Efficient accessing in sparse matrices

Question

I'm working with recommender systems but I'm struggling with the access times of the scipy sparse matrices.

In this case, I'm implementing TrustSVD so I need an efficient structure to operate both in columns and rows (CSR, CSC). I've thought about using both structures, dictionaries,... but either way this is always too slow, especially compared with the numpy matrix operations.

for u, j in zip(*ratings.nonzero()):
    items_rated_by_u = ratings[u, :].nonzero()[1]
    users_who_rated_j = ratings[:, j].nonzero()[0]
    # More code...

Extra: Each loop takes around 0.033s, so iterating once through 35,000 ratings means to wait 19min per iteration (SGD) and for a minimum of 25 iterations we're talking about 8h. Moreover, here I'm just talking about accessing, if I include the factorization part it would take around 2 days.

Answer 1

When you index a sparse matrix, especially just asking for a row or column, it not only has to select the values, but it also has to construct a new sparse matrix. np.ndarray construction is done in compiled code, but most of the sparse construction is pure Python. The nonzero()[1] construct requires converting the matrix to coo format and picking the row and col attributes (look at its code).

I think you could access your row columns faster by looking at the rows attribute of the lil format, or its transpose:

In [418]: sparse.lil_matrix(np.matrix('0,1,0;1,0,0;0,1,1'))
Out[418]: 
<3x3 sparse matrix of type '<class 'numpy.int32'>'
    with 4 stored elements in LInked List format>
In [419]: M=sparse.lil_matrix(np.matrix('0,1,0;1,0,0;0,1,1'))
In [420]: M.A
Out[420]: 
array([[0, 1, 0],
       [1, 0, 0],
       [0, 1, 1]], dtype=int32)
In [421]: M.rows
Out[421]: array([[1], [0], [1, 2]], dtype=object)
In [422]: M[1,:].nonzero()[1]
Out[422]: array([0], dtype=int32)
In [423]: M[2,:].nonzero()[1]
Out[423]: array([1, 2], dtype=int32)
In [424]: M.T.rows
Out[424]: array([[1], [0, 2], [2]], dtype=object)

You could also access these values in the csr format, but it's a bit more complicated

In [425]: M.tocsr().indices
Out[425]: array([1, 0, 1, 2], dtype=int32)