Image_Classification_code.py

## Gradient Descent for Image Classification with a Neural Network mindset
# 
## No loops (for/while) has been used in your code. It has only been used while plotting the learning curves.
# 
## As part of this project, we will 
#     - build the general architecture of a learning algorithm
#     - Initializing parameters
#     - Calculating the cost function and its gradient
#     - Using an optimization algorithm (gradient descent) 
#     - Define a main function -> model to invoke the above functions.

## Importing the required packages. 

import numpy             as     np
import matplotlib.pyplot as     plt
import h5py
import scipy
from   PIL               import Image
from   scipy             import ndimage


# ## 2 - Overview of the Problem set ##
# 
# We will build a simple image-recognition algorithm that can correctly classify pictures as cat or non-cat.
# 

# Loading the data (cat/non-cat)
def load_dataset():
    train_dataset = h5py.File('C:/Users/sarth/Downloads/train_catvnoncat (1).h5', "r")
    train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # train set features
    train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # train set labels

    test_dataset = h5py.File('C:/Users/sarth/Downloads/test_catvnoncat (1).h5', "r")
    test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # test set features
    test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # test set labels

    classes = np.array(test_dataset["list_classes"][:]) # the list of classes
    
    train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))
    test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))
    
    return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes


train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()


# We added "_orig" at the end of image datasets (train and test) because we are going to preprocess them. After preprocessing, we will end up with 
# train_set_x and test_set_x (the labels train_set_y and test_set_y don't need any preprocessing).
# 
# Each line of your train_set_x_orig and test_set_x_orig is an array representing an image. You can visualize an example by running the following code. 

# Example of a picture
index = 25
plt.imshow(train_set_x_orig[index])
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") +  "' picture.")


m_train = train_set_x_orig.shape 
m_test = test_set_x_orig.shape
num_px = train_set_x_orig.shape[1]


print ("Number of training examples: m_train = " + str(m_train[0]))
print ("Number of testing examples: m_test = "   + str(m_test[0]))
print ("Height/Width of each image: num_px = "   + str(num_px))
print ("Each image is of size: ("                + str(num_px)  + ", " + str(num_px) + ", 3)")
print ("train_set_x shape: "                     + str(train_set_x_orig.shape))
print ("train_set_y shape: "                     + str(train_set_y.shape))
print ("test_set_x shape: "                      + str(test_set_x_orig.shape))
print ("test_set_y shape: "                      + str(test_set_y.shape))


# Reshape the training and test examples

train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
test_set_x_flatten  = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T


print ("train_set_x_flatten shape: "    + str(train_set_x_flatten.shape))
print ("train_set_y shape: "            + str(train_set_y.shape))
print ("test_set_x_flatten shape: "     + str(test_set_x_flatten.shape))
print ("test_set_y shape: "             + str(test_set_y.shape))
print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))


# To represent color images, the red, green and blue channels (RGB) must be specified for each pixel, and so the pixel value is actually a vector of 
# three numbers ranging from 0 to 255.
# One common preprocessing step in machine learning is to center and standardize your dataset, meaning that you substract the mean of the whole numpy array 
# from each example, and then divide each example by the standard deviation of the whole numpy array. 
# But for picture datasets, it is simpler and more convenient and works almost as well to just divide every row of the dataset by 255 
# (the maximum value of a pixel channel).
# 
# Let's standardize our dataset.

train_set_x = train_set_x_flatten / 255.
test_set_x  = test_set_x_flatten / 255.

# The main steps for building a Neural Network are:
# 1. Define the model structure (such as number of input features) 
# 2. Initialize the model's parameters
# 3. Loop:
#     - Calculate current loss (forward propagation)
#     - Calculate current gradient (backward propagation)
#     - Update parameters (gradient descent)
# 
# You often build 1-3 separately and integrate them into one function we call `model()`.

# Defining the sigmoid function.

def sigmoid(z):
   
    s = 1 / (1 + np.exp(-z))
    return s

# Let's check results with a basic array.

print ("sigmoid([0, 2]) = " + str(sigmoid(np.array([0,2]))))





# Initialize weights w and bias b with zeros. Declaring the function for the initialization to 0.

def initialize_with_zeros(dim):
    w = np.zeros((dim, 1))
    b = 0

    assert(w.shape == (dim, 1))
    assert(isinstance(b, float) or isinstance(b, int))
    
    return w, b

# Checking the results with a dimension of 2.

dim = 2
w, b = initialize_with_zeros(dim)
print ("w = " + str(w))
print ("b = " + str(b))




# Declaring the propagate function to calculate cost, dw, db. The arguments being passed are:
'''
Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)
'''

def propagate(w, b, X, Y):

    m = X.shape[1]
    
    # FORWARD PROPAGATION (FROM X TO COST)
    A = sigmoid(np.dot(w.T, X) + b)                                                         # compute activation
    cost = (-1/m) * np.sum( Y*np.log(A) + (1-Y)*np.log(1-A) )                               # compute cost
    
    # BACKWARD PROPAGATION (TO FIND GRADIENT)
    dw = 1/m * np.dot(X, (A-Y).T)
    db = 1/m * np.sum(A - Y)

    assert(dw.shape == w.shape)
    assert(db.dtype == float)
    cost = np.squeeze(cost)
    assert(cost.shape == ())
    
    grads = {"dw": dw, "db": db}
    
    return grads, cost

# Let's check results with some basic arrays.

w, b, X, Y = np.array([[1.],[2.]]), 2., np.array([[1.,2.,-1.],[3.,4.,-3.2]]), np.array([[1,0,1]])
grads, cost = propagate(w, b, X, Y)
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))
print ("cost = " + str(cost))




## - Optimization
## - Update the parameters using gradient descent.

def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):
    """
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of shape (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
    num_iterations -- number of iterations of the optimization loop
    learning_rate -- learning rate of the gradient descent update rule
    print_cost -- True to print the loss every 100 steps
    
    Returns:
    params -- dictionary containing the weights w and bias b
    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
    
    """
    
    costs = []
    
    for i in range(num_iterations):
        
        
        # Cost and gradient calculation
        grads, cost = propagate(w, b, X, Y)
        
        # Retrieve derivatives from grads
        dw = grads["dw"]
        db = grads["db"]
        
        # update rule
        w = w - learning_rate*dw
        b = b - learning_rate*db
        
        # Record the costs
        if i % 100 == 0:
            costs.append(cost)
        
        # Print the cost every 100 training iterations
        if print_cost and i % 100 == 0:
            print ("Cost after iteration %i: %f" %(i, cost))
    
    params = {"w": w, "b": b}
    
    grads = {"dw": dw, "db": db}
    
    return params, grads, costs


params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)

print ("w = " + str(params["w"]))
print ("b = " + str(params["b"]))
print ("dw = " + str(grads["dw"]))
print ("db = " + str(grads["db"]))



# predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)

def predict(w, b, X):
    
    '''  
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    
    Returns:
    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
    '''
    
    m = X.shape[1]
    Y_prediction = np.zeros((1,m))
    w = w.reshape(X.shape[0], 1)
    
    # Compute vector "A" predicting the probabilities of a cat being present in the picture
    A = sigmoid( np.dot(w.T,X) + b)
    
    for i in range(A.shape[1]):
        
        # Convert probabilities A[0,i] to actual predictions p[0,i]
        Y_prediction = np.where(A>0.5, 1, 0)
    
    assert(Y_prediction.shape == (1, m))
    
    return Y_prediction

# Let's check with a basic example

w = np.array([[0.1124579],[0.23106775]])
b = -0.3
X = np.array([[1.,-1.1,-3.2],[1.2,2.,0.1]])
print ("predictions = " + str(predict(w, b, X)))




## Merge all functions into a model ##

def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
    
    """
    Arguments:
    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
    print_cost -- Set to true to print the cost every 100 iterations
    
    Returns:
    d -- dictionary containing information about the model.
    """
    
    # initialize parameters with zeros
    w, b = initialize_with_zeros(num_px * num_px * 3)

    # Gradient descent
    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
    
    # Retrieve parameters w and b from dictionary "parameters"
    w = parameters["w"]
    b = parameters["b"]
    
    # Predict test/train set examples
    Y_prediction_test = predict(w, b, X_test)
    Y_prediction_train = predict(w, b, X_train)

    # Print train/test Errors
    print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
    print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

    
    d = {"costs": costs,
         "Y_prediction_test": Y_prediction_test, 
         "Y_prediction_train" : Y_prediction_train, 
         "w" : w, 
         "b" : b,
         "learning_rate" : learning_rate,
         "num_iterations": num_iterations}
    
    return d


# Invoking the function "model" to train your model.

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)



# Training accuracy is close to 100%. 
# Test accuracy is 68%. It is actually not bad for this simple model.
# But, we can see that the model is clearly overfitting the training data. 

# Example of a picture that was wrongly classified.
index = 1
plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))
print ("y = " + str(test_set_y[0,index]) + ", you predicted that it is a \"" + classes[d["Y_prediction_test"][0,index]].decode("utf-8") +  "\" picture.")


# Let's also plot the cost function and the gradients.

# Plot learning curve (with costs)
costs = np.squeeze(d['costs'])
plt.plot(costs)
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(d["learning_rate"]))
plt.show()


# **Interpretation**:
# We can see the cost decreasing. It shows that the parameters are being learned. However, we see that you could train the model even more on the training set. 
# Try to increase the number of iterations in the cell above and rerun the cells. We might see that the training set accuracy goes up, but the test set 
# accuracy goes down. This is called overfitting. 


## Let's experiment with the learning rates.

learning_rates = [0.01, 0.001, 0.0001]
models = {}
for i in learning_rates:
    print ("learning rate is: " + str(i))
    models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
    print ('\n' + "-------------------------------------------------------" + '\n')

for i in learning_rates:
    plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))

plt.ylabel('cost')
plt.xlabel('iterations (hundreds)')

legend = plt.legend(loc='upper center', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()


# **Interpretation**: 
# - Different learning rates give different costs and thus different predictions results.
# - If the learning rate is too large (0.01), the cost may oscillate up and down. 


## Testing with my own image 
my_image = "sarthak.jpg"  


# We preprocess the image to fit your algorithm.
fname = "C:/Users/sarth/Pictures" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
image = image/255.
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
my_predicted_image = predict(d["w"], d["b"], my_image)

plt.imshow(image)
print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") +  
    "\" picture.")