Can anyone explain me StandardScaler

Question

I am unable to understand the page of the StandardScaler in the documentation of sklearn   Can anyone explain this to me in simple terms

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How to calculate it     You can read more here    http   sebastianraschka com Articles 2014 about feature scaling html standardization-and-min-max-scaling

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The idea behind StandardScaler is that it will transform your data such that its distribution will have a mean value 0 and standard deviation of 1  In case of multivariate data  this is done feature-wise  in other words independently for each column of the data   Given the distribution of the data  each value in the dataset will have the mean value subtracted  and then divided by the standard deviation of the whole dataset  or feature in the multivariate case

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The answers above are great  but I needed a simple example to alleviate some concerns that I have had in the past  I wanted to make sure it was indeed treating each column separately  I am now reassured and can t find what example had caused me concern  All columns ARE scaled separately as described by those above  CODE import pandas as pd import scipy stats as ss from sklearn preprocessing import StandardScaler   data    1  1  1  1  1   2  5  10  50  100   3  10  20  150  200   4  15  40  200  300    df   pd DataFrame data  columns   N0    N1    N2    N3    N4    astype  float64    sc X   StandardScaler   df   sc X fit transform df   num cols   len df 0     for i in range num cols       col   df   i      col stats   ss describe col      print col stats   OUTPUT DescribeResult nobs 4  minmax  -1 3416407864998738  1 3416407864998738   mean 0 0  variance 1 3333333333333333  skewness 0 0  kurtosis -1 3599999999999999  DescribeResult nobs 4  minmax  -1 2828087129930659  1 3778315806221817   mean -5 551115123125783e-17  variance 1 3333333333333337  skewness 0 11003776770595125  kurtosis -1 394993095506219  DescribeResult nobs 4  minmax  -1 155344148338584  1 53471088361394   mean 0 0  variance 1 3333333333333333  skewness 0 48089217736510326  kurtosis -1 1471008824318165  DescribeResult nobs 4  minmax  -1 2604572012883055  1 2668071116222517   mean -5 551115123125783e-17  variance 1 3333333333333333  skewness 0 0056842140599118185  kurtosis -1 6438177182479734  DescribeResult nobs 4  minmax  -1 338945389819976  1 3434309690153527   mean 5 551115123125783e-17  variance 1 3333333333333333  skewness 0 005374558840039456  kurtosis -1 3619131970819205   NOTE  The scipy stats module is correctly reporting the  quot sample quot  variance  which uses  n - 1  in the denominator  The  quot population quot  variance would use n in the denominator for the calculation of variance  To understand better  please see the code below that uses scaled data from the first column of the data set above  Code import scipy stats as ss  sc Data     -1 34164079    -0 4472136    0 4472136    1 34164079   col stats   ss describe  -1 34164079  -0 4472136  0 4472136  1 34164079   print col stats  print    mean by hand   0 for row in sc Data      for element in row          mean by hand    element mean by hand    4  variance by hand   0 for row in sc Data      for element in row          variance by hand     mean by hand - element   2 sample variance by hand   variance by hand   3 sample std dev by hand   sample variance by hand    0 5  pop variance by hand   variance by hand   4 pop std dev by hand   pop variance by hand    0 5  print  quot Sample of Population Calcs  quot   print mean by hand  sample variance by hand  sample std dev by hand    n   print  quot Population Calcs  quot   print mean by hand  pop variance by hand  pop std dev by hand   Output DescribeResult nobs 4  minmax  -1 34164079  1 34164079   mean 0 0  variance 1 3333333422778562  skewness 0 0  kurtosis -1 36000000429325   Sample of Population Calcs  0 0 1 3333333422778562 1 1547005422523435  Population Calcs  0 0 1 000000006708392 1 000000003354196

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Intro  I assume that you have a matrix X where each row line is a sample observation and each column is a variable feature  this is the expected input for any sklearn ML function by the way -- X shape should be  number of samples  number of features     Core of method  The main idea is to normalize standardize i e       0 and s   1 your features variables columns of X  individually   before applying any machine learning model  StandardScaler   will normalize the features i e  each column of X  INDIVIDUALLY  so that each column feature variable will have      0 and s   1   P S  I find the most upvoted answer on this page  wrong  I am quoting  quot each value in the dataset will have the sample mean value subtracted quot  -- This is neither true nor correct   See also  How and why to Standardize your data  A python tutorial  Example  from sklearn preprocessing import StandardScaler import numpy as np    4 samples observations and 2 variables features data   np array   0  0    1  0    0  1    1  1    scaler   StandardScaler   scaled data   scaler fit transform data   print data    0  0     1  0     0  1     1  1     print scaled data    -1  -1      1  -1     -1   1      1   1     Verify that the mean of each feature  column  is 0  scaled data mean axis   0  array  0   0     Verify that the std of each feature  column  is 1  scaled data std axis   0  array  1   1      The maths    UPDATE 08 2020  Concerning the input parameters with mean and with std to False True  I have provided an answer here  StandardScaler difference between    with std False or True    and    with mean False or True

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We apply StandardScalar   on a row basis  So  for each row in a column  I am assuming that you are working with a Pandas DataFrame   x new    x original - mean of distribution    std of distribution Few points -  It is called Standard Scalar as we are dividing it by the standard deviation of the distribution  distr  of the feature   Similarly  you can guess for MinMaxScalar     The original distribution remains the same after applying StandardScalar    It is a common misconception that the distribution gets changed to a Normal Distribution  We are just squashing the range into  0  1

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This is useful when you want to compare data that correspond to different units  In that case  you want to remove the units  To do that in a consistent way of all the data  you transform the data in a way that the variance is unitary and that the mean of the series is 0

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Following is a simple working example to explain how standarization calculation works  The theory part is already well explained in other answers    gt  gt  gt import numpy as np  gt  gt  gt data     6  2    4  2    6  4    8  2    gt  gt  gt a   np array data    gt  gt  gt np std a  axis 0  array  1 41421356  0 8660254      gt  gt  gt np mean a  axis 0  array  6    2 5     gt  gt  gt from sklearn preprocessing import StandardScaler  gt  gt  gt scaler   StandardScaler    gt  gt  gt scaler fit data   gt  gt  gt print scaler mean     Xchanged    X-    s  WHERE s is Standard Deviation and    is mean  gt  gt  gt z scaler transform data   gt  gt  gt z   Calculation  As you can see in the output  mean is  6    2 5  and std deviation is  1 41421356  0 8660254    Data is  0 1  position is 2 Standardization    2 - 2 5  0 8660254   -0 57735027  Data in  1 0  position is 4 Standardization    4-6  1 41421356   -1 414  Result After Standardization    Check Mean and Std Deviation After Standardization    Note  -2 77555756e-17 is very close to 0   References   Compare the effect of different scalers on data with outliers What s the difference between Normalization and Standardization  Mean of data scaled with sklearn StandardScaler is not zero

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StandardScaler performs the task of Standardization  Usually a dataset contains variables that are different in scale  For e g  an Employee dataset will contain AGE column with values on scale 20-70 and SALARY column with values on scale 10000-80000  As these two columns are different in scale  they are Standardized to have common scale while building machine learning model

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After applying StandardScaler    each column in X will have mean of 0 and standard deviation of 1   Formulas are listed by others on this page   Rationale  some algorithms require data to look like this  see sklearn docs

[python] Can anyone explain me StandardScaler?

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