Standardization vs. normalization

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In the overall knowledge discovery process, before data mining itself, data preprocessing plays a crucial role. One of the first steps concerns the normalization of the data. This step is very important when dealing with parameters of different units and scales. For example, some data mining techniques use the Euclidean distance. Therefore, all parameters should have the same scale for a fair comparison between them.

Two methods are usually well known for rescaling data. Normalization, which scales all numeric variables in the range [0,1]. One possible formula is given below:

On the other hand, you can use standardization on your data set. It will then transform it to have zero mean and unit variance, for example using the equation below:

Both of these techniques have their drawbacks. If you have outliers in your data set, normalizing your data will certainly scale the “normal” data to a very small interval. And generally, most of data sets have outliers. When using standardization, your new data aren’t bounded (unlike normalization).

So my question is what do you usually use when mining your data and why?

Note: Thanks to Benny Raphael for fruitful discussions on this topic. Thanks to Jim for a correction on May 26th 2014.

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Comments

59 Comments on Standardization vs. normalization

  1. Fay on Thu, 12th Jul 2007 2:47 pm
  2. Sometimes perhaps we can take logarithms of input data when they contain order-of-magnitude larger and smaller values. However, since logarithms are defined for positive values only, we need to take care when the input data may contain zero and negative values.
    You did a very good work on your blog! :)

  3. Will Dwinnell on Thu, 12th Jul 2007 11:00 pm
  4. A few points come to mind:

    1. Monotonic scaling of the data (assuming that distinct values are not collapsed) will have no affect on the most common logical learning algorithms (tree- and rule-induction algorithms).

    2. There are robust alternatives, such as: subtract the median and divide by the IQR, or scale linearly so that the 5th and 95th percentiles meet some standard range.

    3. Outliers (technically, and high leverage points) present an interesting challenge. One possibility is to Winsorize the data after scaling it.

  5. Sandro Saitta on Fri, 13th Jul 2007 3:46 pm
  6. Thanks for your comment fay. I agree with you on taking the log. I use to work with data in the range 10^6 to 10^12 for example. And thanks for the remark :-)

    Will, your suggestions seem very interesting. I don’t know the “winsorize” technique, but it seems it could be used in addition to normalization.

  7. Will Dwinnell on Fri, 13th Jul 2007 6:44 pm
  8. For readers who are not aware of this technique: “Winsorizing” data simlpy means clamping the extreme values.

    This is similar to trimming the data, except that instead of discarding data: values greater than the specified upper limit are replaced with the upper limit, and those below the lower limit are replace with the lower limit. Often, the specified range is indicate in terms of percentiles of the original distribution (like the 5th and 95th percentile).

    This process is sometimes used to make conventional measures more robust, as in the Winsorized variance.

  9. mb on Fri, 30th Nov 2007 1:23 am
  10. Will, can you tell me how I can scale linearly so that the 5th and 95th percentiles meet some standard range?
    Can this be done with both negative and positive values?

    Another question:
    If I want to compute an index where not only the units and scales are different, but also the input metrics into the index have different interpretations – specifically, one metric is better if the values are higher and another one is better if the values are lower, how can I compute an index that represents all numbers concisely and meaningfully?
    Let’s say I have Expenses ($), Profits($) and Turnover (%). Expenses and Turnover are better if lower, but Profits are better if higher.
    If comparing two companies on these metrics, and I want to compute one index to show the “best” performing company on these parameters, how can I do this?
    Sorry, not strictly data-mining relevant, but thought someone here might have an answer!

    Tried using z-scores and normalizing but doesnt work due to different hi-low interpretations.
    Eventually used a reverse-rank for Expenses and Turnover so that all have same order. However, rank does not show quantity difference between the two companies, just their ranks!

    this is a great blog, thanks to all for helpful comments.

  11. Sandro Saitta on Thu, 6th Dec 2007 10:26 am
  12. First, you can normalize/standardize your data. Or, on the contrary, you can maybe decide to manually fix weights to each of these metrics.

    You can for example use an objective function. Let say you want to maximize a function of the Expenses, Profits and Turnover. In the objective function, give a negative weight to Expenses and Turnover and a positive one to Profits. I don’t know if this will work for your problem, but that would be my first guess.

  13. shrawan bhattacharjee on Tue, 14th Sep 2010 12:19 pm
  14. Hi Sandro,
    Interesting article and the comments which followed. I am also dealing with analysis of Mass Spectrometry data. This kind of data suffers a significant variation due to instrumental errors and limitations (even if the same sample is analyzed). Presently I am using log transformation, which is giving satisfactory result. But I am still skeptical of possibilities of false positives, as data is from the range of 10*3 to 10*6. So what do you suggest best method of normalizing this kind of data.

    I am also confused with the two terms as you mentioned ‘standardization’ & ‘normalization’, which to use with mass spectrometry data analysis. Although I only found research articles mentioning normalization for such kind of data not standardization. Although when I explored the internet then both the techniques were referred in similar grounds.
    What is your views regarding this query.

  15. Sandro Saitta on Tue, 4th Jan 2011 6:07 pm
  16. @shrawan: If you know that your data contains several outliers, then I guess you should rather try standardization.

    […] ※normalization(正規化)とstandardization(標準化)の違いについて。 http://www.dataminingblog.com/standardization-vs-normalization/ […]

  17. Mrinal on Wed, 14th Dec 2011 11:05 am
  18. Good discussion. However the fact is… Now I am more confused. LOL!

  19. silvina on Sat, 9th Jun 2012 9:16 pm
  20. Detrending would be standarzisation or normalization or neither?

  21. Ravi on Sun, 10th Jun 2012 1:19 am
  22. Can you please give two basic good on the NOrmalization and Standardization techniques

  23. Rahul Kulkarni on Mon, 30th Jul 2012 8:07 am
  24. Is standardization and z-transform the same thing?

  25. Abraham Aldaco on Fri, 3rd Aug 2012 1:20 am
  26. Is there a scientific journal paper (reference) about this topic, standardization and normalization?

  27. Martin Hlosta on Wed, 26th Sep 2012 10:59 am
  28. Rahul Kulkarni: Yes, its the same.

  29. Arunava on Mon, 29th Oct 2012 6:39 pm
  30. Hi all,

    Apart from standardization and normalization, certain applications require each sample to be divided by their norm to get unit magnitude, mostly in PCA,LDA, sparse coding etc.

    What is the logic behind it. Also under such cases do we need to first apply normalization and then divide by norm?

    Thanks,
    Arunava

  31. Steven on Thu, 6th Dec 2012 10:46 pm
  32. Great Article. I actually have a problem and was wondering if the data should be normalized, and figure I should reach out here.
    I have 15 products a,b,c,d,e, etc.. They were all sent to different amounts of customers, and recieved different amounts of positive responses. The set up in excell would be:
    Product Amount Sent Positive Response
    A 1001 300
    B 395 210
    C 2399 295
    etc..

    I was wondering what would be the best way to scale and/or normalize the data so I can draw some conclusions. Any advice? Thanks for the help

  33. TonyD on Sun, 6th Jan 2013 12:51 am
  34. Just read a great blog post on the distinction between normalization and standardization. I’d used both in the past — but never really understood the distinction.

    Hope the link isn’t automatically removed:
    http://stats.stackexchange.com/questions/10289/whats-the-difference-between-normalization-and-standardization

  35. Sandro Saitta on Mon, 7th Jan 2013 9:20 am
  36. Thanks for the link Tony! Interesting discussion there.

  37. DAVID OMBUNI on Thu, 8th Aug 2013 7:44 am
  38. please send me the importance of standardize data

  39. David Garcia on Fri, 20th Sep 2013 10:23 am
  40. Very interesting thread.

    I have a question. If one has a large collection of data with several atributtes (let’s say 40) each of which follows a different distribution (gaussian or not),

    Does it make any sense to mix normalization and standarization in the same dataset? That is, standardize those attibutes that follow a gaussian distribution and normalize the rest (removing previously possible outliers).

    I presume it may distort the correlation between attibutes and therfore corrupt the results. If that’s the case, one has to choose between normalization and standarization for the whole dataset?.

    Thanks in advance.

  41. Sandro Saitta on Sat, 21st Sep 2013 7:01 pm
  42. @David: Very interesting question! In data mining, normalization/standardization is often used to allow data of different scale (unit) to be comparable by a classification/regression algorithm. So, if you mix both of them, then you loose this use. Attributes that have been standardized may have much more impact than the normalized ones, just because of their ranges.

    […] Standardization vs. normalization […]

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  46. […] Standardization vs. normalization […]

  47. Jim on Mon, 26th May 2014 9:09 pm
  48. The following statement in the original post is not correct: “When using standardization, you make an assumption that your data have been generated with a Gaussian law (with a certain mean and standard deviation).”

    The mean and std dev are definable for any continuous-variable distribution and therefore, regardless of the true underlying distribution, standardization will yield data having a mean of 0 and std dev of 1. There is no assumption that the underlying distribution is Gaussian.

    Of course, if the data are not Gaussian, then you could not, for example, make the claim that approximately 95% of the standardized values should fall between -2 and +2; this would be true only if the population being sampled is normally distributed.

  49. Mustafa on Fri, 5th Dec 2014 2:51 pm
  50. Dear All;

    For logarithmic normalization , i need to know how it improve the data , for example suppress the outliers , is it good to deal non-symmetric data? …\\

    Appreciate your help in advance

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    to miss this opportunity. This service is render to both
    individuals,companies,business men and women. The loan amount
    available ranges from any amount of your choice.

    FIRST INFORMATION NEEDED

    Full Name:
    Personal Phone Number:
    Country:
    Address:
    State:
    Age:
    Have you applied before?:
    Marital Status:
    Loan amount needed as loan:
    Loan Duration:
    Occupation:
    Monthly Income:

    I gladly await your swift response,
    Email:moreganloeloanhome004@outlook.com
    Warm Regards,
    Mr Morgan Leo.

  101. MR DANIEL JOHNSON on Mon, 27th Jul 2015 10:20 am
  102. This is to inform you that DANIEL FINANCE LOAN COMPANY. We offers all kinds of loan at a very

    low interest rate of 2%. so are you tired of looking for loans and mortgages?, have you been tuned

    down by banks and other financial institutions, we well licensed loan company, we give out loans at

    very easy way and there is no social security number required and no credit check required, 100%

    Guaranteed. contact us now via e-mail: {danieljohnsonloancompany@gmail.com}
    Personal Information:

    Your Name:_______________
    Your Country:_____________
    Your Address:______________
    Your Occupation:____________
    Monthly income:____________
    Loan Amount Needed:________
    Loan Duration:_____________
    Mobile phone number:________

    Team Regards,
    DANIEL JOHNSON

    Financial Controller/Operation Manager.

  103. Hwa Jurong on Tue, 28th Jul 2015 12:05 pm
  104. Good Day !!

    I am Hwa Jurong, a Reputable, Legitimate & an accredited money
    Lender. I want to use this medium to inform you that i render reliable beneficiary
    assistance as I’ll be glad to offer you a loan at 2% interest rate to
    reliable individuals.

    Services Rendered include:

    *Home Improvement
    *Inventor Loans
    *Car Loans
    *Debt Consolidation Loan
    *Line of Credit
    *Second Loan
    *Business Loans
    *Personal Loans
    *International Loans.

    Please write back if interested.
    Upon Response, you’ll be mailed a Loan application form to fill. (No social
    security and no credit check, 100% Guaranteed!) I Look forward permitting me to
    be of service to you. You can contact me via e-mail:hwajurong382@yahoo.com hwajurong12@gmail.com
    Yours Sincerely,

    Hwa Jurong(MD).

  105. TEMPLE YORK FINANCE SERVICE on Tue, 28th Jul 2015 10:12 pm
  106. Because we specialize in Residential, Commercial and Business Loans, we know what it takes to get your loan done faster, more efficiently and with more cooperation
    from your local business community. Realtors, Appraisers, Escrow, Loan Processing, Title and Closing… all working together for your new mortgage… There are many mortgage programs available these days.. and each one has its benefits. There are many factors that go into deciding which loan is best suited for your needs. At TEMPLE YORK FINANCE SERVICE we have the programs, the products, and the services to offer our clients the best possible rates, terms and closing costs based on your individual profile.
    Do not need to leverage any assets to acquire capital
    – No Upfront fee or unnecessary garbage fees
    – 0% interest rates for the first 3-6 months
    – Funds can be used same as cash.
    – Quick approval process
    TERMS AND CONDITION APPLY
    TEMPLE YORK FINANCE SERVICE

    Email: info@templeyorkfinanceservices.com
    Email: templeyork5@gmail.com
    Skype : templeyorkfinanceservices
    Tel: +44 (750) 953 1399 (CALL/SMS/TEXT MESSAGES).

  107. Douglas Rodgers on Wed, 29th Jul 2015 11:10 pm
  108. FOR ALL KINDS OF LOAN, APPLY WITH US AND GET FAST APPROVAL TODAY. 100% GUARANTEED…CONTACT US VIA EMAIL: Douglasrodgersloanfirm@live.com

  109. Chris Booby on Thu, 30th Jul 2015 5:21 am
  110. I Can Smile With This Man I Receive A Loan From His Company

    End your financial worries

    I’m Chris Booby from Canada I can smile with this man Andres Williams I received a loan of $75,000.US Dollars from his company and two of my colleagues have also received business loans from this man without any difficulty.with just none collateral fee and transfer option I advise you not to choose the wrong person if you actually apply for a cash loan for your project and any other. I publish this message because Mr Lance Robert made me feel grate with this loan. It is through a friend that I met this honest and generous man who helped me get this loan. To regulate your life, you need money, you are stuck, no access to bank credit, or do not have the benefit of a bank, you need to finance your construction, real estate development, creating your own business up your personal business, you have seen and need to make money, a bad credit or need money to pay bills or debts. So I advise you to contact and meet you for the services you ask of him. His Email address:…………andresloanfirm07@live.com
    Contact him for more information, be clear and honest. Contact him Via email: andresloanfirm07@live.com

    Regards

    Chris Booby

  111. Mr Alexader Dennis on Sat, 1st Aug 2015 4:38 am
  112. DO YOU NEED A LOAN?
    Mr Alexader Dennis now offers loans such as follow.. Home Loans, Business Loans, Personal Loans, Car Loans, Company Loans, Student Loans, Commercial Loans Etc,, Have you been rejected by other banks or other brokers? Do you have bad credit scores and no one is willing to give you loan? Contact us today for urgent and easy loan. We give out loan from $1,000 To $2,000,000 with a very low rate of 3% From the period of 1 to 5 years duration. Note:

    (1) Borrower must be reliable and willing to pay back the loan as promised,
    (2) Borrower should be above 18 years of age
    (3) Borrower must be employed or business owner
    (4) Borrower will start paying back the loan three months after the loan approval Contact: alexaderdennisloans@gmail.com

    * Appointments in the amount ranging from $1,000 to $50,000, 000.00

    * The interest rate is at 3%

    * Choose between 1 and 40 years of repayment.

    * Choose between Monthly and annual repayment plan.

    * Terms and conditions of the loans flexibility.

    All these plans and more, please contact us.

    1. Full Names:……………………….
    2. Contact Address:…………………..
    3. Loan Amount Needed:………………..
    4. Duration of the Loan……………….
    5. Direct Telephone Number:……………
    6. Country…………………………..

    Email:(alexaderdennisloans@gmail.com)

    Best Regards,

    Mr Alexader Dennis

  113. MR DANIEL JOHNSON on Sat, 1st Aug 2015 5:28 am
  114. This is to inform you that DANIEL FINANCE LOAN COMPANY. We offers all kinds of loan at a very low interest rate of 2%. so are you tired of looking for loans and mortgages?, have you been tuned down by banks and other financial institutions, we well licensed loan company, we give out loans at very easy way and there is no social security number required and no credit check required, 100% Guaranteed. contact us now via e-mail: danieljohnsonloancompany@gmail.com

    Personal Information:

    Your Name:_______________
    Your Country:_____________
    Your Address:______________
    Your Occupation:____________
    Monthly income:____________
    Loan Amount Needed:________
    Loan Duration:_____________
    Mobile phone number:________

    Team Regards,
    MR DANIEL JOHNSON
    Financial Controller/Operation Manager.

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