Averaging lists of values with duplicate keys

Question

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?

Answer 1

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]))
    numpy.add.at(output, indices, values)
    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)

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

Answer 2

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