Pages

Machine Learning with Python: Meeting TF-IDF for Text Mining

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

196 comments:

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

    ReplyDelete
  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?

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

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

    Nice work

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

      Delete
  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!!

    ReplyDelete
  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

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

    Data Analytics Courses in Chennai

    ReplyDelete
  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.

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

    ReplyDelete
  9. 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

    ReplyDelete
  10. 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/crm-training/salesforce-admin-training
    https://www.gangboard.com/business-intelligence-training/msbi-training
    https://www.gangboard.com/cloud-computing-training/vmware-training

    ReplyDelete
  11. 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

    ReplyDelete
  12. 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.

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

    ReplyDelete
  14. 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

    For more info on other technologies go with below links

    tableau online training hyderabad

    ServiceNow Online Training

    mulesoft Online Training

    ReplyDelete
  15. 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.

    ReplyDelete
  16. 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.

    ReplyDelete
  17. 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

    ReplyDelete
  18. 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

    ReplyDelete
  19. SUPER
    http://spunksoft.com/course/rpa-training-in-hyderabad/

    ReplyDelete
  20. 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

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

    ReplyDelete
  22. 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

    ReplyDelete

  23. 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

    ReplyDelete

  24. 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

    ReplyDelete
  25. 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

    ReplyDelete
  26. 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

    ReplyDelete
  27. 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

    ReplyDelete
  28. This comment has been removed by the author.

    ReplyDelete
  29. 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

    ReplyDelete
  30. 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

    ReplyDelete
  31. 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

    ReplyDelete
  32. 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
    ‌ ‌

    ReplyDelete
  33. 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

    ReplyDelete
  34. 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

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

    ReplyDelete
  36. This comment has been removed by the author.

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

    ReplyDelete
  38. 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

    ReplyDelete
  39. 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

    ReplyDelete

  40. 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/

    ReplyDelete
  41. 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!

    ReplyDelete
  42. 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

    ReplyDelete
  43. Your content is very impressive and thanks for sharing this article. its very useful.
    Really this is a very useful blog.
    sServicenow service portal training

    ReplyDelete
  44. On jobsupport
    Your content is very impressive and thanks for sharing this article. its very useful.

    ReplyDelete
  45. learn python online
    Your content is very impressive and thanks for sharing this article. its very useful.

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

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

    ReplyDelete
  48. 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.

    ReplyDelete
  49. 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

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

    ReplyDelete
  51. 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

    ReplyDelete
  52. 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

    ReplyDelete
  53. 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

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

    ReplyDelete
  55. 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

    ReplyDelete
  56. 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

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

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

    ReplyDelete
  59. 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

    ReplyDelete
  60. 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.

    ReplyDelete
  61. 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.

    ReplyDelete
  62. 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

    ReplyDelete
  63. 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 .

    ReplyDelete
  64. 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.

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

    360digitmg Internet ofThings Malaysia

    ReplyDelete
  66. 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.

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

    ReplyDelete
  68. 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

    ReplyDelete

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

    ReplyDelete

  70. 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

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

    ReplyDelete
  72. 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!

    ReplyDelete
  73. 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

    ReplyDelete
  74. 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.
    Machine Learning Training In Hyderabad

    ReplyDelete
  75. Nice article. For offshore hiring services visit:
    renaissancetainela

    ReplyDelete
  76. 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

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

    air hostess institute

    ReplyDelete
  78. 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

    ReplyDelete
  79. 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

    ReplyDelete
  80. 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
    PMP Certification Training in Hyderabad
    Data Science Training in Pune
    Data Science Course in Pune

    ReplyDelete
  81. 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

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

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

    ReplyDelete
  84. 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

    ReplyDelete
  85. 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


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

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

    ReplyDelete
  88. 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.

    ReplyDelete
  89. <a href="https://www.excelr.com/business-analytics-training-in-pune/”> Business Analytics Courses </a>
    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 !

    ReplyDelete
  90. 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)
    -Grade change
    -funds recovery

    Email: onlineghosthacker247@ gmail .com

    ReplyDelete
  91. 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)
    -Grade change
    -funds recovery

    Email: onlineghosthacker247@ gmail .com

    ReplyDelete
  92. <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 !

    ReplyDelete
  93. 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.

    ReplyDelete
  94. 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

    ReplyDelete
  95. 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



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

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

    ReplyDelete
  98. 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.

    ReplyDelete
  99. The writer is enthusiastic about purchasing wooden furniture on the web and his exploration about best wooden furniture has brought about the arrangement of this article. ExcelR Data Analyst Course

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

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

    ReplyDelete
  102. 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

    ReplyDelete
  103. 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.
    Artificial Intelligence Training Hyderabad

    ReplyDelete
  104. 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.

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

    ReplyDelete
  106. 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

    ReplyDelete
  107. There is definately a great deal to know about this subject. I like all of the points you've made. data science training in mysore

    ReplyDelete
  108. This is a great article thanks for sharing this informative information. I will visit your blog regularly for some latest post. I will visit your blog regularly for Some latest post. data science course in kanpur

    ReplyDelete
  109. 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,
    data scientist course in hyderabad

    ReplyDelete
  110. 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

    ReplyDelete