How to efficiently partial argsort Pandas dataframe across columns

Question

I would like to replace values with column labels according to the largest 3 values for each row. Let's assume this input:

   p1  p2  p3  p4
0   0   9   1   4
1   0   2   3   4
2   1   3  10   7
3   1   5   3   1
4   2   3   7  10

Given n = 3, I am looking for:

  Top1 Top2 Top3
0   p2   p4   p3
1   p4   p3   p2
2   p3   p4   p2
3   p2   p3   p1
4   p4   p3   p2

I'm not concerned about duplicates, e.g. for index 3, Top3 can be 'p1' or 'p4'.

Attempt 1

My first attempt is a full sort using np.ndarray.argsort:

res = pd.DataFrame(df.columns[df.values.argsort(1)]).iloc[:, len(df.index): 0: -1]

But in reality I have more than 4 columns and this will be inefficient.

Attempt 2

Next I tried np.argpartition. But since values within each partition are not sorted, this required a subsequent sort:

n = 3
parts = np.argpartition(-df.values, n, axis=1)[:, :-1]
args = (-df.values[np.arange(df.shape[0])[:, None], parts]).argsort(1)

res = pd.DataFrame(df.columns[parts[np.arange(df.shape[0])[:, None], args]],
                   columns=[f'Top{i}' for i in range(1, n+1)])

This, in fact, works out slower than the first attempt for larger dataframes. Is there a more efficient way which takes advantage of partial sorting? You can use the below code for benchmarking purposes.

Benchmarking

# Python 3.6.0, NumPy 1.11.3, Pandas 0.19.2

import pandas as pd, numpy as np

df = pd.DataFrame({'p1': [0, 0, 1, 1, 2],
                   'p2': [9, 2, 3, 5, 3],
                   'p3': [1, 3, 10, 3, 7],
                   'p4': [4, 4, 7, 1, 10]})

def full_sort(df):
    return pd.DataFrame(df.columns[df.values.argsort(1)]).iloc[:, len(df.index): 0: -1]

def partial_sort(df):
    n = 3
    parts = np.argpartition(-df.values, n, axis=1)[:, :-1]
    args = (-df.values[np.arange(df.shape[0])[:, None], parts]).argsort(1)
    return pd.DataFrame(df.columns[parts[np.arange(df.shape[0])[:, None], args]])

df = pd.concat([df]*10**5)

%timeit full_sort(df)     # 86.3 ms per loop
%timeit partial_sort(df)  # 158 ms per loop

With more num of cols, you might have better luck with argparition. With 4 cols, it seems not worth it. — Divakar, Dec 06 '18 at 12:22
@Divakar, Yep, you might be right. I just thought there might be some clever NumPy magic (*pre-sorted* `np.argpartition`?) that could help here. Maybe it doesn't exist. — jpp, Dec 06 '18 at 12:23
@Divakar, ~30 columns. For what it's worth, even for this number `full_sort` works out faster. Seems the 2x performance differential persists as column number increases. — jpp, Dec 06 '18 at 12:27
I believe this could be useful: https://stackoverflow.com/questions/42184499/cannot-understand-numpy-argpartition-output/42186357#42186357 — Dani Mesejo, Dec 06 '18 at 13:19

Divakar · Accepted Answer · 2018-12-06T14:06:52.713

With a decent number of columns, we can use np.argpartition with some slicing and indexing, like so -

def topN_perrow_colsindexed(df, N):
    # Extract array data
    a = df.values

    # Get top N indices per row with not necessarily sorted order
    idxtopNpart = np.argpartition(a,-N,axis=1)[:,-1:-N-1:-1]

    # Index into input data with those and use argsort to force sorted order
    sidx = np.take_along_axis(a,idxtopNpart,axis=1).argsort(1)
    idxtopN = np.take_along_axis(idxtopNpart,sidx[:,::-1],axis=1)    

    # Index into column values with those for final output
    c = df.columns.values
    return pd.DataFrame(c[idxtopN], columns=[['Top'+str(i+1) for i in range(N)]])

Sample run -

In [65]: df
Out[65]: 
   p1  p2  p3  p4
0   0   9   1   4
1   0   2   3   4
2   1   3  10   7
3   1   5   3   1
4   2   3   7  10

In [66]: topN_perrow_colsindexed(df, N=3)
Out[66]: 
  Top1 Top2 Top3
0   p2   p4   p3
1   p4   p3   p2
2   p3   p4   p2
3   p2   p3   p4
4   p4   p3   p2

Timings -

In [143]: np.random.seed(0)

In [144]: df = pd.DataFrame(np.random.rand(10000,30))

In [145]: %timeit full_sort(df)
     ...: %timeit partial_sort(df)
     ...: %timeit topN_perrow_colsindexed(df,N=3)
100 loops, best of 3: 7.96 ms per loop
100 loops, best of 3: 13.9 ms per loop
100 loops, best of 3: 5.47 ms per loop

In [146]: df = pd.DataFrame(np.random.rand(10000,100))

In [147]: %timeit full_sort(df)
     ...: %timeit partial_sort(df)
     ...: %timeit topN_perrow_colsindexed(df,N=3)
10 loops, best of 3: 34 ms per loop
10 loops, best of 3: 56.1 ms per loop
100 loops, best of 3: 13.6 ms per loop

How to efficiently partial argsort Pandas dataframe across columns

Attempt 1

Attempt 2

Benchmarking

1 Answers1