## Monday, December 19, 2011

3Hi all,

This month I was studying about information retrieval and text mining, specially how to convert the textual representation of information into a Vector Space Model (VSM).  The VSM is an algebraic model representing the importance of a term (tf-idf) or even the absence or presence (Bag of Words) of it in a document. I'd like to mention the excellent post from the researcher Christian Perone at his blog Pyevolve about Machine learning and Text Mining with TF-IDF, a great post to read.

I decided in this post to be shorter and give some examples using Python . I expect at the end of this post you feel confortamble to use tf-idf at your tasks handling with text mining.

By the way, I extremely recommend you to check the scikit.learn machine learning toolkit. There is a whole package to work with text classification, including TF-IDF with Python!

What is TF-IDF ?

Term Frequency - Inverse Document Frequency is a weighting scheme that is commonly used in information retrieval tasks. The goal is to model each document into a vector space, ignoring the exact ordering of the words in the document while retaining information about the occurrences of each word.

It is composed by two terms: one first computes the normalized Term Frequency, which is the number of times a word appears in a documnet, divided by the total number of words in that document. Then, the second term is the Inverse Document Frequency, which is computed as the logarithm of the number of the documents in the corpus divided by the number of documents where the term ti appears. Or, in symbols:

and

The TF-IDF gives how important is a word to a document in a collection, since it takes in consideration not only the isolated term but also the term within the document collection. The intuition is that a term that occurs frequently in many documents is not a good discriminator ( why emphasize a term which is almost present in the entire corpus of your documents ?)  So it will scale down the frequent terms while scaling up the rare terms; for instance, a term that occurs 10 times more than another isn't 10 times more important thant it.

For computing the TF-IDF weights for each document in the corpus, it is required in the corpus a series of steps:  1) Tokenize the corpus  2)  Model the Vector  Space  and 3) Compute the TF-IDF weight for each document in the corpus.

Let's going through each step:

Tokenization

First we need to tokenize the text. To do this, we can use the NLTK library which is a collection of natural language processing algorithms written in Python. The process of tokenizing the documents in the corpous is a two steps:  First the text is splint into sentences, and then the sentences are split into the individual words. It is important to notice that there are several words that are not relevant, that is, terms like "the, is, at, on", etc...  aren't going to help us, so in the information extraction, we ignore them. Those words are commonly called stop words and they are present in almost all documents, so it is not relevant for us. In portuguese we also have those stop words such as (a, os , as , os, um , umas, que, etc.)

So considering our example below:

We will tokenize this collection of documents and represent them as vectors (rows) of a matrix with |D| x F shape, where |D|  is the cardinality of the document space, or how many documents we have and the F is the number of features, in our example it is represented by the vocabulary size.

So the matrix representation of our vectors above is:

As you have noticed, these matrices representing the term frequencies (tf) tend to be very sparse (lots of  zero-elements),  so you will usually see the representation of these matrices as sparse matrices. The code shown below will tokenize each document in the corpus and compute the term frequencies.

Model the Vector Space

Now that each of the documents in the corpus has been tokenized, the next step is to compute the document frequency quantity, that is, for each term, how many documents that term appears in. Before going to IDF, it is important to normalize the term-frequencies. Why ?  Imagine that we have a repeated term in document with porpuse of improving its ranking on an Information Retrieval System or even create a bias torwards long documents, making them look more important than they are just because of the high frequency of the term in the document. By normalizing the TF vector we can overcome this problem.
The code.

Compute the TF-IDF

Now that you saw how the vector normalization was applied, we will now have to compute the second term of tf-idf: the inverse document frequency. The code is provided below:

The TF-IDF is the product between the TF and IDF.  So a high weight of the tf-idf  is reached when you have a high term frequency (tf) in the given document and low document frequency of the term in the whole collection. Now let's see the tf-idf computed for each term present in the vector space.

The code.

Putting everything together, the following code will compute the TF-IDF weights for each document. And the result matrix it will be:

A row of this matrix would be:

I ommited the zero-values elements of the row.

If we would decide to check the most relevant words for this place, by using the tf-idf I could see that the place has a nice hot chocolate drink (0.420955 <= chocolate quente ótimo), the soft drink nega maluca is also delicious (0.315716 - nega maluca uma delicia),  its Cheese bun is also quite good (0.252573 - pao de queijo muito bom).

And that is how we comput  our $M_{tf\mbox{-}idf}$ matrix.  You can take a look at this link and this one to know how to use it with GenSim and Scikit.Learn respectively.

That's all,  I hope that  you enjoyed this article and help more people to know how to implement the tf-idf weight to mine your collection of texts.  Feel free to comment and make suggestions.

The source code of this example is also available.

Regards,

Marcel Caraciolo

1. Marcelo,thanks a lot for your post. We will use it for teaching the young computer engineers.

2. i don't understand why def idf(word, list_of_docs): the variable is named list_of_doc when the variable vocabulary is input?

1. Yeah, I was wondering the same thing...

3. Thanks for this example. Could you reupload 1st and 2nd images. I think those are formulas.

Nice work

1. 1st and 2nd images are the just the formula for TF and IDF

4. These post were really helpful in understanding the meaning of text mining. It help in putting the unstructured text in a structured form. you can check the website LOGINWORKS http://www.loginworks.com/data-mining/ , to get the accurate data!!

5. Embedded system training: Wiztech Automation Provides Excellent training in embedded system training in Chennai - IEEE Projects - Mechanical projects in Chennai. Wiztech provide 100% practical training, Individual focus, Free Accommodation, Placement for top companies. The study also includes standard microcontrollers such as Intel 8051, PIC, AVR, ARM, ARMCotex, Arduino, etc.

Embedded system training in chennai
Embedded Course training in chennai
Matlab training in chennai
Android training in chennai
LabVIEW training in chennai
Robotics training in chennai
Oracle training in chennai
Final year projects in chennai
Mechanical projects in chennai
ece projects in chennai

6. I like the way you start and then conclude your thoughts. Thanks for this nice information.

Data Analytics Courses in Chennai

7. Hi admin thanks for sharing informative article on hadoop technology. In coming years, hadoop and big data handling is going to be future of computing world. This field offer huge career prospects for talented professionals. Thus, taking Hadoop & Spark Training in Hyderabad will help you to enter big data hadoop & spark technology.

8. Hey how its possible to learn python to assemble machine language through it

Android training in chennai | Oracle dba Training in Chennai | Python Training in chennai

9. tf–idf, short for term frequency–inverse document frequency, is a numerical ... PHP Training in Chennai |
Pega Training in Chennai

10. Useful Post, Thanks for sharing with us

Best engineering colleges in jaipur

11. PHP course is very important nowadays.so learn language quickly & connect a link https://goo.gl/z0JFB7
https://goo.gl/WzKGr2
https://goo.gl/pO7P7J
https://goo.gl/Tshw0J
https://goo.gl/HZJgxn

12. TestComplete can be act as a backbone of the Web Automation Tool.| https://www.gangboard.com/software-testing-training/test-complete-training
https://www.gangboard.com/cloud-computing-training/vmware-training

13. Thank you so much for sharing. it’s useful for me....| Dot Net Training in Annanagar

Dot Net Training

14. Thank you for explaining the programs on python online training

15. It is really a great work and the way in which u r sharing the knowledge is excellent.
Thanks for helping me to understand basic concepts. As a beginner in dot net programming your post help me a lot.Thanks for your informative article.Dot Net training in chennai | dot net training and placement | Dot Net training in velachery

16. Thank for you sharing rèm cửa

17. It is a great thing how well you have created this post, its very unique and informative. This is among the pages that i would bookmark, the information on machine learning with python is quite scary but interesting to read. With a very beautiful Digital Calendar, you will not be required to keep using manual one.Its saves a lot of space, its easy and convenient to use too.

18. Bán thuốc diệt kiến của Nhật Bản Super Arinosu Koroki siêu an toàn, diệt 1 con lây chết cả tổ LH 0983131528

19. the blog is about Machine Learning with Python: Meeting TF-IDF for Text Mining it is useful for students and Python Developers for more updates on python follow the link

Python Online Training

ServiceNow Online Training

mulesoft Online Training

20. Information is very useful and thanks for sharing
NLP Training in Chennai | ramsnlp

21. Good blog and thanks for sharing this information
NLP Certification in Chennai | ramsnlp

22. Nice Blog Thank You for sharing.python Online Training Hyderabad

23. Try to use the Dịch Vụ Làm Visa Trọn Gói 0983131528 Viseca offers a wide selection of Mastercard and Visa credit cards. Read more online now and make a free comparison.

24. Try to use the Dịch Vụ Làm Visa Trọn Gói Hà Nội 0983.1315.28 Viseca offers a wide selection of Mastercard and Visa credit cards. Read more online now and make a free comparison.

25. the blog is good and Interactive it is about Mulesoft Developer it is useful for students and Mulesoft Developers for more updates on Mulesoft mulesoft Online course hyderabad

26. This post is much helpful for us. This is really very massive value to all the readers and it will be the only reason for the post to get popular with great authority.
Best Online Python training

27. SUPER

28. Great Article… I love to read your articles because your writing style is too good, its is very very helpful for all of us and I never get bored while reading your article because, they are becomes a more and more interesting from the starting lines until the end.
Selenium Training in Bangalore | Selenium Training in Bangalore | Selenium Training in Bangalore | Selenium Training in Bangalore

29. If someone looking for the best business opportunity in education sector in India. Brainy India is the best option for you.

30. Nice tips. Very innovative... Your post shows all your effort and great experience towards your work Your Information is Great if mastered very well.
python training in rajajinagar
Python training in bangalore
Python training in usa

31. Very nice article for online training thanks for sharing. Best Python Online Training || Learn Python Course

32. Some us know all relating to the compelling medium you present powerful steps on this blog and therefore strongly encourage
contribution from other ones on this subject while our own child is truly discovering a great deal.
Have fun with the remaining portion of the year.

Selenium training in bangalore | best selenium training in bangalore | advanced selenium training in bangalore

33. Greetings. I know this is somewhat off-topic, but I was wondering if you knew where I could get a captcha plugin for my comment form? I’m using the same blog platform like yours, and I’m having difficulty finding one? Thanks a lot.
Best AWS Training in Chennai | Amazon Web Services Training Institute in Chennai Velachery, Tambaram, OMR
Advanced AWS Training in Bangalore |Best AWS Training Institute in Bangalore BTMLA ,Marathahalli

34. I appreciate your efforts because it conveys the message of what you are trying to say. It's a great skill to make even the person who doesn't know about the subject could able to understand the subject . Your blogs are understandable and also elaborately described. I hope to read more and more interesting articles from your blog. All the best.
microsoft azure training in bangalore
rpa training in bangalore
rpa training in pune
best rpa training in bangalore

35. Superb. I really enjoyed very much with this article here. Really it is an amazing article I had ever read. I hope it will help a lot for all. Thank you so much for this amazing posts and please keep update like this excellent article. thank you for sharing such a great blog with us.
microsoft azure training in bangalore
rpa training in bangalore
rpa training in pune
best rpa training in bangalore

36. Read all the information that i've given in above article. It'll give u the whole idea about it.
Best Devops Training in pune
Devops Training in Bangalore
Power bi training in Chennai

37. This comment has been removed by the author.

38. Hmm, it seems like your site ate my first comment (it was extremely long) so I guess I’ll just sum it up what I had written and say, I’m thoroughly enjoying your blog. I as well as an aspiring blog writer, but I’m still new to the whole thing. Do you have any recommendations for newbie blog writers? I’d appreciate it.
python Online training in chennai
python training institute in marathahalli
python training institute in btm
Python training course in Chennai

39. Nice information, valuable and excellent design, as share good stuff with good ideas and concepts, lots of great information and inspiration, both of which I need, thanks to offer such a helpful information here.
python Course in Pune
python Course institute in Chennai
python Training institute in Bangalore

40. This is quite educational arrange. It has famous breeding about what I rarity to vouch. Colossal proverb.
This trumpet is a famous tone to nab to troths. Congratulations on a career well achieved.
This arrange is synchronous s informative impolite festivity to pity. I appreciated what you ok extremely here.

Selenium training in bangalore
Selenium training in Chennai
Selenium training in Bangalore
Selenium training in Pune
Selenium Online training

41. Hii useful blog very good to read
blue prism training class in chennai

42. Very interesting,good job and thanks for sharing such a good blog.your article is so convincing that I never stop myself to say something about it.You’re doing a great job.Keep it up.python training in mumbai
‌ ‌

43. ,good job and thanks for sharing such a good blog You’re doing a great job.Keep it up !!

machine learning training in jaipur

python training in jaipur

best data science training training in jaipur

44. Hello, I read your blog occasionally, and I own a similar one, and I was just wondering if you get a lot of spam remarks? If so how do you stop it, any plugin or anything you can advise? I get so much lately it’s driving me insane, so any assistance is very much appreciated.
Android Course Training in Chennai | Best Android Training in Chennai
Datascience Course Training in Chennai | Best Data Science Training in Chennai

45. Thank you so much for given such an informative blog. Get the best Website Designing and Development Services by Ogeninfo.
Website Designing Company in Delhi

46. Good Post. I like your blog. Thanks for Sharing
Python Training in Noida

47. Get the best performing Mutual Fund by Mutual Fund Wala and know the best investment schemes.
Mutual Fund Agent

48. This comment has been removed by the author.

49. Awesome blog again thanks for such an informative blog sharing with us.
Lifestyle Magazine India

50. Attend The Python training in bangalore From ExcelR. Practical Python training in bangalore Sessions With Assured Placement Support From Experienced Faculty. ExcelR Offers The Python training in bangalore.
python training in bangalore

51. I have to search sites with relevant information on given topic and provide them to teacher our opinion and the article.
machine learning course in bangalore

52. I feel that is among the live casino malaysia so much vital information for me. And i'm satisfied reading your article. However wanna observation on some basic issues, The website taste is great, the articles is in point of fact nice : D. Just right job, cheers The Gaming Club bears a license from the supervision of Gibraltar, and claims to be one of a choose few casinos that have a license from the Gibraltar government. A devotee of the Interactive Gaming Council (IGC), The Gaming Club follows all the guidelines laid the length of by the organization, something that has in imitation of a long way in it mammal certified as a good area to gamble online.

Everything nearly The Gaming Club feels good; be it the promotions, the big number of games, the combined banking options on offer, the highly developed security measures, or the fair and responsible gaming practices the casino adopts.

The Gaming Club motors along upon software developed by one of the giants of online gaming software move on Microgaming. The software it uses is ahead of its time and has a range of features designed to add together your online gambling experience and create you desire to arrive assist after all circular of gambling you accomplish here.

Another hallmark of a fine casino is the quality of its customer withhold team, and The Gaming Club does not disappoint on this front.
http://magnum4dlive.com/

53. Awesome blog. I enjoyed reading your articles. This is truly a great read for me. I have bookmarked it and I am looking forward to reading Python training in pune new articles. Keep up the good work!

54. Nice blog, thank you so much for sharing this informative blog. Visit Ogen Infosystem for the best Website Designing and Development Services in Delhi, India. Also get Digital Marketing Services like PPC, SEO, Social Media Optimization etc.
SEO Service in Delhi

Really this is a very useful blog.
sServicenow service portal training

56. On jobsupport

57. learn python online

58. Nice blog, Visit Kalakutir Pvt Ltd for Godown Line Marking Painting, Base Company Logo Painting, and School Bus Painting.
School Bus Painting

59. I want to know more about American eagle credit card login

60. Thanks for sharing such a great blog Keep posting..
Python Training in Delhi
Python Course in Delhi

61. Data for a Data Scientist is what Oxygen is to Human Beings. business analytics course with placement this is also a profession where statistical adroit works on data – incepting from Data Collection to Data Cleansing to Data Mining to Statistical Analysis and right through Forecasting, Predictive Modeling and finally Data Optimization.

62. I have seen your blog and really amazing information put in this. If anyone needs Website Designing and Digital Marketing Services in India, visit Ogen Infosystem in Delhi to get a creative and responsive website.
Best Website Designing Company in India

64. Appreciating the persistence you put into your blog and detailed information you provide.
Css training in chennai | Css course in chennai
blue prism training in chennai| Blue prism training course in chennai

65. This concept is a good way to enhance the knowledge.thanks for sharing..

66. Thank you for valuable information.I am privilaged to read this post.microsoft azure training in bangalore

67. Very useful and information content has been shared out here, Thanks for sharing it.google cloud platform training in bangalore

68. These provided information was really so nice,thanks for giving that post and the more skills to develop after refer that post.blue prism training in bangalore

69. Your articles really impressed for me,because of all information so nice.oracle apps scm training in bangalore

70. inking is very useful thing.you have really helped lots of people who visit blog and provide them use full information.sccm training in bangalore

71. Being new to the blogging world I feel like there is still so much to learn. Your tips helped to clarify a few things for me as well as giving.vmware training in bangalore

72. Really it was an awesome article,very interesting to read.You have provided an nice article,Thanks for sharing.aws training in bangalore

73. I know that it takes a lot of effort and hard work to write such an informative content like this.data science training in bangalore

74. Your articles really impressed for me,because of all information so nice.robotic process automation (rpa) training in bangalore

75. Being new to the blogging world I feel like there is still so much to learn. Your tips helped to clarify a few things for me as well as giving.uipath training in bangalore

76. Really it was an awesome article,very interesting to read.You have provided an nice article,Thanks for sharing.blue prism training in bangalore

77. This is really an awesome post, thanks for it. Keep adding more information to this.openspan training in bangalore

78. I am overwhelmed by your post with such a nice topic. Usually I visit your blogs and get updated through the information you include but today’s blog would be the most appreciable. Well done!
Please check ExcelR Data Science Certification

79. Enjoyed reading the article above, really explains everything in detail, the article is very interesting and effective. Thank you and good luck…

Start your journey with Database Developer Training in Bangalore and get hands-on Experience with 100% Placement assistance from experts Trainers @Bangalore Training Academy Located in BTM Layout Bangalore.

80. That was really a great Article.Thanks for sharing information. Continue doing this.

Best SAP EWM Training in Bangalore - Learn from best Real Time Experts Institutes in Bangalore with certified experts & get 100% assistance.

81. You might comment on the order system of the blog. You should chat it's splendid. Your blog audit would swell up your visitors. I was very pleased to find this site.I wanted to thank you for this great read!!
Know more Data Science Course in Pune

82. Such a great word which you use in your article and article is amazing knowledge. thank you for sharing it.

Learn DevOps from the Industry Experts we bridge the gap between the need of the industry. eTechno Soft Solutions provide the Best DevOps Training in Bangalore .

83. Such a great information for blogger iam a professional blogger thanks…

Learn Best PEGA Training in Bangalore from Experts. Softgen Infotech offers the Best PegaTraining in Bangalore.100% Placement Assistance, Live Classroom Sessions, Only Technical Profiles, 24x7 Lab Infrastructure Support.

84. A great website with interesting and unique material what else would you need.

360digitmg Internet ofThings Malaysia

85. Nice Post. Jeewangarg is a Leading Digital Marketing Company which is helping your brand to cut through the Digital Clutter with its best SEO Company in Delhi. Our range of Services includes SEO Services, PPC Services in Delhi, Website Designing Services and Social Media Marketing Services. Being a Google Partners, we provide our client with 100% satisfaction in every aspect of their marketing goals. So, what are you waiting for Connect to the team of best SEO Expert in India, Google Ads Experts, Website Designing Experts, Social Media Experts & more to boost your Digital Presence today with the high quality Digital Marketing Services.

86. This post is really nice and informative. The explanation given is really comprehensive and informative. devops training videos by 10+ years experienced faculty.

87. Snapdeal Winner List here came up with an Offer where you can win Snapdeal prize list 2020 by just playing a game & win prizes.
Snapdeal winner name2020 also check the Snapdeal lucky draw2020

88. This post is very simple to read and appreciate without leaving any details out. Great work! data science course

89. I am really happy to say it’s an interesting post to read . I learn new information from your article , you are doing a great job . Keep it up and a i also want to share some information regarding selenium testing course and selenium training videos

90. Thanks for sharing such a great information. Its really nice and informative learn ai programming.

91. I seriously love your site.. Excellent colors & theme. Did you develop this web site yourself? Please reply back as I’m looking to create my own blog and want to know where you got this from or just what the website theme is called. Thank you!

92. Good Post.Thanks for Sharing
website designing company in Delhi

93. Enjoyed reading this article throughout.Nice post! IoT is the trendy course right now and is going to be in
a great demand in near future as jobs for this domain will be sky rocketted.To be on par with the current trend we have to
gain complete knowledge about the subject. For the complete course online
360Digitmg Iot Certification Training
360Digitmg Internet of things courses online

94. Hi, Thanks for sharing wonderful stuff...

For More:

95. I really enjoy By reading of all your Articles. Simply wanted to inform you that you have people like me who appreciate your work. Definitely a great post. The information that you have provided is very helpful for me.

96. Nice article. For offshore hiring services visit:
renaissancetainela

97. Thanks for the informative article About AWS. This is one of the best resources I have found in quite some time. Nicely written and great info. I really cannot thank you enough for sharing.

Java training in chennai | Java training in annanagar | Java training in omr | Java training in porur | Java training in tambaram | Java training in velachery

98. nice blog about machine lerning & phython information you provide very helpful information.

air hostess institute

99. All the contents you mentioned in post is too good and can be very useful. I will keep it in mind, thanks for sharing the information keep updating, looking forward for more posts.Thanks
Data Science Course in Bangalore

100. This is my first time i visit here and I found so many interesting stuff in your blog especially it's discussion, thank you.
Data Science Training in Bangalore

101. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. Awesome blog. I enjoyed reading your articles. This is truly a great read for me. I have bookmarked it and I am looking forward to reading new articles. Keep up the good work!.
Data Science Course in Bangalore
Data Science Training in Bangalore
Data Science Training in Pune
Data Science Course in Pune

102. Analytics certification is an area of study in the world of data analytics which addresses the process of decision-making using data analysis. machine learning course hyderabad

103. A great website with interesting and unique material what else would you need.data science course

104. If you don"t mind proceed with this extraordinary work and I anticipate a greater amount of your magnificent blog entriesdata science certification

105. Mmm.. good to be here in your article or post, whatever, I think I should also work hard for my own website like I see some good and updated working in your site.data science course in delhi

106. Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing.

Simple Linear Regression

Correlation vs covariance

KNN Algorithm

107. This Was An Amazing ! I Haven't Seen This Type of Blog Ever ! Thankyou For Sharing, data scientist course in hyderabad with placement

108. Thanks for Sharing This Article.It is very so much valuable content. I hope these Commenting lists will help to my website
python training in bangalore

python online training

python training

python training in coimbatore

109. very special. easy to understand…. taking things from root .. stay blessed machine learning online course!

110. Machine Learning Courses in Pune I really enjoy reading and also appreciate your work. I read that Post and got it fine and informative. Please share more like that...
I have bookmarked your website because this site contains valuable information in it. I am really happy with articles quality and presentation. Thanks a lot for keeping great stuff. I am very much thankful for this site.

I am always searching online for articles that can help me. There is obviously a lot to know about this. I think you made some good points in Features also. Keep working, great job !

112. This professional hacker is absolutely reliable and I strongly recommend him for any type of hack you require. I know this because I have hired him severally for various hacks and he has never disappointed me nor any of my friends who have hired him too, he can help you with any of the following hacks:

-Phone hacks (remotely)
-Credit repair
-Bitcoin recovery (any cryptocurrency)
-Make money from home (USA only)
-Social media hacks
-Website hacks
-Erase criminal records (USA & Canada only)
-funds recovery

Email: onlineghosthacker247@ gmail .com

113. This professional hacker is absolutely reliable and I strongly recommend him for any type of hack you require. I know this because I have hired him severally for various hacks and he has never disappointed me nor any of my friends who have hired him too, he can help you with any of the following hacks:

-Phone hacks (remotely)
-Credit repair
-Bitcoin recovery (any cryptocurrency)
-Make money from home (USA only)
-Social media hacks
-Website hacks
-Erase criminal records (USA & Canada only)
-funds recovery

Email: onlineghosthacker247@ gmail .com

114. <a href="https://www.excelr.com/business-analytics-training-in-pune/”> Courses in Business Analytics</a> have express a few of the articles on your website now, and I really like your style of blogging. I added it to my favorite’s blog site list and will be checking back soon…
I am always searching online for articles that can help me. There is obviously a lot to know about this. I think you made some good points in Features also. Keep working, great job !

115. Looking for JOB in core industry? We're offering additional discount on early enrollment on full module Automation Training. Certificate will be given to those who completed their training and also get 100% Job assistance(Life Time).Call 9953489987, 9711287737.

116. It's really a good blog kindly thank you for sharing this.
3D Scanning Services Near Me

117. The article is very interesting and effective.
PYthon Training in Gurgaon

118. Easily, the article is actually the best topic on this registry related issue. I fit in with your conclusions and will eagerly look forward to your next updates. Just saying thanks will not just be sufficient, for the fantasti c lucidity in your writing. I will instantly grab your rss feed to stay informed of any updates.
Data Science Training

119. I am really happy with your blog because your article is very unique and powerful for new reader.
DevOps Training in Chennai

DevOps Course in Chennai

120. I really thank you for the valuable info on this great subject and look forward to more great posts ExcelR Business Analytics Courses

121. I read that Post and got it fine and informative. Please share more like that...
data science in malaysia

122. Thank you for sharing this amazing blog.
Thanks a lot.
I want to share infographic of applications of Machine Learning
You can also hire AI and Machine Learning Developers from Dark Bears.

124. This Blog is very useful and informative.
ai course in noida

125. Thanks for the information about Blogspot very informative for everyone
data scientist course

126. I cannot thank you enough for the blog.Thanks Again. Keep writing.
data science training
python training
angular js training
selenium trainings
sql server dba training

127. Very amazing and interesting post, thank you for sharing
Data Science Training In Pune

128. Looking for the best online Arabic Classes in Malaysia? Join Ziyyara as we have the best selected online Arabic tutors for you in Malaysia.
Contact no:- @9654271931
Visit On:- Online Arabic Class in Malaysia

129. I love to have this kind of information. www.hairsalonmarinadelrey.com

130. cơ hội đầu tư cho bạn tại Big Đầu tư

131. Join now and be the first to enjoy the advantages that come with Artificial Intelligence Training in Hyderabad and build your career in the field of Artificial Intelligence by joining AI Patasala.

132. Studyprovider has experts team are giving the homework help, assignment help, report, thesis, research writing services and lab report assignment help available 24/7 seven days a week contact now.

133. Thanks for sharing valuable information..
Great post.Keep posting great article like this with us.
HSC Training in kerala|Safety Courses In Kerala

134. I want you to thank for your time of this wonderful read!!! I definately enjoy every little bit of it and I have you bookmarked to check out new stuff of your blog a must read blog!
data scientist certification malaysia

135. Nice blog! Thanks for sharing this valuable information
RPA Training in Gurgaon

136. This is really an amazing article. Your article is really good and your article has always good content with a good powerpoint with informative information.
Best Hospital in Jaipur
cardiology hospital in Jaipur
Super speciality hospital in Jaipur
asthma and Allergy hospital in Jaipur
endocrinology hospital in Jaipur
Neurology hospital in Jaipur

137. Your blog provided us with valuable information to work with. Each & every tips of your post are awesome. Thanks a lot for sharing. Keep blogging,

138. Great article, thank you for sharing.
RPA Training

139. Thank you the sharing the most informative blog for us. It may helpfull for you all.

Java Training in Chennai
Java Training Institute in Chennai

140. Thanks for sharing this information. Machine Learning Course in Pune

141. very useful and informative blog.
artificial intelligence Classes in Pune

142. Nice blog Post. Thanks for posting.
Visit Python Classes in Pune

143. Azure DevOps Training Online
Azure DevOps Online Training
Azure DevOps Training in Ameerpet
Snowflake Training