I have a large csr_matrix
and I am interested in the top ten values and their indices each row. But I did not find a decent way to manipulate the matrix.
Here is my current solution and the main idea is to process them row by row:
row = csr_matrix.getrow(row_number).toarray()[0].ravel()
top_ten_indicies = row.argsort()[-10:]
top_ten_values = row[row.argsort()[-10:]]
By doing this, the advantages of csr_matrix
is not fully used. It's more like a brute force solution.
The function csr_matrix() is used to create a sparse matrix of compressed sparse row format whereas csc_matrix() is used to create a sparse matrix of compressed sparse column format.
Description. n = nnz(X) returns the number of nonzero elements in matrix X . The density of a sparse matrix is nnz(X)/prod(size(X)) .
The compressed sparse row (CSR) or compressed row storage (CRS) or Yale format represents a matrix M by three (one-dimensional) arrays, that respectively contain nonzero values, the extents of rows, and column indices. It is similar to COO, but compresses the row indices, hence the name.
I don't see what the advantages of csr
format are in this case. Sure, all the nonzero values are collected in one .data
array, with the corresponding column indexes in .indices
. But they are in blocks of varying length. And that means they can't be processed in parallel or with numpy
array strides.
One solution is the pad those blocks into common length blocks. That's what .toarray()
does. Then you can find the maximum values with argsort(axis=1) or with
argpartition`.
Another is to break them into row sized blocks, and process each of those. That's what you are doing with the .getrow
. Another way of breaking them up is convert to lil
format, and process the sublists of the .data
and .rows
arrays.
A possible third option is to use the ufunc
reduceat
method. This lets you apply ufunc
reduction
methods to sequential blocks of an array. There are established ufunc
like np.add
that take advantage of this. argsort
is not such a function. But there is a way of constructing a ufunc
from a Python function, and gain some modest speed over regular Python iteration. [I need to look up a recent SO question that illustrates this.]
I'll illustrate some of this with a simpler function, sum over rows.
If A2
is a csr matrix.
A2.sum(axis=1) # the fastest compile csr method
A2.A.sum(axis=1) # same, but with a dense intermediary
[np.sum(l.data) for l in A2] # iterate over the rows of A2
[np.sum(A2.getrow(i).data) for i in range(A2.shape[0])] # iterate with index
[np.sum(l) for l in A2.tolil().data] # sum the sublists of lil format
np.add.reduceat(A2.data, A2.indptr[:-1]) # with reduceat
A2.sum(axis=1)
is implemented as a matrix multiplication. That's not relevant to the sort problem, but still an interesting way of looking at the summation problem. Remember csr
format was developed for efficient multiplication.
For a my current sample matrix (created for another SO sparse question)
<8x47752 sparse matrix of type '<class 'numpy.float32'>'
with 32 stored elements in Compressed Sparse Row format>
some comparative times are
In [694]: timeit np.add.reduceat(A2.data, A2.indptr[:-1])
100000 loops, best of 3: 7.41 µs per loop
In [695]: timeit A2.sum(axis=1)
10000 loops, best of 3: 71.6 µs per loop
In [696]: timeit [np.sum(l) for l in A2.tolil().data]
1000 loops, best of 3: 280 µs per loop
Everything else is 1ms or more.
I suggest focusing on developing your one-row function, something like:
def max_n(row_data, row_indices, n):
i = row_data.argsort()[-n:]
# i = row_data.argpartition(-n)[-n:]
top_values = row_data[i]
top_indices = row_indices[i] # do the sparse indices matter?
return top_values, top_indices, i
Then see how if fits in one of these iteration methods. tolil()
looks most promising.
I haven't addressed the question of how to collect these results. Should they be lists of lists, array with 10 columns, another sparse matrix with 10 values per row, etc.?
sorting each row of a large sparse & saving top K values & column index - Similar question from several years back, but unanswered.
Argmax of each row or column in scipy sparse matrix - Recent question seeking argmax
for rows of csr
. I discuss some of the same issues.
how to speed up loop in numpy? - example of how to use np.frompyfunc
to create a ufunc
. I don't know if the resulting function has the .reduceat
method.
Increasing value of top k elements in sparse matrix - get the top k elements of csr (not by row). Case for argpartition
.
The row summation implemented with np.frompyfunc
:
In [741]: def foo(a,b):
return a+b
In [742]: vfoo=np.frompyfunc(foo,2,1)
In [743]: timeit vfoo.reduceat(A2.data,A2.indptr[:-1],dtype=object).astype(float)
10000 loops, best of 3: 26.2 µs per loop
That's respectable speed. But I can't think of a way of writing a binary function (takes to 2 arguments) that would implement argsort
via reduction. So this is probably a deadend for this problem.
Just to answer the original question (for people like me who found this question looking for copy-pasta), here's a solution using multiprocessing based on @hpaulj's suggestion of converting to lil_matrix
, and iterating over rows
from multiprocessing import Pool
def _top_k(args):
"""
Helper function to process a single row of top_k
"""
data, row = args
data, row = zip(*sorted(zip(data, row), reverse=True)[:k])
return data, row
def top_k(m, k):
"""
Keep only the top k elements of each row in a csr_matrix
"""
ml = m.tolil()
with Pool() as p:
ms = p.map(_top_k, zip(ml.data, ml.rows))
ml.data, ml.rows = zip(*ms)
return ml.tocsr()
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