How to speed up cosine similarity between a numpy array and a very very large matrix?

Question

I have a problem where a need to calculate cosine similarities between a numpy array of shape (1, 300) and a matrix of shape (5000000, 300). I have tried multiple different flavors of codes and now I am wondering if there is a way to reduce the run time substantially :

Version 1 : I divide my big matrix into 5 smaller matrix of size 1Mil each:

from scipy import spatial
from concurrent.futures import ThreadPoolExecutor, ProcessPoolExecutor

def cos_matrix_multiplication(vector,matrix_1):

    v = vector.reshape(1, -1)
    scores1=spatial.distance.cdist(matrix_1, v, 'cosine')

    return((scores1[:1]))

pool = ThreadPoolExecutor(8)


URLS=[mat_small1,mat_small2,mat_small3,mat_small4,mat_small5]

neighbors=[]
with concurrent.futures.ThreadPoolExecutor(max_workers=30) as executor:
    # Start the load operations and mark each future with its URL
    future_to_url = {executor.submit(cos_matrix_multiplication,vec,mat_col): mat_col for mat_col in URLS}
    for future in concurrent.futures.as_completed(future_to_url):
        url = future_to_url[future]
        data = future.result()
        neighbors.append(data)

Runtime : 2.48secs

Version 2: Using Numba jit : inspired by this SO answer

@numba.jit('void(f4, f4)',nogil=True)
def cosine_sim(A,B):
    scores = np.zeros(A.shape[0])
    for i in range(A.shape[0]):
        v = A[i]
        m = B.shape[1]
        udotv = 0
        u_norm = 0
        v_norm = 0
    for j in range(m):


        udotv += B[0][j] * v[j]
        u_norm += B[0][j] * B[0][j]
        v_norm += v[j] * v[j]

    ratio =  udotv/((u_norm*v_norm)**0.5)
    scores[i] = ratio
    i += 1
return scores

cosine_sim(matrix,vec)

Runtime 2.34 secs

Version 3: Using Cuda jit (can't really get to work in a reproducible manner each time)

@cuda.jit
def cosine_sim(A,B,C):
#scores = np.zeros(A.shape[0])
    for i in range(A.shape[0]):
        v = A[i]
        m = B.shape[1]
        udotv = 0
        u_norm = 0
        v_norm = 0
        for j in range(m):

            udotv += B[0][j] * v[j]
            u_norm += B[0][j] * B[0][j]
            v_norm += v[j] * v[j]

    u_norm = math.sqrt(u_norm)
    v_norm = math.sqrt(v_norm)


    if (u_norm == 0) or (v_norm == 0):
        ratio = 1.0
    else:
        ratio = udotv / (u_norm * v_norm)
    C[i,1] = ratio
    i += 1


matrix = mat_small1

A_global_mem = cuda.to_device(matrix)
B_global_mem = cuda.to_device(vec)

C_global_mem = cuda.device_array((matrix.shape[0], 1))


threadsperblock = (16, 16)
blockspergrid_x = int(math.ceil(A_global_mem.shape[0] / threadsperblock[0]))
blockspergrid_y = int(math.ceil(B_global_mem.shape[1] / threadsperblock[1]))
blockspergrid = (blockspergrid_x, blockspergrid_y)


cosine_sim[blockspergrid, threadsperblock](A_global_mem, B_global_mem, C_global_mem)


C = C_global_mem.copy_to_host()

results in : CudaAPIError: [702] Call to cuMemcpyDtoH results in CUDA_ERROR_LAUNCH_TIMEOUT

The matrix is dense, and the My GPU is 8gb ram, and total size of the matrix is about 4.7gb. Can a GPU expedite this at all?

You could give [`np.apply_along_axis`](https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.apply_along_axis.html) a try. I.E. `np.apply_along_axis(lambda v: spatial.distance.cosine(matrix_1, v), axis=1, arr=matrix_2)` — Chris Mueller, Dec 05 '17 at 21:29

score 2 · Answer 1 · answered Jul 22 '18 at 07:43

2

Please try replacing ThreadPoolExecutor with ProcessPoolExecutor (you already have it declared). Former one is for async calls not for CPU bound tasks, although this is not specified in the docs directly.

answered Jul 22 '18 at 07:43

Anatoly Alekseev

2,011
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How to speed up cosine similarity between a numpy array and a very very large matrix?

1 Answers1