quantile normalization on pandas dataframe

Question

Simply speaking, how to apply quantile normalization on a large Pandas dataframe (probably 2,000,000 rows) in Python?

PS. I know that there is a package named rpy2 w

Answer 1

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.)

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

Ok I implemented the method myself of relatively high efficiency.

After finishing, this logic seems kind of easy but, anyway, I decided to post it here for any one feels confused like I was when I couldn't googled the available code.

The code is in github: Quantile Normalize