Total Pageviews

Sunday 21 August 2011

Micro- and Macro-average of Precision, Recall and F-Score

I posted several articles explaining how precision and recall can be calculated, where F-Score is the equally weighted harmonic mean of them. I was wondering- how to calculate the average precision, recall and harmonic mean of them of a system if the system is applied to several sets of data.

Tricky, but I found this very interesting. There are two methods by which you can get such average statistic of information retrieval and classification.

1. Micro-average Method

In Micro-average method, you sum up the individual true positives, false positives, and false negatives of the system for different sets and the apply them to get the statistics. For example, for a set of data, the system's

True positive (TP1)= 12
False positive (FP1)=9
False negative (FN1)=3

Then precision (P1) and recall (R1) will be 57.14 and 80

and for a different set of data, the system's


True positive (TP2)= 50
False positive (FP2)=23
False negative (FN2)=9

Then precision (P2) and recall (R2) will be 68.49 and 84.75

Now, the average precision and recall of the system using the Micro-average method is

Micro-average of precision = (TP1+TP2)/(TP1+TP2+FP1+FP2) = (12+50)/(12+50+9+23) = 65.96
Micro-average of recall = (TP1+TP2)/(TP1+TP2+FN1+FN2) = (12+50)/(12+50+3+9) = 83.78

The Micro-average F-Score will be simply the harmonic mean of these two figures.

2. Macro-average Method

The method is straight forward. Just take the average of the precision and recall of the system on different sets. For example, the macro-average precision and recall of the system for the given example is

Macro-average precision = (P1+P2)/2 = (57.14+68.49)/2 = 62.82
Macro-average recall = (R1+R2)/2 = (80+84.75)/2 = 82.25

The Macro-average F-Score will be simply the harmonic mean of these two figures.

Suitability
Macro-average method can be used when you want to know how the system performs overall across the sets of data. You should not come up with any specific decision with this average.

On the other hand, micro-average can be a useful measure when your dataset varies in size.

505 comments:

  1. Thanks for the article, just a minor typo: second to last paragraph: Micro rather than macro.

    ReplyDelete
    Replies
    1. Thanks a lot, Yahya. I corrected it. But the typo is in the last paragraph. If your dataset varies in size, micro-average is the useful tool.

      Delete
    2. hi, thank you for the article, please i have a general question related to learning algorithms. I found this expression in an article : The training data for the SVM classi ers are highly unbalanced as the proportion of positive training web pages ranges from 2% to 18%.
      What do we mean by unbalanced data? and by positive/negative training?
      ReplyDelete

      Delete
  2. This comment has been removed by the author.

    ReplyDelete
  3. I think there's a problem with your macro-average precision calculation. the denominator should be the sum of true positives and false positives. The micro average for precision and recall are the same. See here:
    http://metaoptimize.com/qa/questions/8284/does-precision-equal-to-recall-for-micro-averaging

    ReplyDelete
  4. @Pallika. The scenarios are different. In my case, one classifier is applied on two different datasets. The number of instances are different in two datasets. But the example you provided is classifier performance for three different class labels. So the sum of positive and negative is always 27. The two macro and micro evaluation is different.

    ReplyDelete
  5. Hi..Thank you for the article. I did some exparimentation on Text classification which consists 7 (labled documents prepared on my own)ctegories of documents.I did too much stemming and i got average precision 57%, micro precision=macro precision=1,micro recall=macro recall=0.please suggests me something to improve results(like bad training set,light stemming, threshold value and threshold step size modification, k if classifier is knn,how to improve recall for better F1 score).
    Thanks.

    ReplyDelete
  6. Good article.... if you explain what is micro and macro average in 3 lines it will be more hepful for readers...

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

    ReplyDelete
  8. Really sweet, thank you! That was hell of a good explanation! :)

    ReplyDelete
  9. Excellent article. Very interesting to read. I really love to read such a nice article. Thanks! keep rocking. Data Science online Training Hyderabad

    ReplyDelete
  10. Thank you very much for sharing your article

    ReplyDelete
  11. sklearn implements 'macro' f1 as average of the two f1's and not harmonic means of the average precision and recall.

    f1 = (f1_1 + f1_2) / 2

    Check: https://github.com/scikit-learn/scikit-learn/blob/51a765a/sklearn/metrics/classification.py#L1098

    ReplyDelete
  12. the blog is very use for me .keep sharing like this.web design company in velachery

    ReplyDelete
  13. This is a great inspiring article.I am pretty much pleased with your good work.You put really very helpful information.web design company in velachery

    ReplyDelete
  14. Thanks for sharing, very informative. Top Programming Languages in 2020.

    ReplyDelete
  15. Really a awesome blog for the freshers. Thanks for posting the information.
    Data Science Training in Delhi
    Data Science Course in Delhi

    ReplyDelete
  16. Such a very useful article. Very interesting to read this article.I would like to thank you for the efforts you had made for writing this awesome article.
    data analytics courses in mumbai
    data science interview questions

    ReplyDelete
  17. I finally found great post here.I will get back here. I just added your blog to my bookmark sites. thanks.Quality posts is the crucial to invite the visitors to visit the web page, that's what this web page is providing.
    data science course Mumbai
    data science interview questions
    data analytics course in mumbai

    ReplyDelete
  18. This degree will be acceptable not only nationally as well as globally also. Digital marketing is the best source to make your carrier bright.
    ExcelR Digital Marketing Courses In Bangalore

    ReplyDelete
  19. Hey there! I simply wish to offer you a big thumbs up for the excellent information you have right here on this post. I am coming back to your web site for more soon.
    Techno

    ReplyDelete
  20. Thanks for sharing such a great information..Its really nice and informative.. software testing course

    ReplyDelete
  21. This post is really nice and informative. The explanation given is really comprehensive and informative. I also want to say about the digital marketing course

    ReplyDelete
  22. Good information and, keep sharing like this.

    7 tips to start a career in digital marketing

    “Digital marketing is the marketing of product or service using digital technologies, mainly on the Internet, but also including mobile phones, display advertising, and any other digital medium”. This is the definition that you would get when you search for the term “Digital marketing” in google. Let’s give out a simpler explanation by saying, “the form of marketing, using the internet and technologies like phones, computer etc”.

    we have offered to the advanced syllabus course digital marketing for available join now

    more details click the link now

    https://www.webdschool.com/digital-marketing-course-in-chennai.html

    ReplyDelete
  23. Amazing blog is very nice

    Web designing trends in 2020

    When we look into the trends, everything which is ruling today’s world was once a start up and slowly begun getting into. But Now they have literally transformed our lives on a tremendous note. To name a few, Facebook, Whats App, Twitter can be a promising proof for such a transformation and have a true impact on the digital world.

    we have offered to the advanced syllabus course web design and development for available join now

    more details click the link now

    https://www.webdschool.com/web-development-course-in-chennai.html

    ReplyDelete
  24. Such a very useful article. Very interesting to read this article.I would like to thank you for the efforts you had made for writing this awesome article. digital marketing course Bangalore

    ReplyDelete
  25. Thanks for the interesting blog that you have implemented here. Very helpful and innovative. Waiting for your next upcoming article.
    Java training in chennai
    Java training institute in chennai
    Java course in chennai
    Java training classes
    Java training
    Java programming classes
    core java coure
    <a

    ReplyDelete
  26. Thanks for this blog are more informative contents step by step. I here attached my site would you see this blog.

    7 tips to start a career in digital marketing

    “Digital marketing is the marketing of product or service using digital technologies, mainly on the Internet, but also including mobile phones, display advertising, and any other digital medium”. This is the definition that you would get when you search for the term “Digital marketing” in google. Let’s give out a simpler explanation by saying, “the form of marketing, using the internet and technologies like phones, computer etc”.

    we have offered to the advanced syllabus course digital marketing for available join now.

    more details click the link now.

    https://www.webdschool.com/digital-marketing-course-in-chennai.html

    ReplyDelete
  27. Amazing article useful information.

    Web designing trends in 2020

    When we look into the trends, everything which is ruling today’s world was once a start up and slowly begun getting into. But Now they have literally transformed our lives on a tremendous note. To name a few, Facebook, Whats App, Twitter can be a promising proof for such a transformation and have a true impact on the digital world.

    we have offered to the advanced syllabus course web design and development for available join now.

    more details click the link now.

    https://www.webdschool.com/web-development-course-in-chennai.html



    ReplyDelete
  28. This is a topic that's near to my heart... Web develop Thank you! Exactly where are your contact details though?

    ReplyDelete
  29. I become greater than happy to uncover this notable internet site on line. I need to to thank you to your time due to this brilliant examine latest!! I genuinely loved each bit of it and I have you ever bookmarked to look new information to your blog.

    ReplyDelete
  30. I have to search sites with relevant information on given topic and provide them to teacher our opinion and the article.
    ExcelR digital marketing courses in mumbai

    ReplyDelete
  31. Really Nice Post, Thanks for sharing & keep up the good work.
    Oflox Is The Website Design Service In Dehradun

    ReplyDelete
  32. Thanks for sharing this informatiions.
    artificial intelligence training in coimbatore

    Blue prism training in coimbatore

    RPA Course in coimbatore

    C and C++ training in coimbatore

    big data training in coimbatore

    hadoop training in coimbatore

    aws training in coimbatore

    ReplyDelete
  33. Learn digital marketing live, Coimbatore – an institute perfected in coaching the digital marketing training course by covering the following topics said to be SEO, SEM, SMM and Email marketing that would educate individuals in the finest part of the choice.

    digital marketing course in coimbatore
    digital marketing training course in coimbatore
    digital marketing training in coimbatore

    ReplyDelete
  34. First of all I would like to thank you for writing this post I love both writing and reading new posts and I was just looking at new posts to see me something new, only then I saw your post and the rest of the post is praiseworthy.
    sofeeya.com

    ReplyDelete
  35. Really nice and interesting post. I was looking for this kind of information and enjoyed reading this one. Keep posting. Thanks for sharing.....bangalore digital marketing course

    ReplyDelete
  36. I am very impressed by your excellent writing abilities. Please keep up the good informational writing.
    SAP training in Kolkata
    Best SAP training in Kolkata
    SAP training institute in Kolkata

    ReplyDelete
  37. I must say you are very skilled at persuasive writing if you can convince me to share your views
    SAP training in Mumbai
    Best SAP training in Mumbai
    SAP training institute Mumbai

    ReplyDelete
  38. There are many things mentioned in this article I would not have thought of on my own. This material is inspirational, interesting and it allows the readers to open up their minds to original thinking.
    SAP training in Kolkata
    SAP training Kolkata
    Best SAP training in Kolkata
    SAP course in Kolkata
    SAP training institute Kolkata

    ReplyDelete
  39. Very Interesting blog. Thanks for sharing this blog. You can also go through blog which is related to this which is providing variety of movies also. For details you can visit our official website.

    ReplyDelete
  40. A backlink is a link created when one website links to another. Backlinks are important to SEO & impact for higher ranking. In my 7+ years seo Career i see, without backlinks a website doesn't rank higher on google SERP.

    Get Your 300+ High Quality DoFollow Backlinks Here!

    Order Now with Full Confidence & 100% satisfaction.

    ReplyDelete
  41. Great post! I am actually getting ready to across this information, It’s very helpful for this blog.Also great with all of the valuable information you have Keep up the good work you are doing well. share more.
    Ai & Artificial Intelligence Course in Chennai
    PHP Training in Chennai
    Ethical Hacking Course in Chennai Blue Prism Training in Chennai
    UiPath Training in Chennai

    ReplyDelete
  42. Forex Signals, MT4 and MT5 Indicators, Strategies, Expert Advisors, Forex News, Technical Analysis and Trade Updates in the FOREX IN WORLD

    Forex Signals Forex Strategies Forex Indicators Forex News Forex World

    ReplyDelete
  43. Thanks for sharing valuable information and very well explained. keep posting.

    workday studio training
    workday studio online training

    ReplyDelete
  44. It was not first article by this author as I always found him as a talented author.
    Star Lord Jacket

    ReplyDelete
  45. I am happy for sharing on this blog its awesome blog I really impressed. thanks for sharing. Youtube Mp3 Converter

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

    ReplyDelete
  47. iot training in chennai -Internet of things is an technology which is basically to connect every product with the Internet.Definitely Best IOT Training Institute in Chennai will train you in this technology with an assured placements.

    DevOps training in chennai - It's right time to learn the trending technolgy such as DevOps. Try to find a Best DeVops training Institute in Chennai.

    blue prism training in Chennai - Blue prism is an developing and future technology of IT and start to start for Best Blue prism technology in Chennai.

    uipath training in Chennai - Best uipath course and training in Chennai will also create a better path for your future.

    microsoft azure training in chennai - Best azure training in Chennai offering the courses with guidance for Microsoft azure training.

    ReplyDelete
  48. You can get Apple-certified repairs and service at the Apple Store or with one of our Apple Authorized Service Providers.
    mobile phone repair in Niles
    Worked as a Senior SEO & Digital & Social Media & Graphics Design & cpa & Drop shipping & Video Editing And Youtube & Web Design And Development & Affiliate Marketing trainer at BITM (BASIS Institute of Technology & Management) since 2014-2018. Successfully completed 50+ SEO batches, 20+
    Affiliate Marketing batches and 30+ workshop on Freelancing under SEIP (Skills for Employment Investment Program).
    Best Graphic Design training in Bangladesh
    Free bangla sex video:careful

    ReplyDelete
  49. Nice post!

    Worried About QuickBooks Error ?Get in touch with QuickBooks expert for instant solution.
    Click Here to know how to fix QuickBooks Form 941 Error

    Dial on QuickBooks Error Support Phone Number +1-855-977-7463.

    ReplyDelete
  50. Very educating story, saved your site for hopes to read more! ExcelR Data Analytics Courses

    ReplyDelete
  51. Thank you for sharing, I am very happy to know your blog. Here are some blogs I would like to send you. Please don't delete the link, hi
    thiennhanstone
    cuốn thư đá
    doithuong.biz/game-no-hu-doi-thuong
    ivip
    làm bằng lái xe máy
    làm cavet xe

    ReplyDelete
  52. Great post. I'm about to write something similar in my site All About Python .

    ReplyDelete
  53. Thumbs up guys your doing a really good job. 인증업체

    ReplyDelete
  54. Wow what a Great Information about World Day its exceptionally pleasant educational post. a debt of gratitude is in order for the post. 먹튀검증사이트

    ReplyDelete
  55. Samsung mobile phone is a very popular mobile company not only in Bangladesh but also all over the world. But its price is so high. When you are searching for a brand new mobile phone & it becomes hard. Then you can find a Samsung second hand mobile price in bangladesh for your urgency.

    ReplyDelete
  56. What a really awesome post this is. Truly, one of the best posts I've ever witnessed to see in my whole life. Wow, just keep it up.
    data science online course

    ReplyDelete
  57. ExcelR provides data analytics course. It is a great platform for those who want to learn and become a data analytics Courses. Students are tutored by professionals who have a degree in a particular topic. It is a great opportunity to learn and grow.

    data analytics course
    data analytics courses

    ReplyDelete
  58. Nice Blog !
    QuickBooks Error 248 can occur when a user tries to run payroll for the employees. You may also encounter this issue when you are taking a backup of your company file.call us and get the best possible solutions to resolve QuickBooks Error 248.

    ReplyDelete
  59. Exactly, the very information that I was looking for. I was looking for such kind of article on the Internet and finally ended up here. thanks for the help!
    Top 10 CBSE School in Meerut
    SEO Expert in Meerut
    Software Development Company In Delhi NCR
    Digital Marketing Company in Hapur
    Web Development Meerut

    ReplyDelete
  60. Your blog is very nice and has sets of the fantastic piece of information. Thanks for sharing with us. If you face any technical issue or error, visit:

    Quickbooks customer service

    ReplyDelete
  61. Your blog is very nice and has sets of the fantastic piece of information. Thanks for sharing with us. If you face any technical issue or error, visit:

    Quickbooks customer service

    ReplyDelete
  62. Nice and Well written Blog!!.However, many times, you may face several snags in QuickBooks that can restrict your work. In case you are looking for the best technical help for QuickBooks, contact:
    QuickBooks Support number

    ReplyDelete
  63. Thanks a lot very much for the high quality and results-oriented help. I won’t think twice to endorse your blog post to anybody who wants and needs support in this area. same as your blog i found another one Mobile Marketing .Actually I was looking for the same information on internet for Mobile Marketing and came across your blog. I am impressed by the information that you have on this blog. Thanks once more for all the details.

    ReplyDelete
  64. Its a great post keep sharing this kind of wonderful post !
    Free piping course pdms training in Chennai

    ReplyDelete
  65. Hey Nice Blog!! Thanks For Sharing!!! Wonderful blog & good post. Its really helpful for me. If you want to Earn Money Online, Read Blogging Making Money. Rision Digital is the best site to learn online tips to earn money. Click link to read.

    ReplyDelete
  66. Thanks for spending all your pleasant time to make such a Creative content for us. AWS Training in Chennai

    ReplyDelete
  67. Thanks a lot for sharing kind of information. Your article provides such great information with good knowledge. Digital Marketing Courses in Pune with Placement

    ReplyDelete
  68. Hello everyone, We are Children's Furniture – Bao An Kids. Surely when you come to this page, you are looking for a professional children's interior design and construction unit to help you advise and choose for your family and baby to have a perfect and comfortable living space. the safest. Thank you very much for trusting and wanting to accompany Bao An Kids. Phòng ngủ trẻ em

    ReplyDelete
  69. Dermaklinic's Institute for Aesthetic Studies (DIAS), a brain child of Dr. Neeraj Pandey (MBBS, MD Dermatology, FADS International Skin Centre, Singapore), came into being to meet the ever-growing demand of skilled professionals in the field of dermatology. Our courses are designed with expertise to hone the skills of the students by imparting sound technical knowledge. Keeping ourselves abreast with the global trends we endeavor to create a capable and efficient support team for the aesthetic industry.
    :
    Register today to begin your career!
    -
    website: https://www.thedias.org/
    Contact Number: +917703000777
    Emails: info@thedias.org / knockdiasforsuccess@gmail.com

    ReplyDelete
  70. I had the option to discover great data from your blog articles. news updates

    ReplyDelete
  71. Top 15 Digital marketing courses in Mumbai.

    ReplyDelete
    Replies
    1. https://www.anuvaa.com/blog-post/digital-marketing-courses-in-mumbai/

      Delete
  72. Anuvaa- Top 15 Digital marketing courses in Mumbai.

    ReplyDelete
  73. This is very interesting blog and insightfull too. If you want to learn digital marketing then visit this link-https://www.anuvaa.com/blog-post/digital-marketing-courses-in-mumbai/

    ReplyDelete
  74. https://www.anuvaa.com/blog-post/digital-marketing-courses-in-mumbai/

    ReplyDelete
  75. This is an interesting blog. For more knowlegde on Digital marketing follow- Anuvaa

    ReplyDelete
  76. It’s an interesting blog. Check this out too Top Digital Marketing courses in Mumbai

    ReplyDelete
  77. Very informative and interesting. Am sure it is going to be very helpful to a lot of people like me looking for such information. Thanks again https://www.anuvaa.com/blog-post/digital-marketing-courses-in-mumbai/

    ReplyDelete
  78. Thank you for your blog , it was usefull and informative "AchieversIT is the best Training institute for Full Stack development training. Full Stack developement training in bangalore "

    ReplyDelete
  79. Thank you for your blog,it was usefull and informative "AchieversIT is the best Training institute for Python training. Full Python training in bangalore "

    ReplyDelete

  80. Nice post check my site for super fast Satta king Result also check Sattaking

    ReplyDelete

  81. You should be a piece of a challenge for probably the best website on the web. I will suggest this site!

    best interiors

    ReplyDelete
  82. Your substance is extremely rousing and appriciating I truly like it kindly visit my site for Satta King Result likewise check Sattaking and furthermore check satta king furthermore, for speedy outcome check my site Satta king and for very quick outcome check Satta king result likewise check my site for very quick Satta king

    ReplyDelete
  83. Thanks for sharing...Are you Looking for an Abroad MBBS education consultant? Here is a suggestion for a free consultant, Named Shri Hari consultancy working for many years in Jaipur, and have completed so many dreams of aspiring students
    Shri Hari Consultancy

    ReplyDelete
  84. Hey! Lovely blog. Your blog contains all the details and information related to the topic. In case you are a QuickBooks user, here is good news for you. You may encounter any error like QuickBooks Error, visit at QuickBooks Customer Service Phone Number for quick help.

    ReplyDelete
  85. It is looking like such a creative blog and you are explained your blog in details, which is very easy to understand and also helpful for all. I have no words for say I just say thanks because it is helpful for those who wants to do this.Feel The Beauty of Golden Triangle Tour

    ReplyDelete
  86. Your article is such an informative article. It is glad to read such those articles thanks for sharing. XO Varsity Jacket

    ReplyDelete


  87. Great to become visiting your weblog once more, it has been a very long time for me. Pleasantly this article i've been sat tight for such a long time. I will require this post to add up to my task in the school, and it has identical subject along with your review. Much appreciated, great offer. data science course in nagpur

    ReplyDelete
  88. hello sir,I truly appreciate this post. I?ve been looking everywhere for this! Thank goodness I found it on Bing. You have made my day Thanks Icecream PDF Split Merge Pro Crack

    ReplyDelete
  89. This impressed me so much amazing. Keep working and providing information
    activator

    ReplyDelete
  90. Content was great! Very in-depth and informative. Loved how you mentioned every aspect of the subject in this piece, thank you.
    Machine Learning Training in Hyderabad
    Machine Learning Course in Hyderabad

    ReplyDelete
  91. I am very happy to read the posts on this site which contain a lot of useful information, thank you for providing this kind of information. Keep it up man and also give us some more informative posts. Cheers!
    Free Download

    ReplyDelete
  92. Leawo Prof. Media is an amazing Post with good content.FIND CRACK is the best crack software site for all Mac and Windows users all over the world.

    ReplyDelete



  93. Click this link
    Click this link
    Directory Opus is a complete replacement for Explorer, with far more power and functionality than any other file manager available today. Single or dual pane file display and folder trees. Tabbed interface let you keep multiple folders open and switch quickly between them.

    ReplyDelete
  94. Nice post from your side, your are such a good writer. You should keep writing blog like this.The Satta King is the satta king result provider website, Which provide the satta king fast result in Ghaziabad Satta King, Faridabad Satta King, Delhi satta king, Desawar Gali result and many more.

    Best Satta King Result Site: Satta King

    ReplyDelete
  95. This post gave me a lot of useful information, and I was really impressed with it.
    Rekordbox DJ

    ReplyDelete
  96. Thank you for reading,
    I hope this post was useful to you.
    I appreciate you sharing such an informative and interesting post.
    Adobe effect CC crack


    ReplyDelete
  97. east imperial magic partition crack In the case of FDM, you have to open the main windows of FDM from the taskbar and change Mode to limit the speed

    ReplyDelete
  98. If someone is being mean, they are being unkind to another person, for example by not allowing them to do somethingadobe pagemaker

    ReplyDelete
  99. Add up all of the numbers and divide by the number of numbers in the data set.adguard premium/

    ReplyDelete
  100. Thanks for sharing in this blog...its very useful for us...keep on going...
    Oracle Performance Tuning Training

    ReplyDelete
  101. Hello Nice Blog!! A debt of gratitude is in order For Sharing!!!Wonderful blog and great post. Its truly accommodating for me, hanging tight for an all the more new post. Continue To blog!

    AI Training in Hyderabad

    ReplyDelete
  102. Really a great addition. I have read this marvelous post. Thanks for sharing information about it. I really like that. Thanks so lot for your convene.
    IMBATCH CRACK

    ReplyDelete
  103. I definitely enjoy every little bit of it. It is a great website and nice share. I want to thank you. Good job! You guys do a great blog, and have some great contents. Keep it up
    Online School Management Software

    ReplyDelete

  104. Your post has help us to find new ideas for our kitchen renovation, utility room designs, outdoor dining experiences. This make us easy to share our dream interior with kitchen manufacturer in Etobicoke this helps a lot!

    ReplyDelete
  105. Thank you for sharing such detailed Blog. I am learning a lot from you. Visit my website to get best Information About Best IAS coaching in Mumbai
    Best IAS coaching in Mumbai
    Top IAS coaching in Mumbai

    ReplyDelete
  106. Great Post! Thanks for sharing. Keep sharing such information.

    MEAN Training in Noida

    For more details about the course fee, duration, classes, certification, and placement call our expert at 70-70-90-50-90

    ReplyDelete
  107. Thank you very much for sharing such a great article. Great post I must say and thanks for the information. Education is definitely a sticky subject. very informative. Take care.Digital marketing training Mumbai

    ReplyDelete
  108. A backlink is a link created when one website links to another. Backlinks are important to SEO & impact for higher ranking.digital marketing course Mumbai

    ReplyDelete
  109. Thank you for your post. This is excellent information. It is amazing and wonderful to visit your site.
    Check out German Language Courses In Pune

    ReplyDelete
  110. Really enjoyed this article post.Really looking forward to read more. Will read on...private placement program

    ReplyDelete
  111. This post is so interactive and informative.keep update more information...
    Importance of Software Testing Tool
    Software Testing Tool

    ReplyDelete
  112. Really an awesome blog and informative content. If you want to become a data scientist, then check out the following link.
    Data Scientist Training in Hyderabad

    ReplyDelete
  113. Great post.
    Visit our website - https://www.firstdigishala.com/

    ReplyDelete
  114. Thanks for the amazing content. I'm really looking forward to more blog posts like this. Please visit our website for more posts related to beauty courses

    ReplyDelete
  115. Given article is useful and informative Thanks For Sharing!!! Wonderful blog & good post. It's really helpful for me
    Looking to get the Best Body massage center in Coimbatore? Riverdayspa™ is the Best Body massage center in Coimbatore. For More Details Visit us contact us:91 7539984562

    ReplyDelete
  116. Thank you for sharing this amazing blog post. Very informative. Check outDigital Marketing Services in Ravet

    ReplyDelete
  117. Positive site, where did u come up with the information on this posting? I'm pleased I discovered it though, ill be checking back soon to find out what additional posts you include.girl attitude quotes in hindi for whatsapp dp download

    ReplyDelete
  118. Thanks for sharing this amazing and educative blog post. This is excellent information. It is amazing and wonderful to visit your site.
    Check out Digital Marketing Courses In Pimpri Chinchwad

    ReplyDelete
  119. Great Information! Thank you for sharing this amazing blog with us. Keep sharing. Visit the best Digital Marketing Courses atDigital Marketing Training Institute In Pune

    ReplyDelete
  120. I want to thank you for sharing such a good information that provides you, that's great. Satta Result

    ReplyDelete
  121. This article is very useful for me thanks for writing this article. check out Digital Marketing Classes in Pune

    ReplyDelete
  122. Thank you so much for providing such informative blog. And those who are searching for Digital Marketing Courses in Nigeria can refer the following blog, thank you.

    Digital marketing courses in Nigeria

    ReplyDelete
  123. Thank you for the explanation and your effort. May help many people. Content Writing Course in Bangalore

    ReplyDelete
  124. Thank you for helping me learn the meaning and various types of Search Engine Marketing. To know more about them visit the below website.
    Search Engine Marketing

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

    ReplyDelete
  126. Nice post. Good explanation. Looking to learn digital marketing in Dehradun with hands on training provided by the industry experts then visit us: <a href=" https://iimskills.com/top-15-digital-marketing-course-in-dehradun/> Digital Marketing Course in Dehradun </a>

    ReplyDelete
  127. Thanks for providing this post. We all are learning too.
    Do visit our website about Content Writing Course in Bangalore and update your skills. Content Writing Course in Bangalore

    ReplyDelete