# Machine Learning :: Text feature extraction (tf-idf) – Part II

This post is a延续of the first part where we started to learn the theory and practice about text feature extraction and vector space model representation. I really recommend you阅读第一部分后一系列以遵循这个第二。

Since a lot of people liked the first part of this tutorial, this second part is a little longer than the first.

### 介绍

The tf-idf weight comes to solve this problem. What tf-idf gives is how important is a word to a document in a collection, and that’s why tf-idf incorporates local and global parameters, because it takes in consideration not only the isolated term but also the term within the document collection. What tf-idf then does to solve that problem, is to scale down the frequent terms while scaling up the rare terms; a term that occurs 10 times more than another isn’t 10 times more important than it, that’s why tf-idf uses the logarithmic scale to do that.

But let’s go back to our definition of the$\ mathrm {TF}（T，d）$which is actually the term count of the term$Ť$在文档中$d$。The use of this simple term frequency could lead us to problems like滥用关键字，which is when we have a repeated term in a document with the purpose of improving its ranking on an IR (Information Retrieval）系统，甚至对创建长文档偏见，使他们看起来比他们只是因为手册中出现的高频更重要。

### 矢量归

Suppose we are going to normalize the term-frequency vector$\vec{v_{d_4}}$我们在本教程的第一部分已经计算。该文件$D4$from the first part of this tutorial had this textual representation:

D4：We can see the shining sun, the bright sun.

And the vector space representation using the non-normalized term-frequency of that document was:

$\vec{v_{d_4}} = (0,2,1,0)$

$\ displaystyle \帽子{v} = \压裂vec {v}} {\ vec {v} {\ | \ \ |_p}$

$\hat{v}$是单位矢量，或者归一化矢量，所述$\ VEC {V}$是个vector going to be normalized and the$\ | \ VEC {V} \ | _p$是矢量的范数（大小，长度）$\ VEC {V}$in the$L^p$space (don’t worry, I’m going to explain it all).

The unit vector is actually nothing more than a normalized version of the vector, is a vector which the length is 1.

### Lebesgue spaces

Usually, the length of a vector$\ {VEC U】=（U_1，U_2，U_3，\ ldots，u_n）$is calculated using the欧几里得范-一个准则是在矢量空间中分配一个严格正长度或大小于所有矢量的函数-, which is defined by:

$\ | \ VEC【U} \ |= \ SQRT【U ^ 2_1 + U ^ 2_2 + U ^ 2_3 + \ ldots + U ^ 2_n}$

$\的DisplayStyle \ | \ VEC【U} \ | _p =（\左| U_1 \右| ^ P + \左| U_2 \右| ^ P + \左| U_3 \右| ^ P + \ ldots + \左|u_n \右| ^ p）^ \压裂{1} {p}$

$\displaystyle \|\vec{u}\|_p = (\sum\limits_{i=1}^{n}\left|\vec{u}_i\right|^p)^\frac{1}{p}$

$\displaystyle \|\vec{u}\|_1 = ( \left|u_1\right| + \left|u_2\right| + \left|u_3\right| + \ldots + \left|u_n\right|)$

Note that you can also use any norm to normalize the vector, but we’re going to use the most common norm, the L2-Norm, which is also the default in the 0.9 release of thescikits.learn。You can also find papers comparing the performance of the two approaches among other methods to normalize the document vector, actually you can use any other method, but you have to be concise, once you’ve used a norm, you have to use it for the whole process directly involving the norm (a unit vector that used a L1-norm isn’t going to have the length 1 if you’re going to take its L2-norm later).

### Back to vector normalization

$\hat{v} = \frac{\vec{v}}{\|\vec{v}\|_p} \\ \\ \hat{v_{d_4}} = \frac{\vec{v_{d_4}}}{||\vec{v_{d_4}}||_2} \\ \\ \\ \hat{v_{d_4}} = \frac{(0,2,1,0)}{\sqrt{0^2 + 2^2 + 1^2 + 0^2}} \\ \\ \hat{v_{d_4}} = \frac{(0,2,1,0)}{\sqrt{5}} \\ \\ \small \hat{v_{d_4}} = (0.0, 0.89442719, 0.4472136, 0.0)$

### The term frequency – inverse document frequency (tf-idf) weight

Train Document Set: d1: The sky is blue. d2: The sun is bright. Test Document Set: d3: The sun in the sky is bright. d4: We can see the shining sun, the bright sun.

Your document space can be defined then as$d = \ {D_1，D_2，\ ldots，D_N \}$where$ñ$是个文件数in your corpus, and in our case as$D_ {火车} = \ {D_1，D_2 \}$$D_{test} = \{d_3, d_4\}$。我们的文档空间的基数被定义$\left|{D_{train}}\right| = 2$$\左| {{D_测试}} \右|= 2$，since we have only 2 two documents for training and testing, but they obviously don’t need to have the same cardinality.

$\displaystyle \mathrm{idf}(t) = \log{\frac{\left|D\right|}{1+\left|\{d : t \in d\}\right|}}$

where$\left|\{d : t \in d\}\right|$是个文件数其中术语$Ť$看来,当term-frequency function satisfies$\ mathrm {TF}（T，d）\neq 0$，我们只加1代入公式，以避免零分。

The formula for the tf-idf is then:

$\mathrm{tf\mbox{-}idf}(t) = \mathrm{tf}(t, d) \times \mathrm{idf}(t)$

Now let’s calculate the idf for each feature present in the feature matrix with the term frequency we have calculated in the first tutorial:

$M_ {}列车= \begin{bmatrix} 0 & 1 & 1 & 1\\ 0 & 2 & 1 & 0 \end{bmatrix}$

$\ mathrm {IDF}（T_1）= \log{\frac{\left|D\right|}{1+\left|\{d : t_1 \in d\}\right|}} = \log{\frac{2}{1}} = 0.69314718$

$\ mathrm {IDF}（T_2）= \日志{\压裂{\左| d \右|} {1+ \左| \ {d：T_2 \在d \} \右|}} = \日志{\压裂{2} {3}} = -0.40546511$

$\ mathrm {IDF}（t_3处）= \日志{\压裂{\左| d \右|} {1+ \左| \ {d：t_3处\在d \} \右|}} = \日志{\压裂{2} {3}} = -0.40546511$

$\ mathrm {IDF}（T_4）= \日志{\压裂{\左| d \右|} {1+ \左| \ {d：T_4 \在d \} \右|}} = \日志{\压裂{2} {2}} = 0.0$

$vec {idf_ \{火车}}= (0.69314718, -0.40546511, -0.40546511, 0.0)$

$M_ {} IDF= \begin{bmatrix} 0.69314718 & 0 & 0 & 0\\ 0 & -0.40546511 & 0 & 0\\ 0 & 0 & -0.40546511 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix}$

$M_ {TF \ MBOX { - }} IDF= M_{train} \times M_{idf}$

${bmatrix} \ \开始mathrm {tf} (t_1 d_1) & \ mathrm {Ťf}(t_2, d_1) & \mathrm{tf}(t_3, d_1) & \mathrm{tf}(t_4, d_1)\\ \mathrm{tf}(t_1, d_2) & \mathrm{tf}(t_2, d_2) & \mathrm{tf}(t_3, d_2) & \mathrm{tf}(t_4, d_2) \end{bmatrix} \times \begin{bmatrix} \mathrm{idf}(t_1) & 0 & 0 & 0\\ 0 & \mathrm{idf}(t_2) & 0 & 0\\ 0 & 0 & \mathrm{idf}(t_3) & 0\\ 0 & 0 & 0 & \mathrm{idf}(t_4) \end{bmatrix} \\ = \begin{bmatrix} \mathrm{tf}(t_1, d_1) \times \mathrm{idf}(t_1) & \mathrm{tf}(t_2, d_1) \times \mathrm{idf}(t_2) & \mathrm{tf}(t_3, d_1) \times \mathrm{idf}(t_3) & \mathrm{tf}(t_4, d_1) \times \mathrm{idf}(t_4)\\ \mathrm{tf}(t_1, d_2) \times \mathrm{idf}(t_1) & \mathrm{tf}(t_2, d_2) \times \mathrm{idf}(t_2) & \mathrm{tf}(t_3, d_2) \times \mathrm{idf}(t_3) & \mathrm{tf}(t_4, d_2) \times \mathrm{idf}(t_4) \end{bmatrix}$

Let’s see now a concrete example of this multiplication:

$M_ {TF \ MBOX { - }} IDF= M_{train} \times M_{idf} = \\ \begin{bmatrix} 0 & 1 & 1 & 1\\ 0 & 2 & 1 & 0 \end{bmatrix} \times \begin{bmatrix} 0.69314718 & 0 & 0 & 0\\ 0 & -0.40546511 & 0 & 0\\ 0 & 0 & -0.40546511 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix} \\ = \begin{bmatrix} 0 & -0.40546511 & -0.40546511 & 0\\ 0 & -0.81093022 & -0.40546511 & 0 \end{bmatrix}$

And finally, we can apply our L2 normalization process to the$M_ {TF \ MBOX { - }} IDF$matrix. Please note that this normalization is“逐行”because we’re going to handle each row of the matrix as a separated vector to be normalized, and not the matrix as a whole:

$M_ {TF \ MBOX { - }} IDF= \frac{M_{tf\mbox{-}idf}}{\|M_{tf\mbox{-}idf}\|_2}$ $= \begin{bmatrix} 0 & -0.70710678 & -0.70710678 & 0\\ 0 & -0.89442719 & -0.4472136 & 0 \end{bmatrix}$

And that is our pretty normalized tf-idf weight of our testing document set, which is actually a collection of unit vectors. If you take the L2-norm of each row of the matrix, you’ll see that they all have a L2-norm of 1.

### Python practice

The first step is to create our training and testing document set and computing the term frequency matrix:

from sklearn.feature_extraction.text import CountVectorizer train_set = ("The sky is blue.", "The sun is bright.") test_set = ("The sun in the sky is bright.", "We can see the shining sun, the bright sun.") count_vectorizer = CountVectorizer() count_vectorizer.fit_transform(train_set) print "Vocabulary:", count_vectorizer.vocabulary # Vocabulary: {'blue': 0, 'sun': 1, 'bright': 2, 'sky': 3} freq_term_matrix = count_vectorizer.transform(test_set) print freq_term_matrix.todense() #[[0 1 1 1] #[0 2 1 0]]

from sklearn.feature_extraction.text import TfidfTransformer tfidf = TfidfTransformer(norm="l2") tfidf.fit(freq_term_matrix) print "IDF:", tfidf.idf_ # IDF: [ 0.69314718 -0.40546511 -0.40546511 0. ]

Ťf_idf_matrix = tfidf.transform(freq_term_matrix) print tf_idf_matrix.todense() # [[ 0. -0.70710678 -0.70710678 0. ] # [ 0. -0.89442719 -0.4472136 0. ]]

And that is it, theŤf_idf_matrix其实我们以前$M_ {TF \ MBOX { - }} IDF$matrix. You can accomplish the same effect by using theVectorizer类Scikit.learn的这是一个矢量器自动结合CountVectorizer和ŤheTfidfTransformerŤo you. SeeŤhis exampleŤo know how to use it for the text classification process.

I really hope you liked the post, I tried to make it simple as possible even for people without the required mathematical background of linear algebra, etc. In the next Machine Learning post I’m expecting to show how you can use the tf-idf to calculate the cosine similarity.

If you liked it, feel free to comment and make suggestions, corrections, etc.

### References

Wikipedia :: tf-idf

The classic Vector Space Model

Sklearn文本特征提取码

### 更新

13 Mar 2015-格式化，固定图像的问题。

## 103个想法“机器学习::文本特征提取（TF-IDF） - 第二部分”

1. Severtcev 说：

Wow!
Perfect intro in tf-idf, thank you very much! Very interesting, I’ve wanted to study this field for a long time and you posts it is a real gift. It would be very interesting to read more about use-cases of the technique. And may be you’ll be interested, please, to shed some light on other methods of text corpus representation, if they exists?
（对不起，糟糕的英语，我正在努力对其进行改进，但仍然有很多工作要做的）

2. Excellent work Christian! I am looking forward to reading your next posts on document classification, clustering and topics extraction with Naive Bayes, Stochastic Gradient Descent, Minibatch-k-Means and Non Negative Matrix factorization

Also, the documentation of scikit-learn is really poor on the text feature extraction part (I am the main culprit…). Don’t hesitate to join the mailing list if you want to give a hand and improve upon the current situation.

1. Great thanks Olivier. I really want to help sklearn, I just have to get some more time to do that, you guys have done a great work, I’m really impressed by the amount of algorithms already implemented in the lib, keep the good work !

3. I like this tutorial better for the level of new concepts i am learning here.
这就是说，学习scikits您正在使用哪个版本？
The latest as installed by easy_install seems to have a different module hierarchy (i.e doesn’t find feature_extraction in sklearn). If you could mention the version you used, i will just try out with those examples.

1. Hello Anand, I’m glad you liked it. I’ve added the information about the environment used just before the section “Python practice”, I’m using the scikits.learn 0.9 (released a few weeks ago).

4. siamii 说：

Where’s part 3? I’ve got to submit an assignment on Vector Space Modelling in 4 days. Any hope of putting it up over the weekend?

1. I’ve no date to publish it since I haven’t got any time to write it =(

5. 说：

谢谢again for this complete and explicit tutorial and I am waiting for the coming section.

6. 吴季刚 说：

谢谢克里斯Ťian! a very nice work on vector space with sklearn. I just have one question, suppose I have computed the ‘tf_idf_matrix’, and I would like to compute the pair-wise cosine similarity (between each rows). I was having problem with the sparse matrix format, can you please give an example on that? Also my matrix is pretty big, say 25k by 60k. Thanks a lot!

7. 哈立德 说：

伟大的职位......我明白了什么TF-IDF以及如何与一个具体的例子实施。但我发现2周的事情，我不知道：
1- You called the 2 dimensional matrix M_train, but it has the tf values of the D3 and D4 documents, so you should’ve called that matrix M_test instead of M_train. Because D3 and D4 are our test documents.
2 - 当你计算IDF值的T2（这是“太阳”），它应该是日志（2/4）。因为文件的数目是2 D3有词“太阳” 1次，D4有它的2倍。这使得3，但是我们也加1到值摆脱0分的问题。这使得4 ...我说得对不对还是我失去了一些东西？
谢谢。

1. Victoria 说：

You are correct: these are excellent blog articles, but the author REALLY has a duty/responsibility to go back and correct errors, like this (and others, e.g. Part 1; …): missing training underscores; setting the stop_words parameter; also on my computer, the vocabulary indexing is different.

As much as we appreciate the effort (kudos to the author!), it is also a significant disservice to those who struggle past those (uncorrected) errors in the original material.

1. Victoria 说：

re: my ‘you are correct comment’ (above), I should have added:

“… noting also Frédérique Passot’s comment (below) regarding the denominator:

“......我们用的是什么确实是在发生的一个术语，无论任何给定的文档中出现的术语次数的文件数量。在这种情况下，然后，在用于T2（“太阳”）的IDF值分母确实2 + 1（2个文件具有“太阳”术语，1以避免潜在的零分割误差）。“

2. Yeshwant 说：

哈立德，
This is a response to a very old question. However, I still want to respond to communicate what I understand from the article.
Your question 2: “When you calculate the idf value for the t2 (which is ‘sun’) it should be log(2/4)”
My understanding: The denominator in log term should be (number of documents in which the term appears + 1) and not frequency of the term. The number of documents the term “Sun” appears is 2 (1 time in D3 and 2 times in D4 — totally it appears 3 times in two documents. 3 is frequency and 2 is number of documents). Hence the denominator is 2 + 1 = 3.

8. arzu 说：

Ťhanks… excellent post…

9. Jack 说：

优秀的帖子！
I have some question. From the last tf-idf weight matrix, how can we get the importance of term respectively(e.g. which is the most important term?). How can we use this matrix to classify documents

10. Thanuj 说：

非常感谢。你在这样一个简单的方法来解释它。这是非常有用的。再次感谢了很多。

11. Thanuj 说：

我有同样的疑问，杰克（最后的评论）。从上个TF-IDF权重矩阵，我们怎么能拿到各自任期的重要性（例如，这是最重要的用语？）。我们如何利用这个矩阵来区分文档。

12. Ťintin 说：

我有个问题..
在TF-IDF操作后，我们得到与值的numpy的阵列。假设我们需要从阵列中获得最高50个值。我们怎样才能做到这一点？

1. ashwin sudhini 说：

high value of f(idf) denotes that the particular vector(or Document) has high local strength and low global strength, in which case you can assume that the terms in it has high significance locally and cant be ignored. Comparing against funtion(tf) where only the term repeats high number of times are the ones given more importance,which most of the times is not a proper modelling technique.

13. Vikram Bakhtiani 说：

嘿，
Thanx fr d code..was very helpful indeed !

1.适用于文档聚类，计算反相的术语频率之后，shud我使用任何关联性系数等Jaccards系数，然后应用聚类算法中像k均值或shud我计算反转术语频率后直接适用d k均值到文档向量？

2.您是如何评价倒词频为calcuating文档向量文本聚类？

谢谢a ton fr the forth coming reply!

14. @Khalid: what you’re pointing out in 1- got me confused too for a minute (M_train vs M_test). I think you are mistaken on your second point, though, because what we are using is really the number of documents in which a term occurs, regardless of the number of times the term occurs in any given document. In this case, then, the denominator in the idf value for t2 (“sun”) is indeed 2+1 (2 documents have the term “sun”, +1 to avoid a potential zero division error).

I’d love to read the third installment of this series too! I’d be particularly interested in learning more about feature selection. Is there an idiomatic way to get a sorted list of the terms with the highest tf.idf scores? How would you identify those terms overall? How would you get the terms which are the most responsible for a high or low cosine similarity (row by row)?

Thank you for the _great_ posts!

1. Bonnie Varghese 说：

Should idf(t2) be log 2/4 ?

15. Matthys Meintjes 说：

优秀文章和一个伟大的介绍TD-IDF正常化。

你必须解释这些复杂的概亚洲金博宝念非常清晰，结构化的方法。

谢谢！

1. 谢谢for the feedback Matthys, I’m glad you liked the tutorial series.

1. param 说：

very good & infomative tutorial…. please upload more tutorials related to documents clustering process.

16. 洛朗 说：

Excellent article ! Thank you Christian. You did a great job.

17. Gavin Igor 说：

Can you provide any reference for doing cosine similarity using tfidf so we have the matrix of tf-idf how can we use that to calculate cosine. Thanks for fantastic article.

18. 薰衣草 说：

谢谢so much for this and for explaining the whole tf-idf thing thoroughly.

1. 感谢您的反馈，我很高兴你喜欢这个系列教程。

19. Please correct me if i’m worng
从“频率后的公式Calculated in the first tutorial:” should Mtest not Mtrain. also after starting ‘These idf weights can be represented by a vector as:” should be idf_test not idf_train.

Btw great series, can you give an simple approach for how to implement classification?

20. 迪夫亚 说：

Excellent it really helped me get through the concept of VSM and tf-idf. Thanks Christian

21. 塞尔吉奥 说：

Very good post. Congrats!!

Showing your results, I have a question:

我读了维基百科：
成比例的TF-IDF值增加到的次数的字出现在文档中，但是通过在语料库中的字，这有助于控制的事实，一些词语通常比另一些更常见的频率偏移。

When I read it, I understand that if a word apperars in all documents is less important that a word that only appears in one document:

然而，在结果中，“太阳”或“明亮”是比“天空”最重要的。

我不知道的完全地理解它。

22. Awesome! Explains TF-IDF very well. Waiting eagerly for your next post.

23. awesome work with a clear cut explanation . Even a layman can easily understand the subject..

1. Great thanks for the feedback Rahul !

24. Jeremie 说：

Hello,

The explanation is awesome. I haven’t seen a better one yet. I have trouble reproducing the results. It might be because of some update of sklearn.
Would it be possible for you to update the code?

It seem that the formula for computing the tf-idf vector has changed a little bit. Is a typo or another formula. Below is the link to the source code.

https://github.com/scikit-learn/scikit-learn/blob/master/sklearn/feature_extraction/text.py#L954

Many thanks

25. Susan 说：

Terrific! I was familiar with tf-idf before but I found your scikits examples helpful as I’m trying to learn that package.

1. 我很高兴你喜欢苏珊，感谢您的反馈！

26. 谢谢你写这么详细的职位。我学会了配发。

27. 尤金Chinveeraphan 说：

优秀的帖子！一次偶然的机会找上CountVectorizer更多信息，无意中发现了这一点，但我很高兴我通过两个您的文章（第1部分和第2部分）的读取。

现在用书签您的博客

1. 为回馈尤金十分感谢，我真的很高兴你喜欢这个系列教程。

28. 说：

Does not seem to fit_transform() as you describe..
任何想法，为什么？
>>> TS
(‘The sky is blue’, ‘The sun is bright’)
>>> v7 = CountVectorizer()
>>> v7.fit_transform(ts)
<2×2 sparse matrix of type '’
with 4 stored elements in COOrdinate format>
>>>打印v7.vocabulary_
{u'is’：0，u'the”：1}

1. Ash 说：

Actually, there are two small errors in the first Python sample.
1. CountVectorizer should be instantiated like so:
count_vectorizer = CountVectorizer（STOP_WORDS = '英语'）
这将确保“是”，“的”等被删除。

2.要打印的词汇，你必须在末尾添加下划线。
打印“词汇：” count_vectorizer.vocabulary_

Excellent tutorial, just small things. hoep it helps others.

1. 德罗戈 说：

由于灰。虽然文章是相当自我解释的，您的评论使整个差异。

29. 约翰·凯尔文 说：

30. I’m using scikit learn v .14. Is there any reason my results for running the exact same code would result in different results?

31. Karthik 说：

32. Vijay 说：

Its useful…..thank you explaining the TD_IDF very elaborately..

33. 麦克风 说：

谢谢for the great explanation.

I have a question about calculation of the idf(t#).
In the first case, you wrote idf(t1) = log(2/1), because we don’t have such term in our collection, thus, we add 1 to the denominator. Now, in case t2, you wrote log(2/3), why the denominator is equal to 3 and not to 4 (=1+2+1)? In case t3, you write: log(2/3), thus the denominator is equal 3 (=1+1+1). I see here kind of inconsistency. Could you, please, explain, how did calculate the denominator value.

谢谢。

1. Hello Mike, thanks for the feedback. You’re right, I just haven’t fixed it yet due to lack of time to review it and recalculate the values.

2. xpsycho 说：

你理解错了，分母你不把这个词的总和每个文档中，你只是总结所有具有词的至少一个aparition的文件。

3. mik 说：

yes, I had the same question…

34. huda 说：

This is good post

35. huda 说：

it is good if you can provide way to know how use ft-idf in classification of document. I see that example (python code) but if there is algorithm that is best because no all people can understand this language.

谢谢

36. Ganesh神 说：

Great post, really helped me understand the tf-idf concept!

37. Samuel Kahn 说：

好贴

38. 尼斯。一种解释有助于正确看待这个事情。是TF-IDF的好办法做聚类（例如，从已知的语料用杰卡德分析或方差相对于平均值设定）？

Keep writing:)

39. Neethu Prem 说：

嗨基督徒，

这让我非常兴奋和幸运，读亚洲金博宝这篇文章。你理解的清晰反映了文件的清晰度。这让我重拾我的信心在机器学习领域。

谢谢a ton for the beautiful explanation.

Would like to read more from you.

谢谢，
Neethu

1. Great thanks for the kind wors Neethu ! I’m very glad you liked the tutorial series.

40. esra'a ok 说：

非常感谢你非常，非常亚洲金博宝美妙的和有用的。

1. 感谢您的反馈Esra'a。

41. 阿恩 说：

谢谢你的良好的收官之作。你提到一些这比较L1和L2规范的论文，我计划研究，多一点深入。你还知道他们的名字？

42. seher 说：

我如何能计算TF IDF为自己的文本文件，它位于一些地方在我的电脑？

43. Shubham 说：

Brilliant article.

By far the easiest and most sound explanation of tf-tdf I’ve read. I really liked how you explained the mathematics behind it.

44. 我hrab 说：

superb article for newbies

1. Dayananda 说：

优良的材质。优秀的！！！

45. Derrick 说：

嗨，伟大的职位！我使用的是TfidVectorizer模块scikit学习产生与规范= L2的TF-IDF矩阵。我把它叫做tfidf_matrix语料的fit_transform后，我一直在检查TfidfVectorizer的输出。我总结了行，但他们并不总和为1的代码是VECT = TfidfVectorizer（use_idf =真，sublunar_tf =真，规范=” L2）。tfidf_matrix = vect.fit_transform（数据）。当我运行tfidf_matrix.sum（轴= 1）的载体是大于1也许我看错矩阵或我误解如何正常化的作品。我希望有人能澄清这一点！谢谢

46. 克里斯 说：

Can I ask when you calculated the IDF, for example, log(2/1), did you use log to base 10 (e) or some other value? I’m getting different calculations!

47. Gonzalo G 说：

伟大的教程，刚开始在ML一份新工作，这很清楚，因为它应该是解释的事情。亚洲金博宝

48. Harsimranpal 说：

But I need more information, As you show the practical with python, Can you provide it with JAVA language..

49. Sebastian 说：

I’m a little bit confused why tf-idf gives negative numbers in this case? How do we interpret them? Correct me if I am wrong, but when the vector has a positive value, it means that the magnitude of that component determines how important that word is in that document. If the it is negative, I don’t know how to interpret it. If I were to take the dot product of a vector with all positive components and one with negative components, it would mean that some components may contribute negatively to the dot product even though on of the vectors has very high importance for a particular word.

50. Hi,
非常感谢您对这个主题这个详细的解释，真是太好了。无论如何，你可以给我一个提示，这可能是我的错误，我不断看到的来源：

freq_term_matrix = count_vectorizer.transform（TEST_SET）
AttributeError: ‘matrix’ object has no attribute ‘transform’

Am I using a wrong version of sklearn?

51. 莫希特古普塔 说：

Awesome simple and effective explaination.Please post more topics with such awesome explainations.Looking forward for upcoming articles.
谢谢

52. Alexandro 说：

Thank you Chris, you are the only one on the web who was clear about the diagonal matrix.

53. ishpreet 说：

Great tutorial for Tf-Idf. Excellent work . Please add for cosine similarity also:)

54. sherlockatsz 说：

我明白了TF-IDF计算处理。不过这是什么矩阵均值，以及我们如何使用TFIDF矩阵计算相似度让我困惑。你能解释一下，我们如何利用TFIDF矩阵.thanks

55. lightningstrike 说：

THX为你的露骨和详细的解释。

56. Anonymous 说：

谢谢，ñice post, I’m trying it out

57. Anonymous 说：

非常感谢您对这样一个惊人的详细的解释！

58. Akanksha Pande 说：

最好的解释..非常有帮助。亚洲金博宝你能告诉我如何绘制矢量文本分类的SVM ..我在微博分类工作。我很困惑，请帮助我。

59. Koushik 说：

I learned so many things. Thanks Christian. Looking forward for your next tutorial.

60. MHR 说：

您好，我很抱歉，如果我有错，但我不明白是怎么|| VD4 || 2 = 1。
D4 =的值（0.0，0.89,0.44,0.0），因此归一化将是= SQRT（正方形（0.89）+平方（0.44））= SQRT（0.193）= 0.44

61. 李催情 说：

嗨，这是一个伟大的博客！
If I need to do bi-gram cases, how can I use sklearn to finish it?

62. alireza 说：

it is very great. i love your teach. very very good

63. Ritesh 说：

我没有得到相同的结果，当我执行相同的脚本。
print (“IDF:”, tfidf.idf_) : IDF: [ 2.09861229 1. 1.40546511 1. ]

My python version is: 3.5
Scikit了解的版本是：o.18.1

what does i need to change? what might be the possible error?

谢谢，

1. It can be many things, since you’re using a different Python interpreter version and also a different Scikit-Learn version, you should expect differences in the results since they may have changed default parameters, algorithms, rounding, etc.

1. Ravithej Chikkala 说：

I am also getting: IDF: [2.09861229 1. 1.40546511 1. ]

64. Victor 说：

完美的介绍！
No hocus pocus. Clear and simple, as technology should be.
亚洲金博宝很有帮助
Thank you very much.
Keep posting!

65. 亚太区首席技术官Matt南卡尼 说：

为什么| d |= 2，在IDF方程。它不应该是4，因为| d |代表的审议的文件数量，我们有2从测试，2个来自火车。

66. LÊ VĂN HẠNH 说：

这篇文章很有意思。我喜欢这个岗位？

67. Bren 说：

明确的，重点突出的解释... .great

68. Shipika辛格 说：

hey , hii Christian
your post is really helpful to me to understand tfd-idf from the basics. I’m working on a project of classification where I’m using vector space model which results in determining the categories where my test document should be present. its a part of machine learning . it would be great if you suggest me something related to that. I’m stuck at this point.
Ťhank you

69. Eshwar S G 说：

看到这个例子就知道如何使用它的文本分类过程。“这个”链接不起作用了。能否请您提供相关链接，例如。

谢谢

70. 阿曼达 说：

such a great explanation! thankyou!

71. alternative investing 说：

wow, awesome post.Much thanks again. Will read on

Say, you got a nice post.Really thank you! Fantastic.

73. Ťogel online 说：

哇，伟大的文章post.Much再次感谢。真棒。

74. Mobile Computer 说：

75. Chocopie 说：

1vbXlh你提出了一个非常美妙的细节，欣赏它的职位。亚洲金博宝

76. I know this site provides quality based articles or
reviews and additional data, is there any other web page which presents these kinds of
information in quality?

77. Rousse 说：

在第一个例子。IDF（T1），日志（2/1）由计算器= 0.3010。为什么他们获得0.69 ..请有什么不对？

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