Different size python convolution

Question

I am trying to implement a convolutional neural network in Python.
However, when I use signal.convolve or np.convolve, it cannot perform convolution on X, Y (X - 3d, Y - 2d). X - training mini-quotes. Y - filters. I do not want to do a loop for each training vector, for example:

for i in xrange(X.shape[2]):
    result = signal.convolve(X[:,:,i], Y, 'valid')
    ....

So, is there any function that I can use effectively for convolution?

Answer 1

Scipy implements standard N-dimensional convolutions, so the folded matrix and core are N-dimensional.

Y, Y 3-:

result = signal.convolve(X, Y[..., None], 'valid')

, , [width, height, image_idx] ( [height, width, image_idx]). , ( C-), Y[..., None] Y[None, ...].

Y[..., None] Y, 3- [kernel_width, kernel_height, 1] , , ​​.

. , - width x height, CNN.

---

EDIT: , @.

:

def test(S, N, K):
    """ S: image size, N: num images, K: kernel size"""
    a = np.random.randn(S, S, N)
    b = np.random.randn(K, K)
    valid = [slice(K//2, -K//2+1), slice(K//2, -K//2+1)]

    %timeit signal.convolve(a, b[..., None], 'valid')
    %timeit signal.fftconvolve(a, b[..., None], 'valid')
    %timeit ndimage.convolve(a, b[..., None])[valid]

:

• S:

  >>> test(100, 50, 11) # 100x100 images
  1 loop, best of 3: 909 ms per loop
  10 loops, best of 3: 116 ms per loop
  10 loops, best of 3: 54.9 ms per loop
  
  >>> test(1000, 50, 11) # 1000x1000 images
  1 loop, best of 3: 1min 51s per loop
  1 loop, best of 3: 16.5 s per loop
  1 loop, best of 3: 5.66 s per loop
  

• N:

  >>> test(100, 5, 11) # 5 images
  10 loops, best of 3: 90.7 ms per loop
  10 loops, best of 3: 26.7 ms per loop
  100 loops, best of 3: 5.7 ms per loop
  
  >>> test(100, 500, 11) # 500 images
  1 loop, best of 3: 9.75 s per loop
  1 loop, best of 3: 888 ms per loop
  1 loop, best of 3: 727 ms per loop
  

• K:

  >>> test(100, 50, 5) # 5x5 kernels
  1 loop, best of 3: 217 ms per loop
  10 loops, best of 3: 100 ms per loop
  100 loops, best of 3: 11.4 ms per loop
  
  >>> test(100, 50, 31) # 31x31 kernels
  1 loop, best of 3: 4.39 s per loop
  1 loop, best of 3: 220 ms per loop
  1 loop, best of 3: 560 ms per loop
  

, , ndimage.convolve , , ( K = 31 ).