# Averaging lists of values with duplicate keys

I have gene expression data that I represent as a list of genes and a list of lists of values. I average the expression data for any genes with the same name.

For example:

genes = ['A', 'C', 'C', 'B', 'A']
vals  = [[2.0, 2.0, 9.0, 9.0], # A: will be averaged with row=4
[3.0, 3.0, 3.0, 3.0], # C: will be averaged with row=2
[8.0, 8.0, 2.0, 2.0], # C: will be averaged with row=1
[4.0, 4.0, 4.0, 3.0], # B: is fine
[1.0, 1.0, 1.0, 1.0]] # A: will be averaged with row=0

is converted to

genes = ['A', 'B', 'C']
vals  = [[1.5, 1.5, 5.0, 5.0],
[4.0, 4.0, 4.0, 3.0],
[5.5, 5.5, 2.5, 2.5]]

Here is my function:

def avg_dups(genes, values):
"""Finds duplicate genes and averages their expression data.
"""
unq_genes = np.unique(genes)
out_values = np.zeros((unq_genes.shape[0], values.shape[1]))
for i, gene in enumerate(unq_genes):
dups = values[genes==gene]
out_values[i] = np.mean(dups, axis=0)
return (unq_genes, out_values)

This function is slower than any other part of my data pipeline, taking 5-10 seconds when other steps that also operate on the whole dataset take sub-seconds. Any thoughts on how I can improve this?

• On an average about how many unique items can be present in genes? – Ashwini Chaudhary Feb 20 '15 at 0:29
• @AshwiniChaudhary, ~20,000. – gwg Feb 20 '15 at 0:34
• Can you give realistically sized and distributed example data? It helps a ton when trying to optimize. – Veedrac Feb 20 '15 at 0:43
• @Veedrac, that's hard to answer because there is a lot of variance in the data. Here is an example dataset: ftp.ncbi.nlm.nih.gov/geo/series/GSE43nnn/GSE43805/soft. The leftmost column, ILMN..., needs to be converted to gene symbols, of which there are only 20,000[1], so I suspect there will be quite a few duplicates. [1]There are many more than 20,000 gene symbols, but I convert them to a subset for humans. – gwg Feb 20 '15 at 1:03
• I was trying to indicate that the shape and cleanliness of the data can vary significantly. I have seen both 10KB and 20GB files, shapes ranging from (400000,3) to (1000,20), and duplicates ranging from 0 to >75%. – gwg Feb 20 '15 at 1:33

This seems to be the fastest so far:

import numpy
from numpy import newaxis

def avg_dups(genes, values):
folded, indices, counts = np.unique(genes, return_inverse=True, return_counts=True)

output = numpy.zeros((folded.shape[0], values.shape[1]))
output /= counts[:, newaxis]

return folded, output

This finds the unique genes to fold the values into, along with the current index → new index mapping and the number of repeated values that map to the same index:

folded, indices, counts = np.unique(genes, return_inverse=True, return_counts=True)

It adds the row from each current index to the new index in the new output:

output = numpy.zeros((folded.shape[0], values.shape[1]))

numpy.add.at(output, indices, values) is used over output[indices] += values because the buffering used in += breaks the code for repeated indices.

The mean is taken with a simple division of the number of repeated values that map to the same index:

output /= counts[:, newaxis]

Using Ashwini Chaudhary's generate_test_data(2000) (giving a 10000x4 array), my rough timings are:

name             time/ms  Author
avg_dups           230    gwg
avg_dups_fast       33    Ashwini Chaudhary
avg_dups_python     45    Ashwini Chaudhary
avg_dups           430    Veedrac
avg_dups             5    Veedrac with Jaime's improvement
• You can do folded, indices, counts = np.unique(genes, return_inverse=True, return_counts=True) and spare yourself all those broadcasting comparisons, which typically cripple performance. On the other hand, nice use of add.at! – Jaime Feb 20 '15 at 8:50
• @Jaime Blimey, that's fast indeed. +1 – Veedrac Feb 20 '15 at 16:58
• @Veedrac, this is very fast. Thanks! Averaging duplicates in my test SOFT file (originally picked at random) using my original function took 5.22903513908 seconds. Your function took 0.000233888626099 seconds. Thanks! – gwg Feb 24 '15 at 15:54

Your current approach is slow because it takes $\mathcal{O}(n^2)$ time, for each unique gene you're checking for its index in genes.

One not-pure NumPy approach that I can think of will take $\mathcal{O}(n \log n)$ time for this (explanation in comments).

from collections import defaultdict
from itertools import count
import numpy as np

def avg_dups_fast(genes, values):
# Find the sorted indices of all genes so that we can group them together
sorted_indices = np.argsort(genes)
# Now create two arrays using sorted_indices where similar genes and
# the corresponding values are now grouped together
sorted_genes = genes[sorted_indices]
sorted_values = values[sorted_indices]
# Now to find each individual group we need to find the index where the
# gene value changes. We can use numpy.where with numpy.diff for this.
# But as numpy.diff won't work with string, so we need to generate
# some unique integers for genes, for that we can use
# collections.defaultdict with itertools.count.
# This dict will generate a new integer as soon as a
# new string is encountered and will save it as well so that same
# value is used for repeated strings.
d = defaultdict(count(0).next)
unique_ints = np.fromiter((d[x] for x in sorted_genes), dtype=int)
# Now get the indices
split_at = np.where(np.diff(unique_ints)!=0)[0] + 1
# split the sorted_values at those indices.
split_items = np.array_split(sorted_values, split_at)
return np.unique(sorted_genes), np.array([np.mean(arr, axis=0) for arr in split_items])

Also a Pure Python approach that will take only $\mathcal{O}(n)$ time. Here I've simply used a dictionary with the gene as key and the corresponding values are going to be appended in a list:

from collections import defaultdict
from itertools import izip

def avg_dups_python(genes, values):
d = defaultdict(list)
for k, v in izip(genes, values):
d[k].append(v)
return list(d), [np.mean(val, axis=0) for val in d.itervalues()]

Timing comparisons:

>>> from string import ascii_letters
>>> from itertools import islice, product

>>> def generate_test_data(n):
genes = np.array([''.join(x) for x in  islice(product(ascii_letters, repeat=3), n)]*5, dtype='S3')
np.random.shuffle(genes)
vals  = np.array([[2.0, 2.0, 9.0, 9.0], # A: will be averaged with row=4
[3.0, 3.0, 3.0, 3.0], # C: will be averaged with row=2
[8.0, 8.0, 2.0, 2.0], # C: will be averaged with row=1
[4.0, 4.0, 4.0, 3.0], # B: is fine
[1.0, 1.0, 1.0, 1.0]]*n) # A: will be averaged with row=0
return genes, vals
...

>>> data = generate_test_data(20000)
>>> %timeit avg_dups(*data)
1 loops, best of 3: 18.4 s per loop
>>> %timeit avg_dups_fast(*data)
10 loops, best of 3: 166 ms per loop
>>> %timeit avg_dups_python(*data)
1 loops, best of 3: 253 ms per loop
>>> (avg_dups(*data)[1] == avg_dups_fast(*data)[1]).all()
True
• "we need to generate some unique integers for genes" → If they need to be unique, you should avoid hash - it does not guarantee uniqueness. – Veedrac Feb 20 '15 at 1:23
• @Veedrac Interesting! So, two different strings can hash to same value in a given process(considering strings have their own __hash__ method)?(Python 2.7) A simple alternative will be to use d = defaultdict(count(0).next), this will return a unique value each time a new string is encountered. – Ashwini Chaudhary Feb 20 '15 at 2:42
• Yes, the whole point of hashing a string is that the hash is short. Loss of information is inevitable, hence collisions. – Janne Karila Feb 20 '15 at 6:39
• @JanneKarila You're right, not sure what I was thinking. :/ – Ashwini Chaudhary Feb 20 '15 at 11:38
• @JanneKarila: Hash collisions don't take place due to "loss of information", but due to the fact that we do not have a perfect hash function --i.e. a hash function that guarantees that no two inputs will ever be mapped/hashed to the same output. – code_dredd Oct 8 '15 at 1:43