其它¶
绘制样本和过滤器¶
注意
此部分的代码可从此处下载。
要绘制样本，我们需要做的是获取可见单元，这是一个平整的图像（没有2D结构的可见单元，只有1D字符串的激活单元），并将其重塑成2D图像。来自1D数组的点进入2D图像的顺序由初始MNIST图像转换成1D数组的顺序给出。幸运的是，这只是一个numpy.reshape函数的调用。
绘制权重有点更棘手。我们有n_hidden个隐藏单元，每个隐藏单元对应于权重矩阵的一列。列具有与可见图像相同的形状，其中对应于具有可见单元
的连接的权重在位置。因此，如果我们使用numpy.reshape重塑每一个这样的列，我们得到一个过滤器图像，告诉我们这个隐藏单元如何受到输入图像的影响。
我们需要一个utility函数，它接受一个minibatch或者权重矩阵，并将每一行（对于权重矩阵，我们做一个转置）转换成一个2D图像，然后将这些图像平铺在一起。在我们将minibatch或权重转换成平铺的图片之后，我们可以使用PIL绘图并保存。PIL是一个处理图像的标准python库。
为我们平铺minibatch的是通过我们在这里提供的tile_raster_image函数完成。
def scale_to_unit_interval(ndar, eps=1e-8):
""" Scales all values in the ndarray ndar to be between 0 and 1 """
ndar = ndar.copy()
ndar -= ndar.min()
ndar *= 1.0 / (ndar.max() + eps)
return ndar
def tile_raster_images(X, img_shape, tile_shape, tile_spacing=(0, 0),
scale_rows_to_unit_interval=True,
output_pixel_vals=True):
"""
Transform an array with one flattened image per row, into an array in
which images are reshaped and layed out like tiles on a floor.
This function is useful for visualizing datasets whose rows are images,
and also columns of matrices for transforming those rows
(such as the first layer of a neural net).
:type X: a 2-D ndarray or a tuple of 4 channels, elements of which can
be 2-D ndarrays or None;
:param X: a 2-D array in which every row is a flattened image.
:type img_shape: tuple; (height, width)
:param img_shape: the original shape of each image
:type tile_shape: tuple; (rows, cols)
:param tile_shape: the number of images to tile (rows, cols)
:param output_pixel_vals: if output should be pixel values (i.e. int8
values) or floats
:param scale_rows_to_unit_interval: if the values need to be scaled before
being plotted to [0,1] or not
:returns: array suitable for viewing as an image.
(See:`Image.fromarray`.)
:rtype: a 2-d array with same dtype as X.
"""
assert len(img_shape) == 2
assert len(tile_shape) == 2
assert len(tile_spacing) == 2
# The expression below can be re-written in a more C style as
# follows :
#
# out_shape = [0,0]
# out_shape[0] = (img_shape[0] + tile_spacing[0]) * tile_shape[0] -
# tile_spacing[0]
# out_shape[1] = (img_shape[1] + tile_spacing[1]) * tile_shape[1] -
# tile_spacing[1]
out_shape = [(ishp + tsp) * tshp - tsp for ishp, tshp, tsp
in zip(img_shape, tile_shape, tile_spacing)]
if isinstance(X, tuple):
assert len(X) == 4
# Create an output numpy ndarray to store the image
if output_pixel_vals:
out_array = numpy.zeros((out_shape[0], out_shape[1], 4), dtype='uint8')
else:
out_array = numpy.zeros((out_shape[0], out_shape[1], 4), dtype=X.dtype)
#colors default to 0, alpha defaults to 1 (opaque)
if output_pixel_vals:
channel_defaults = [0, 0, 0, 255]
else:
channel_defaults = [0., 0., 0., 1.]
for i in range(4):
if X[i] is None:
# if channel is None, fill it with zeros of the correct
# dtype
out_array[:, :, i] = numpy.zeros(out_shape,
dtype='uint8' if output_pixel_vals else out_array.dtype
) + channel_defaults[i]
else:
# use a recurrent call to compute the channel and store it
# in the output
out_array[:, :, i] = tile_raster_images(X[i], img_shape, tile_shape, tile_spacing, scale_rows_to_unit_interval, output_pixel_vals)
return out_array
else:
# if we are dealing with only one channel
H, W = img_shape
Hs, Ws = tile_spacing
# generate a matrix to store the output
out_array = numpy.zeros(out_shape, dtype='uint8' if output_pixel_vals else X.dtype)
for tile_row in range(tile_shape[0]):
for tile_col in range(tile_shape[1]):
if tile_row * tile_shape[1] + tile_col < X.shape[0]:
if scale_rows_to_unit_interval:
# if we should scale values to be between 0 and 1
# do this by calling the `scale_to_unit_interval`
# function
this_img = scale_to_unit_interval(X[tile_row * tile_shape[1] + tile_col].reshape(img_shape))
else:
this_img = X[tile_row * tile_shape[1] + tile_col].reshape(img_shape)
# add the slice to the corresponding position in the
# output array
out_array[
tile_row * (H+Hs): tile_row * (H + Hs) + H,
tile_col * (W+Ws): tile_col * (W + Ws) + W
] \
= this_img * (255 if output_pixel_vals else 1)
return out_array