual Information, Chi Squared) to find important words and then we used them for the classification task. We compared the result at the end.

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Text Classification

In this project, we used 3 different metrics (Information Gain, Mutual Information, Chi Squared) to find important words and then we used them for the classification task. We compared the result at the end.

To read jupyter notebook complete code click on Codes

Each document can be represented by the set of its words.
But some words are more important and has more effect and more meaning. These words can be used for determining the context of a document.
In this part, we are going to find a set of 100 words that are more infomative for document classification.

Data Set

The dataset for this task is "همشهری" (Hamshahri) that contains 8600 persian documents.

class_name
['ورزش', 'اقتصاد', 'ادب و هنر', 'اجتماعی', 'سیاسی']

There is some statistcs information about out dataset.

vocab size: 65880
number of terms (all tokens): 3506727
number of docs: 8600
number of classes: 5

The probability of each classes are stored in the table below.

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0
0 0.232558
1 0.255814
2 0.058140
3 0.209302
4 0.244186

Calculation of our metrics for each words in Vocabulary

We are going to find 100 words that are good indicator of classes.
We want to use 3 different type of metrics

  • Information Gain
  • Mutual Information
  • $\chi$ square

Information Gain

The top 10 words with highest information gain can be seen in the table below.

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information_gain word
0 0.612973 ورزشی
1 0.516330 تیم
2 0.297086 اجتماعی
3 0.293313 سیاسی
4 0.283891 فوتبال
5 0.267878 اقتصادی
6 0.225276 بازی
7 0.223381 جام
8 0.197755 قهرمانی
9 0.177807 اسلامی

If you think about the meaning of these words you can agree that since they a have high information gain they can be really good identifiers for categorizing a doc.
In the table below, you can see 5 worst words.

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information_gain word
65875 0.000042 تبهکاران
65876 0.000042 پذیرفتم
65877 0.000041 توقف
65878 0.000031 سلمان
65879 0.000027 چهارمحال

Mutual Information

We found two formulas for this metrics. The first one only calculates the MI in the case that w = 1, ci = 1. The second one calculates all 4 possible combinations of (w, ci) and multiplies them by their probabilities.
We used both of them and then choose the better set.
Let's see the result of each of those different formulas.

First Formula

The formula is:

formula-1

The result for this formula

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mutual information(MI) main class MI main_class word
0 0.524418 1.782409 ادب و هنر مایکروسافت
1 0.524418 1.782409 ادب و هنر باغات
2 0.524418 1.782409 ادب و هنر نباریدن
3 0.524191 1.703799 اقتصاد آلیاژی
4 0.524191 1.703799 اقتصاد دادمان
5 0.524191 1.703799 اقتصاد فرازها
6 0.524191 1.703799 اقتصاد سیاتل
7 0.521680 1.782409 ادب و هنر سخیف
8 0.521680 1.782409 ادب و هنر کارناوال
9 0.521680 1.782409 ادب و هنر تحتانی

But there is a problem here

The words in the above table are infrequent words.
They can give us high information in the case that they appear in our text. But when they do not appear in our document, the absence of those words do not give us any information about the class. So these words are only useful for those documents that have these words. So for most of the documents, these words are not useful.
It seems like it is important to consider the frequency of different cases of (w, ci) and also its mutual information.

You can see the number of occurrences of some of these words in each class:

word_occurance_frequency_vs_class[word_index['نباریدن']], word_occurance_frequency_vs_class[word_index['مایکروسافت']],  word_occurance_frequency_vs_class[word_index['آلیاژی']]
(array([0, 4, 1, 0, 0]), array([0, 4, 1, 0, 0]), array([0, 5, 1, 0, 0]))

Second Model

In the second model, the above problem is solved because we multiplied the frequency of different cases (probability) by its mutual information.

The Second formula is:

formula-2

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mutual information(MI) main class MI main_class word
0 0.202674 0.606665 ورزش ورزشی
1 0.173929 0.512590 ورزش تیم
2 0.099833 0.279402 ورزش فوتبال
3 0.094818 0.258578 سیاسی سیاسی
4 0.088517 0.232945 اقتصاد اقتصادی
5 0.085858 0.265246 اجتماعی اجتماعی
6 0.076582 0.209092 ورزش بازی
7 0.076098 0.217883 ورزش جام
8 0.070387 0.195426 ورزش قهرمانی
9 0.056253 0.155666 ورزش بازیکن

These words are better

They are not rare
You can see the frequency of some of these words in each classes:

print (list(reversed(class_name)))
word_occurance_frequency_vs_class[word_index['ورزشی']], word_occurance_frequency_vs_class[word_index['سیاسی']],  word_occurance_frequency_vs_class[word_index['پیروزی']],
['سیاسی', 'اجتماعی', 'ادب و هنر', 'اقتصاد', 'ورزش']





(array([1866,    9,    8,   66,   16]),
 array([  35,  300,   71,  372, 1602]),
 array([497,  44,  24,  60, 191]))

$ \chi$ Squared

Another Metric is $ \chi$ Squared.
Now we are goind to see the result of using $\chi$ squared as a mesure of importance.

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chi squared main class chi main_class word
0 2234.591600 7376.515420 ورزش ورزشی
1 2028.186959 6701.136193 ورزش تیم
2 1302.947803 4296.622009 ورزش فوتبال
3 1050.289281 3459.737651 ورزش جام
4 1043.478941 3138.957039 سیاسی سیاسی
5 1029.481451 3055.759330 اقتصاد اقتصادی
6 1027.311167 3254.137538 ورزش بازی
7 967.923254 3299.353018 اجتماعی اجتماعی
8 961.078769 3169.912598 ورزش قهرمانی
9 772.041205 2558.041173 ورزش بازیکن

Result Comparison

We can compare our three set of words here.
In the table below, you can see top 20 words for each metrics.
For mutual information, there are two sets because we used two different formula.

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information gain1 chi squared1 mutual information_model_2 mutual information_model_1
0 ورزشی ورزشی ورزشی مایکروسافت
1 تیم تیم تیم باغات
2 اجتماعی فوتبال فوتبال نباریدن
3 سیاسی جام سیاسی آلیاژی
4 فوتبال سیاسی اقتصادی دادمان
5 اقتصادی اقتصادی اجتماعی فرازها
6 بازی بازی بازی سیاتل
7 جام اجتماعی جام سخیف
8 قهرمانی قهرمانی قهرمانی کارناوال
9 اسلامی بازیکن بازیکن تحتانی
10 بازیکن بازیکنان اسلامی معراج
11 مجلس فدراسیون بازیکنان خلافت
12 بازیکنان مسابقات فدراسیون نجیب
13 فدراسیون دلار مسابقات زبون
14 مسابقات قیمت دلار صحیفه
15 شورای مسابقه مسابقه مشمئزکننده
16 مسابقه آسیا مجلس ارتجاع
17 دلار گذاری قیمت ذبیح
18 آسیا صنایع شورای وصنایع
19 مردم سرمایه گذاری توپخانه

Output File

The output files are stored in CSV format files.
These files contain 100 most important words for each metrics.

Conclusion of Part 1 (Finding important words for classification)

When we look at the last table we can see first three columns are similar to each other and have nearly the same words but last columns' (mutual information with formula 1) words differse from other columns
We can conclude that the Formula 1 has different behavior and probably is not efficient. So it is better to use formula 2 to calculate Mutual Information

For more accurate comparisons on which of these three metrics are better, we can test it.

In part 2 we are going to test which metric is better, with a classification task.

Part 2 (Classifying using words in part 1)

In Part 1 we tried to find good features to vectorize documents. We used three metrics and extracted three set of 100 words.
Each document can be represented by the set of words that appear in the document.
In this part we want to use these sets of features to classify documents with SVM.

Evaluation

To evaluate our classification we used k-fold cross-validation with k=5.
We reported our average of these 5 confusion matrices.

Vectorizing Documents

We wanted to vectorize our documents. We used 4 different methods:

  1. Using 1000 most frequent words as features set
  2. Using Information Gain features
  3. Using Mutual Information features
  4. Using $\chi$ square features

1) Using 1000 most frequent words as feature set

There is an ambiguity in defining the meaning of frequent.

  • First meaning: A word is frequent if in lots of document there is at least one occurrence of this word.
  • Second meaning: A word is frequent if the sum of the number of occurrence of this word in all documents is high. (Maybe in one document there are lots of occurrences but in another document, there is no occurrence.)

In this code, we chose the first meaning.

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0 1
0 8415 و
1 8352 در
2 8241 به
3 7956 از
4 7838 این
5 7382 با
6 7240 که
7 6923 را
8 6912 است
9 6859 می

The above words are 10 most frequent words in our dataset. And all of them are stop words.

Making Vector X

We want to make the vector for each document and then use this vectors for classification.
We used our 1000 words for vectorizing.

Using SVM for classification

We used svm classifier for our classification.

Confusion Matrix for 1000 most frequent

accuracy: 0.8787209302325582 

confusion matrix:
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0 1 2 3 4
0 389.0 2.2 0.0 6.4 2.4
1 0.2 414.2 0.2 6.4 19.0
2 1.2 10.8 37.2 44.2 6.6
3 1.6 18.4 1.6 300.6 37.8
4 1.0 19.2 0.0 29.4 370.4

2) Using 100-dimensional vector with Information Gain

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information_gain word
0 0.612973 ورزشی
1 0.516330 تیم
2 0.297086 اجتماعی
3 0.293313 سیاسی
4 0.283891 فوتبال
5 0.267878 اقتصادی
6 0.225276 بازی
7 0.223381 جام
8 0.197755 قهرمانی
9 0.177807 اسلامی

Making Vector X

We made vector for each document and then we used this vectors for classification with SVM.

accuracy: 0.806279069767442 

confusion matrix:
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0 1 2 3 4
0 376.0 7.6 0.2 11.4 4.8
1 1.4 382.6 0.2 22.0 33.8
2 4.0 24.0 7.2 55.0 9.8
3 2.4 30.8 1.0 268.8 57.0
4 2.4 31.6 0.2 33.6 352.2

3) Using 100-dimensional vector with Mutal Information

We used the better formula for selecting 100 words.

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mutual information main class score main class word
0 0.202674 0.606665 ورزش ورزشی
1 0.173929 0.512590 ورزش تیم
2 0.099833 0.279402 ورزش فوتبال
3 0.094818 0.258578 سیاسی سیاسی
4 0.088517 0.232945 اقتصاد اقتصادی
5 0.085858 0.265246 اجتماعی اجتماعی
6 0.076582 0.209092 ورزش بازی
7 0.076098 0.217883 ورزش جام
8 0.070387 0.195426 ورزش قهرمانی
9 0.056253 0.155666 ورزش بازیکن 
accuracy: 0.804186046511628 

confusion matrix:
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0 1 2 3 4
0 375.2 8.2 0.0 11.4 5.2
1 1.4 379.8 0.2 22.6 36.0
2 3.8 23.0 7.0 56.4 9.8
3 2.0 31.4 1.0 270.0 55.6
4 2.4 31.2 0.2 35.0 351.2

4) Using 100-dimensional vector with $\chi$ Squared

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chi squared main class score main class word
0 2234.591600 7376.515420 ورزش ورزشی
1 2028.186959 6701.136193 ورزش تیم
2 1302.947803 4296.622009 ورزش فوتبال
3 1050.289281 3459.737651 ورزش جام
4 1043.478941 3138.957039 سیاسی سیاسی
5 1029.481451 3055.759330 اقتصاد اقتصادی
6 1027.311167 3254.137538 ورزش بازی
7 967.923254 3299.353018 اجتماعی اجتماعی
8 961.078769 3169.912598 ورزش قهرمانی
9 772.041205 2558.041173 ورزش بازیکن 
accuracy: 0.8025581395348838 

confusion matrix:
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0 1 2 3 4
0 375.2 8.2 0.0 11.4 5.2
1 1.4 380.8 0.2 22.2 35.4
2 3.8 25.0 6.6 55.6 9.0
3 2.4 31.2 0.8 267.2 58.4
4 2.4 31.8 0.2 35.0 350.6

Comparision

We compare our result with these 4 methods with confusion matrix and accuracy.
The result is as follows.

accuracy:
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1000words InfoGain chi squared mutual info
0 0.878721 0.806279 0.802558 0.804186 
preview = pd.concat([pd.DataFrame(first_method_confusion_matrix),       
                     pd.DataFrame(second_method_confusion_matrix),
                     pd.DataFrame(third_method_confusion_matrix),
                     pd.DataFrame(forth_method_confusion_matrix)], axis=1)
print ("confusion matrix:")
print ("\t1000 words\t\t\t IG \t\t \t MI \t\t   chi squared")
preview
confusion matrix:
	1000 words			 IG 		 	 MI 		   chi squared
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0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
0 389.0 2.2 0.0 6.4 2.4 376.0 7.6 0.2 11.4 4.8 375.2 8.2 0.0 11.4 5.2 375.2 8.2 0.0 11.4 5.2
1 0.2 414.2 0.2 6.4 19.0 1.4 382.6 0.2 22.0 33.8 1.4 379.8 0.2 22.6 36.0 1.4 380.8 0.2 22.2 35.4
2 1.2 10.8 37.2 44.2 6.6 4.0 24.0 7.2 55.0 9.8 3.8 23.0 7.0 56.4 9.8 3.8 25.0 6.6 55.6 9.0
3 1.6 18.4 1.6 300.6 37.8 2.4 30.8 1.0 268.8 57.0 2.0 31.4 1.0 270.0 55.6 2.4 31.2 0.8 267.2 58.4
4 1.0 19.2 0.0 29.4 370.4 2.4 31.6 0.2 33.6 352.2 2.4 31.2 0.2 35.0 351.2 2.4 31.8 0.2 35.0 350.6

Visualization

We are going to show each one in separated tables:

# plt.figure()
# plot_confusion_matrix(first_method_cm, classes=class_name,
#                       title='Confusion matrix visualization for chi squared');
plt.figure()
plot_confusion_matrix(first_method_cm, classes=class_name,
                      title='Confusion matrix visualization for 1000 most frequent_normalized', normalize=True);
plt.show()

png

plt.figure()
plot_confusion_matrix(second_method_cm, classes=class_name,
                      title='Confusion matrix visualization for Information gain_normalized', normalize=True);
plt.show()

png

plt.figure()
plot_confusion_matrix(third_method_cm, classes=class_name,
                      title='Confusion matrix visualization for Mutual information_normalized', normalize=True);
plt.show()

png

plt.figure()
plot_confusion_matrix(forth_method_cm, classes=class_name,
                      title='Confusion matrix visualization for chi squared_normalized', normalize=True);
plt.show()

png

Now we want to test the result for most 100 frequent word vectors

Because maybe this is not fair to compare 1000 frequent words with 100 words in other metrics.

Confusion Matrix for 100 most frequent

accuracy: 0.803953488372093 

confusion matrix:
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0 1 2 3 4
0 375.6 8.2 0.0 11.4 4.8
1 1.4 382.4 0.4 22.0 33.8
2 3.2 24.8 7.2 55.2 9.6
3 1.8 30.8 1.0 267.4 59.0
4 2.4 32.6 0.2 34.6 350.2

png

Conclusion

We know that 1000 words are not best words because these words include stop words that they are not informative. But because they are 1000 words rather than 100 words, the result is going to be better.
We test a set of 100 most frequent words. The result was acc = 0.8049 which is similar to other three methods. We also show the confusion matrix for 100 most frequent in the last table above. And you can see this table is also similar to other three ones
So we can guess that there is no significant difference between choosing these metrics for selecting words in document classification task.
And we also know that Information Gain doesn't store every class information gains (We only stored one number Information Gain for every word). But we can consider each class information gain if we split the Sigma over classes in information gain formula.(And consider the meaning of Entropy for each class). So it has the same functionality as other metrics.
We guess that if the dimension of our vector increase we probably are going to get more accuracy.
And also maybe if we use different features depending on the sequence of words that appear each document, we can get more accuracy.

About

In this project, we used 3 different metrics (Information Gain, Mutual Information, Chi Squared) to find important words and then we used them for the classification task. We compared the result at the end.

Topics

mutual-information information-gain chi-squared docuement-classification

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