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old_but_works.py
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old_but_works.py
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import numpy as np
from PIL import Image
from matplotlib import pyplot as plt
from pickle import dump, load
# https://towardsdatascience.com/building-a-convolutional-neural-network-from-scratch-using-numpy-a22808a00a40
# https://towardsdatascience.com/convolutional-neural-networks-explained-9cc5188c4939
class ConvolutionLayer:
'''
Convolution layer for a Convolutional Neural Network
Attributes
----------
`kernel_num: int`
The number of kernels (filters) associated with the convolution layer
`kernel_size: int`
The size of the kernels (filters) associated with the convolution layer
Methods
-------
`segmentGenerator(image: np.array)` -> `height, width`
Generate smaller segments of an image
`forwardProp(image: np.array)` -> `convolution_output: np.array`
Carries out the convolution for each generated portion of the image
`back_prop(dE_dY, alpha)` -> `dE_dK: np.array`
Calculate the gradient of the loss function
'''
def __init__(self, kernel_num: int, kernel_size: int) -> None:
'''
Initialise the Convolution layer of a Convolutional Neural Network
Parameters
------
`kernel_num: Integer`
The number of kernels (filters) to pass through
`kernel_size: Integer`
The size of the kernels (filters)
Returns
-------
`None`
Example
-------
`cl = ConvolutionalLayer(2, 3)`
'''
self.kernel_num = kernel_num
self.kernel_size = kernel_size
# Generate kernels x*y in size with random variables to be trained, normalisation by with kernel_size ** 2
self.kernels = np.random.randn(kernel_num, kernel_size, kernel_size) / kernel_size ** 2
def segmentGenerator(self, image: np.array):
'''
Generate smaller segments of an image
Parameters
----------
`image: np.array`
numpy array representation of the image
Returns
-------
`Portion: np.array`
The portion of the image
`Height: int`
The starting height value of the portion
`Width: int`
The starting width value of the portion
### Yields each portion of the image with respect to the kernel size
'''
height, width, *_ = image.shape
self.image = image
for h in range(height-self.kernel_size+1):
for w in range(width-self.kernel_size+1):
segment = image[h:h+(self.kernel_size), w:w+(self.kernel_size)]
yield segment, h, w
def forwardProp(self, image: np.array):
'''
Carries out the convolution for each generated portion of the image
Parameters
----------
`image: np.array`
numpy array representation of the image
Returns
-------
`convolution_output: np.array`
Output of the convolution layer
'''
image_height,image_width,*_ = image.shape
# Create an array of zeros with the size of the convolution output that will be modified.
convolution_output = np.zeros((image_height-self.kernel_size+1, image_width-self.kernel_size+1, self.kernel_num))
# Run convolution on each segment of the image
# Convolution = Sum of Segments x Kernels to apply bias
for segment, h, w in self.segmentGenerator(image):
convolution_output[h,w] = np.sum(segment*self.kernels)
return convolution_output
def back_prop(self, dE_dY, alpha):
'''
Calculate the gradient of the loss function
Parameters
----------
`dE_dY`
Derivative of the error in respect to the output
`alpha`
The learning rate of the model
Returns
-------
`dE_dK: np.array`
Derivative of the error in respect to the kernels
'''
dE_dk = np.zeros(self.kernel.shape)
for patch, h, w in self.segmentGenerator(self.image):
for f in range(self.kernel_num):
dE_dk[f] += patch * dE_dY[h, w, f]
self.kernel -= alpha*dE_dk
return dE_dk
class PoolingLayer:
'''
Pooling layer for a Convolutional Neural Network
Attributes
----------
`kernel_size: int`
The size of the kernels (filters) associated with the pooling layer
Methods
-------
`segmentGenerator(image: np.array)` -> `segment, height, width`
Generate smaller segments of an image
`forwardProp(image: np.array)` -> `max_pooling_output: np.array`
Carries out the max pooling for each generated portion of the image
`back_prop(dE_dY, alpha)` -> `dE_dK: np.array`
Calculate the gradient of the loss function
'''
def __init__(self, kernel_size: int) -> None:
'''
Initialise the Pooling layer of a Convolutional Neural Network
Parameters
----------
`kernel_size: Integer`
The size of the kernels (filters)
Returns
-------
`None`
Example
-------
`pl = PoolingLayer(2)`
'''
self.kernel_size = kernel_size
def segmentGenerator(self, image):
'''
Generate smaller segments of an image
Parameters
----------
`image: np.array`
numpy array representation of the image
Returns
-------
`Portion: np.array`
The portion of the image
`Height: int`
The starting height value of the portion
`Width: int`
The starting width value of the portion
### Yields each portion of the image with respect to the kernel size
'''
# Height of each segment in reference to kernels
# `//` -> Floor division
height = image.shape[0] // self.kernel_size
width = image.shape[1] // self.kernel_size
self.image = image
for h in range(height):
for w in range(width):
# Create the segment of the image based on the kernel size and position
segment = image[(h*self.kernel_size):(h*self.kernel_size+self.kernel_size), (w*self.kernel_size):(w*self.kernel_size+self.kernel_size)]
# Yield generated object
yield segment, h, w
def forward_prop(self, image):
'''
Carries out the max pooling for each generated portion of the image
Parameters
----------
image: np.array
numpy array representation of the image
Returns
-------
max_pooling_output: np.array
Output of the max pooling layer
'''
image_h, image_w, num_kernels = image.shape
# Max val in each segment
max_pooling_output = np.zeros((image_h//self.kernel_size, image_w//self.kernel_size, num_kernels))
for segment, h, w in self.segmentGenerator(image):
# np.amax -> Array maximum value of each segment
max_pooling_output[h,w] = np.amax(segment, axis=(0,1))
return max_pooling_output
def back_prop(self, dE_dY):
'''
Calculate the gradient of the loss function
Parameters
----------
`dE_dY`
Derivative of the error in respect to the output
Returns
-------
`dE_dK: np.array`
Derivative of the error in respect to the kernels
'''
# Initialise the array for holding the error
dE_dk = np.zeros(self.image.shape)
for patch,h,w in self.patches_generator(self.image):
image_h, image_w, num_kernels = patch.shape
max_val = np.amax(patch, axis=(0,1))
for height_index in range(image_h):
for width_index in range(image_w):
for kernel_index in range(num_kernels):
if patch[height_index,width_index,kernel_index] == max_val[kernel_index]:
dE_dk[h*self.kernel_size+height_index, w*self.kernel_size+width_index, kernel_index] = dE_dY[h,w,kernel_index]
return dE_dk
class FullyConnectedLayer:
'''
Fully connected layer for a Convolutional Neural Network
Attributes
----------
`input_units: int`
The number of input units of the fully connected layer
`output_units: int`
The number of output units of the fully connected layer
Methods
-------
`forward_prop(image: np.array)` -> `softmax_output: np.array`
Carries out the softmax for each generated portion of the image
`back_prop(dE_dY, alpha)` -> `dE_dX: np.array`
Calculate the gradient of the loss function
'''
def __init__(self, input_units, output_units):
'''
Initialise the Fully connected layer of a Convolutional Neural Network
Parameters
----------
`input_units: int`
The number of input units of the fully connected layer
`output_units: int`
The number of output units of the fully connected layer
Returns
-------
`None`
Example
-------
`fcl = FullyConnectedLayer(2, 3)`
'''
self.input_units = input_units
self.output_units = output_units
self.weight = np.random.randn(input_units, output_units)/input_units
self.bias = np.zeros(output_units)
def forward_prop(self, image):
'''
Carries out the sigmoid on the image
Parameters
----------
`image: np.array`
numpy array representation of the image
Returns
-------
sigmoid_output: float
Output of the sigmoid function
'''
self.original_shape = image.shape
image_flattened = image.flatten()
self.flattened_input = image_flattened
first_output = np.dot(image_flattened, self.weight) + self.bias
self.output = first_output
sigmoid_output = np.exp(first_output) / np.sum(np.exp(first_output), axis=0)
return sigmoid_output
def back_prop(self, dE_dY, alpha):
'''
Calculate the gradient of the loss function
Parameters
----------
`dE_dY`: np.array
Derivative of the error in respect to the output
`alpha`: float
The learning rate of the model
Returns
-------
`dE_dX: np.array`
Derivative of the error in respect to the kernels
'''
# Loop through each gradient in the derivative of the error in respect to the output
for i, gradient in enumerate(dE_dY):
if gradient == 0:
continue
# Calculate the transformation equation and total sum
transformation_eq = np.exp(self.output)
S_total = np.sum(transformation_eq)
# Calculate dY_dZ (derivative of the output in respect to the input)
dY_dZ = -transformation_eq[i]*transformation_eq / (S_total**2)
dY_dZ[i] = transformation_eq[i]*(S_total - transformation_eq[i]) / (S_total**2)
# Calculate dZ_dw, dZ_db, and dZ_dX
dZ_dw = self.flattened_input
dZ_db = 1
dZ_dX = self.weight
# Calculate dE_dZ
dE_dZ = gradient * dY_dZ
# Calculate dE_dw, dE_db, and dE_dX
dE_dw = dZ_dw[np.newaxis].T @ dE_dZ[np.newaxis]
dE_db = dE_dZ * dZ_db
dE_dX = dZ_dX @ dE_dZ
# Update weight and bias using gradient descent
self.weight -= alpha*dE_dw
self.bias -= alpha*dE_db
# Reshape dE_dX to its original shape
return dE_dX.reshape(self.original_shape)
class CNN:
'''
Convolutional Neural Network
Attributes
----------
`layers: list`
A list of layers in the network, in the order they were applied
Methods
-------
`add_layer(layer)`
Add a layer to the neural network
`train(image, label)`
Train the neural network on a single image-label pair
`predict(image)`
Predict the label of an image
'''
def __init__(self, layers:list | None=None):
'''
Initialise the Convolutional Neural Network
Parameters
----------
`layers`: list (optional)
A list of layers in the network, in the order they were applied
Returns
-------
`None`
Example
-------
`cnn = CNN([layers])`
'''
self.layers = layers if layers else []
def add_layer(self, layer):
'''
Add a layer to the neural network
Parameters
----------
`layer`
The layer to be added to the neural network
Returns
-------
`None`
'''
self.layers.append(layer)
def train(self, inputs, expected_output, alpha=0.05):
'''
Train the neural network on a single image-label pair
Parameters
----------
`inputs`: np.array
The input images for the network
`expected_output`: np.array
The expected output of the network
`alpha`: float
The learning rate for the backpropagation. Defaults to 0.05.
Returns
-------
`loss`: float
The loss (cross-entropy) of the network after training
`accuracy`: int
The accuracy of the network after training
'''
# Forward step
for input, exp_output in zip(inputs, expected_output):
output = self.predict(image)
loss = -np.log(output[exp_output])
gradient = np.zeros(10)
#
gradient[output] = -1/output[output]
gradient_back = CNN_backprop(gradient, self.layers, alpha)
# Initial gradient
# Backprop step
def predict(self, image):
'''
Predict the label of an image
Parameters
----------
`image`: np.array
The input image to the network
Returns
-------
`label`: int
The predicted label of the image
'''
# Forward step
output, *_ = CNN_forward(image, 0, self.layers)
# Return the label with the highest probability
return np.argmax(output)
def CNN_forward(image, label, layers):
'''
Forward propagation of a convolutional neural network.
[Runs through the network]
Parameters
----------
`image`: np.array
The input image to the network
`label`
The label of the image
`layers`: list
A list of layers in the network, in the order they were applied
Returns
-------
`output`: np.array
The output of the network after forward propagation
`loss`: float
The loss (cross-entropy) of the network after forward propagation
`accuracy`: int
The accuracy of the network after forward propagation
'''
# Normalize the input image
output = image/255.
# Forward propagate through each layer
for layer in layers:
output = layer.forward_prop(output)
# Compute loss (cross-entropy) and accuracy
loss = -np.log(output[label])
accuracy = 1 if np.argmax(output) == label else 0
return output, loss, accuracy
def CNN_backprop(gradient, layers, alpha=0.05):
"""
Backpropagates the given gradient through the layers of a convolutional neural network.
Parameters
----------
`gradient`: ndarray
The gradient to backpropagate.
`layers`: list
A list of layers in the network, in the order they were applied.
`alpha`: float, optional
The learning rate for the backpropagation. Defaults to 0.05.
Returns
-------
`ndarray`: The gradient after backpropagation through all layers.
"""
# Initialize the gradient to be backpropagated
grad_back = gradient
# Backpropagate through each layer in reverse order
for layer in layers[::-1]:
if type(layer) in [ConvolutionLayer, FullyConnectedLayer]:
grad_back = layer.back_prop(grad_back, alpha)
elif type(layer) == PoolingLayer:
grad_back = layer.back_prop(grad_back)
return grad_back
def CNN_training(image, label, layers, alpha=0.05):
'''
Train a convolutional neural network by taking checking the
output against the loss and accuracy of the model.
Parameters
----------
`image`: np.array
The input image to the network
`label`: int
The true label of the image
`layers`: list
A list of layers in the network, in the order they were applied
`alpha`: float
The learning rate for the backpropagation. Defaults to 0.05.
Returns
-------
`loss`: float
The loss (cross-entropy) of the network after training
`accuracy`: int
The accuracy of the network after training
'''
# Forward step
output, loss, accuracy = CNN_forward(image, label, layers)
# Initial gradient
gradient = np.zeros(10)
gradient[label] = -1/output[label]
# Backprop step
gradient_back = CNN_backprop(gradient, layers, alpha)
return loss, accuracy
def save_params(layers:list):
for layer in layers:
with open(f'{layer.__class__.__name__}_params.pickle', 'wb') as f:
dump(layer, f)
def load_params(layers:list):
params = list()
for layer in layers:
with open(f'{layer.__name__}_params.pickle', 'rb') as f:
layer = load(f)
params.append(layer)
return params
if __name__ == "__main__":
cl = ConvolutionLayer(5, 3)
filename = "image.jpg"
image = Image.open(filename).convert("L")
image.save(f"{filename}_greyscale.jpg")
image = np.asarray(image)
img = cl.forwardProp(image)
pl = PoolingLayer(4)
max_pooling_output = pl.forward_prop(img)
print(max_pooling_output.shape)
fcl_input_size = max_pooling_output.shape[0] * max_pooling_output.shape[1] * max_pooling_output.shape[2]
print(fcl_input_size)
fcl = FullyConnectedLayer(fcl_input_size, 10)
output = fcl.forward_prop(max_pooling_output)
print(output)
cnn = CNN([cl, pl, fcl])
save_params([cl, pl, fcl])
[cl, pl, fcl] = load_params([ConvolutionLayer, PoolingLayer, FullyConnectedLayer])
for i in range(len(img[0][0])):
plt.imshow(img[:,:,i], cmap='gray')
plt.savefig(f"{filename}_output_{i}.jpg", dpi=img.shape[0])
# plt.show()