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numclassification.py
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numclassification.py
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import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
digits=load_digits()
import pylab as pl
#Define variables
n_samples=len(digits.images)
x=digits.images.reshape((n_samples,-1))
y=digits.target
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(x, y, test_size = 0.2, random_state = 0)
# Feature Scaling
from sklearn.preprocessing import StandardScaler
sc = StandardScaler()
X_train = sc.fit_transform(X_train)
X_test = sc.transform(X_test)
X_train=X_train.T
X_test=X_test.T
y_train=y_train.reshape(y_train.shape[0],1)
y_test=y_test.reshape(y_test.shape[0],1)
y_train=y_train.T
y_test=y_test.T
Y_train_=np.zeros((10,y_train.shape[1]))
for i in range(y_train.shape[1]):
Y_train_[y_train[0,i],i]=1
Y_test_=np.zeros((10,y_test.shape[1]))
for i in range(y_test.shape[1]):
Y_test_[y_test[0,i],i]=1
# initialize parameters for deep neural networks
def initialize_parameters_deep(layer_dims):
np.random.seed(3)
parameters = {}
L = len(layer_dims)
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l - 1]) * 0.01
parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
assert (parameters['W' + str(l)].shape == (layer_dims[l], layer_dims[l - 1]))
assert (parameters['b' + str(l)].shape == (layer_dims[l], 1))
return parameters
def linear_forward(A, W, b):
Z = np.dot(W, A) + b
assert (Z.shape == (W.shape[0], A.shape[1]))
cache = (A, W, b)
return Z, cache
# use ful activation functions and their derivatives
def sigmoid_(Z):
return 1/(1+np.exp(-Z))
def relu_(Z):
return Z*(Z>0)
def drelu_(Z):
return 1. *(Z>0)
def dsigmoid_(Z):
return sigmoid_(Z)*(1-sigmoid_(Z))
def sigmoid(Z):
return sigmoid_(Z),Z
def relu(Z):
return relu_(Z),Z
def linear_activation_forward(A_prev, W, b, activation):
if activation == "sigmoid":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
assert (A.shape == (W.shape[0], A_prev.shape[1]))
cache = (linear_cache, activation_cache)
return A, cache
# implementation of forward propogation for L layer neural network
def L_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for l in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev,parameters['W'+str(l)],parameters['b'+str(l)],"relu")
caches.append(cache)
AL, cache = linear_activation_forward(A,parameters['W'+str(L)],parameters['b'+str(L)],"sigmoid")
caches.append(cache)
return AL, caches
# cost function
def compute_cost(AL, Y):
m=Y.shape[1]
cost = -(1/m)*np.sum((Y*np.log(AL)+(1-Y)*np.log(1-AL)))
cost=np.squeeze(cost)
assert(cost.shape == ())
return cost
def linear_backward(dZ, cache):
A_prev, W, b = cache
m = A_prev.shape[1]
dW = (1 / m) * np.dot(dZ, A_prev.T)
db = (1 / m) * np.sum(dZ, axis=1, keepdims=True)
dA_prev = np.dot(W.T, dZ)
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
def relu_backward(dA,activation_cache):
return dA* drelu_(activation_cache)
def sigmoid_backward(dA,activation_cache):
return dA* dsigmoid_(activation_cache)
def linear_activation_backward(dA, cache, activation):
linear_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif activation == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
# back propogation for L layers
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches)
m = AL.shape[1]
# Y = Y.reshape(AL.shape)
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
current_cache = caches[L - 1]
grads["dA" + str(L - 1)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL,
current_cache,
"sigmoid")
for l in reversed(range(L - 1)):
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l + 1)], current_cache, "relu")
grads["dA" + str(l)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
#update parameters
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2
for l in range(L):
parameters["W" + str(l+1)] = parameters["W" + str(l+1)]-(learning_rate)*grads["dW"+str(l+1)]
parameters["b" + str(l+1)] = parameters["b" + str(l+1)]-(learning_rate)*grads["db"+str(l+1)]
return parameters
# N layer neural network
layers_dims = [64, 60, 10, 10]
def L_layer_model(X, Y, layers_dims, learning_rate=0.005, num_iterations=3000, print_cost=False):
np.random.seed(1)
costs = []
parameters = initialize_parameters_deep(layers_dims)
for i in range(0, num_iterations):
AL, caches = L_model_forward(X, parameters)
cost = compute_cost(AL, Y)
grads = L_model_backward(AL, Y, caches)
parameters = update_parameters(parameters, grads, learning_rate)
if print_cost and i % 1000 == 0:
print("Cost after iteration %i: %f" % (i, cost))
costs.append(cost)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
return parameters
parameters = L_layer_model(X_train, Y_train_, layers_dims, num_iterations = 50000, print_cost = True)
def predict_L_layer(X,parameters):
AL,caches=L_model_forward(X,parameters)
prediction=np.argmax(AL,axis=0)
return prediction.reshape(1,prediction.shape[0])
predictions_train_L = predict_L_layer(X_train, parameters)
print("Training Accuracy : "+ str(np.sum(predictions_train_L==y_train)/y_train.shape[1] * 100)+" %")
predictions_test_L=predict_L_layer(X_test,parameters)
print("Testing Accuracy : "+ str(np.sum(predictions_test_L==y_test)/y_test.shape[1] * 100)+" %")
import random
for j in range(15):
i=random.randint(0,n_samples)
pl.gray()
pl.matshow(digits.images[i])
pl.show()
img=digits.images[i].reshape((64,1)).T
img = sc.transform(img)
img=img.T
predicted_digit=predict_L_layer(img,parameters)
print('Predicted digit is : '+str(predicted_digit))
print('True digit is: '+ str(y[i]))