quantile normalization on pandas dataframe

Using the example dataset from Wikipedia article:

df = pd.DataFrame({'C1': {'A': 5, 'B': 2, 'C': 3, 'D': 4},
                   'C2': {'A': 4, 'B': 1, 'C': 4, 'D': 2},
                   'C3': {'A': 3, 'B': 4, 'C': 6, 'D': 8}})

df
Out: 
   C1  C2  C3
A   5   4   3
B   2   1   4
C   3   4   6
D   4   2   8

For each rank, the mean value can be calculated with the following:

rank_mean = df.stack().groupby(df.rank(method='first').stack().astype(int)).mean()

rank_mean
Out: 
1    2.000000
2    3.000000
3    4.666667
4    5.666667
dtype: float64

Then the resulting Series, rank_mean, can be used as a mapping for the ranks to get the normalized results:

df.rank(method='min').stack().astype(int).map(rank_mean).unstack()
Out: 
         C1        C2        C3
A  5.666667  4.666667  2.000000
B  2.000000  2.000000  3.000000
C  3.000000  4.666667  4.666667
D  4.666667  3.000000  5.666667

Possibly more robust to use the median on each row rather than mean (based on code from Shawn. L):

def quantileNormalize(df_input):
    df = df_input.copy()
    #compute rank
    dic = {}
    for col in df:
        dic[col] = df[col].sort_values(na_position='first').values
    sorted_df = pd.DataFrame(dic)
    #rank = sorted_df.mean(axis = 1).tolist()
    rank = sorted_df.median(axis = 1).tolist()
    #sort
    for col in df:
        # compute percentile rank [0,1] for each score in column 
        t = df[col].rank( pct=True, method='max' ).values
        # replace percentile values in column with quantile normalized score
        # retrieve q_norm score using calling rank with percentile value
        df[col] = [ np.nanpercentile( rank, i*100 ) if ~np.isnan(i) else np.nan for i in t ]
    return df

The code below gives identical result as preprocessCore::normalize.quantiles.use.target and I find it simpler clearer than the solutions above. Also performance should be good up to huge array lengths.

import numpy as np

def quantile_normalize_using_target(x, target):
    """
    Both `x` and `target` are numpy arrays of equal lengths.
    """

    target_sorted = np.sort(target)

    return target_sorted[x.argsort().argsort()]

Once you have a pandas.DataFrame easy to do:

quantile_normalize_using_target(df[0].as_matrix(),
                                df[1].as_matrix())

(Normalizing the first columnt to the second one as a reference distribution in the example above.)

I am new to pandas and late to the question, but I think answer might also be of use. It builds off of the great answer from @ayhan:

def quantile_normalize(dataframe, cols, pandas=pd):

    # copy dataframe and only use the columns with numerical values
    df = dataframe.copy().filter(items=cols)

    # columns from the original dataframe not specified in cols
    non_numeric = dataframe.filter(items=list(filter(lambda col: col not in cols, list(dataframe))))


    rank_mean = df.stack().groupby(df.rank(method='first').stack().astype(int)).mean()  

    norm = df.rank(method='min').stack().astype(int).map(rank_mean).unstack()


    result = pandas.concat([norm, non_numeric], axis=1)
    return result

the main difference here is closer to some real world applications. Often you just have matrices of numerical data in which case the original answer is sufficient.

Sometimes you have text based data in there as well. This lets you specify the columns cols of your numerical data and will run quantile normalization on those columns. At the end it will merge back the non-numeric (or not to be normalized) columns from your original data frame.

e.g. if you added some ‘meta-data’ (char) to the wiki example:

df = pd.DataFrame({
    'rep1': [5, 2, 3, 4],
    'rep2': [4, 1, 4, 2],
    'rep3': [3, 4, 6, 8],
    'char': ['gene_a', 'gene_b', 'gene_c', 'gene_d']
}, index = ['a', 'b', 'c', 'd'])

you can then call

quantile_normalize(t, ['rep1', 'rep2', 'rep3'])

to get

    rep1        rep2        rep3        char
a   5.666667    4.666667    2.000000    gene_a
b   2.000000    2.000000    3.000000    gene_b
c   3.000000    4.666667    4.666667    gene_c
d   4.666667    3.000000    5.666667    gene_d

One thing worth noticing is that both ayhan and shawn’s code use the smaller rank mean for ties, but if you use R package processcore’s normalize.quantiles() , it would use the mean of rank means for ties.

Using the above example:

> df

   C1  C2  C3
A   5   4   3
B   2   1   4
C   3   4   6
D   4   2   8

> normalize.quantiles(as.matrix(df))

         C1        C2        C3
A  5.666667  5.166667  2.000000
B  2.000000  2.000000  3.000000
C  3.000000  5.166667  4.666667
D  4.666667  3.000000  5.666667

As pointed out by @msg, none of the solutions here take ties into account. I made a python package called qnorm which handles ties, and correctly recreates the Wikipedia quantile normalization example:

import pandas as pd
import qnorm

df = pd.DataFrame({'C1': {'A': 5, 'B': 2, 'C': 3, 'D': 4},
                   'C2': {'A': 4, 'B': 1, 'C': 4, 'D': 2},
                   'C3': {'A': 3, 'B': 4, 'C': 6, 'D': 8}})

print(qnorm.quantile_normalize(df))
         C1        C2        C3
A  5.666667  5.166667  2.000000
B  2.000000  2.000000  3.000000
C  3.000000  5.166667  4.666667
D  4.666667  3.000000  5.666667

Installation can be done with either pip or conda

pip install qnorm

or

conda config --add channels conda-forge
conda install qnorm

This is a minor adjustment but I imagine that many have noticed the subtle ‘flaw’ in @ayhan ‘s answer.

I have made a small adjustment to it, which gets the ‘correct’ answer, while not having to resort to any external libraries for such an exceedingly simple function.

The only adjustment necessary is the [Add interpolated values] section.

import pandas as pd

df = pd.DataFrame({'C1': {'A': 5, 'B': 2, 'C': 3, 'D': 4},
                   'C2': {'A': 4, 'B': 1, 'C': 4, 'D': 2},
                   'C3': {'A': 3, 'B': 4, 'C': 6, 'D': 8}})

def quant_norm(df):
    ranks = (df.rank(method="first")
              .stack())
    rank_mean = (df.stack()
                   .groupby(ranks)
                   .mean())
    # Add interpolated values in between ranks
    finer_ranks = ((rank_mean.index+0.5).to_list() +
                    rank_mean.index.to_list())
    rank_mean = rank_mean.reindex(finer_ranks).sort_index().interpolate()
    return (df.rank(method='average')
              .stack()
              .map(rank_mean)
              .unstack())
quant_norm(df)

Out[122]: 
         C1        C2        C3
A  5.666667  5.166667  2.000000
B  2.000000  2.000000  3.000000
C  3.000000  5.166667  4.666667
D  4.666667  3.000000  5.666667

Note that scikit-learn offers a module for quantile normalization:

import pandas as pd
import sklearn.preprocessing

df = pd.DataFrame({'C1': {'A': 5, 'B': 2, 'C': 3, 'D': 4},
                   'C2': {'A': 4, 'B': 1, 'C': 4, 'D': 2},
                   'C3': {'A': 3, 'B': 4, 'C': 6, 'D': 8}})
sklearn.preprocessing.quantile_transform(df)

array([[1.  , 1.  , 0.  ],
       [0.  , 0.  , 0.33],
       [0.33, 1.  , 0.67],
       [0.67, 0.33, 1.  ]])

It is also possible to adjust the data to a normal distribution instead of a uniform distribution:

sklearn.preprocessing.quantile_transform(df, output_distribution="normal")

array([[ 5.2 ,  5.2 , -5.2 ],
       [-5.2 , -5.2 , -0.43],
       [-0.43,  5.2 ,  0.43],
       [ 0.43, -0.43,  5.2 ]])