neural Networks for handwritten Digit Recognition, Multiclass

 import numpy as np

import tensorflow as tf

from tensorflow.keras.models import Sequential

from tensorflow.keras.layers import Dense

from tensorflow.keras.activations import linear, relu, sigmoid

%matplotlib widget

import matplotlib.pyplot as plt

plt.style.use('./deeplearning.mplstyle')

import logging

logging.getLogger("tensorflow").setLevel(logging.ERROR)

tf.autograph.set_verbosity(0)

from public_tests import * 

from autils import *

from lab_utils_softmax import plt_softmax

np.set_printoptions(precision=2)

plt_act_trio()

def my_softmax(z):  

    """ Softmax converts a vector of values to a probability distribution.

    Args:

      z (ndarray (N,))  : input data, N features

    Returns:

      a (ndarray (N,))  : softmax of z

    """    

    ### START CODE HERE ### 

    

    N = len(z)

    a = np.zeros(N)

    ez_sum = 0

    for k in range(N):

        ez_sum += np.exp(z[k])

    for j in range(N):

        a[j] = np.exp(z[j]) / ez_sum

    

    ### END CODE HERE ### 

    return a

z = np.array([1., 2., 3., 4.])

a = my_softmax(z)

atf = tf.nn.softmax(z)

print(f"my_softmax(z):         {a}")

print(f"tensorflow softmax(z): {atf}")

# BEGIN UNIT TEST  

test_my_softmax(my_softmax)

# END UNIT TEST 

plt.close("all")

plt_softmax(my_softmax)

# load dataset

X, y = load_data()

print ('The first element of X is: ', X[0])

print ('The first element of y is: ', y[0,0])

print ('The last element of y is: ', y[-1,0])

print ('The shape of X is: ' + str(X.shape))

print ('The shape of y is: ' + str(y.shape))

import warnings

warnings.simplefilter(action='ignore', category=FutureWarning)

# You do not need to modify anything in this cell

m, n = X.shape

fig, axes = plt.subplots(8,8, figsize=(5,5))

fig.tight_layout(pad=0.13,rect=[0, 0.03, 1, 0.91]) #[left, bottom, right, top]

#fig.tight_layout(pad=0.5)

widgvis(fig)

for i,ax in enumerate(axes.flat):

    # Select random indices

    random_index = np.random.randint(m)

    

    # Select rows corresponding to the random indices and

    # reshape the image

    X_random_reshaped = X[random_index].reshape((20,20)).T

    

    # Display the image

    ax.imshow(X_random_reshaped, cmap='gray')

    

    # Display the label above the image

    ax.set_title(y[random_index,0])

    ax.set_axis_off()

    fig.suptitle("Label, image", fontsize=14)

tf.random.set_seed(1234) # for consistent results

model = Sequential(

    [               

        ### START CODE HERE ### 

        tf.keras.Input(shape = (400,)),

        Dense(25, activation = 'relu', name = 'L1'),

        Dense(15, activation = 'relu', name = 'L2'),

        Dense(10, activation = 'linear', name = 'L3')

        

        

        

        ### END CODE HERE ### 

    ], name = "my_model" 

)

# BEGIN UNIT TEST     

test_model(model, 10, 400)

# END UNIT TEST   

[layer1, layer2, layer3] = model.layers

#### Examine Weights shapes

W1,b1 = layer1.get_weights()

W2,b2 = layer2.get_weights()

W3,b3 = layer3.get_weights()

print(f"W1 shape = {W1.shape}, b1 shape = {b1.shape}")

print(f"W2 shape = {W2.shape}, b2 shape = {b2.shape}")

print(f"W3 shape = {W3.shape}, b3 shape = {b3.shape}")

model.compile(

    loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),

    optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),

)

history = model.fit(

    X,y,

    epochs=40

)

model.compile(

    loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),

    optimizer=tf.keras.optimizers.Adam(learning_rate=0.001),

)

history = model.fit(

    X,y,

    epochs=40

)

plot_loss_tf(history)

image_of_two = X[1015]

display_digit(image_of_two)

prediction = model.predict(image_of_two.reshape(1,400))  # prediction

print(f" predicting a Two: \n{prediction}")

print(f" Largest Prediction index: {np.argmax(prediction)}")

prediction_p = tf.nn.softmax(prediction)

print(f" predicting a Two. Probability vector: \n{prediction_p}")

print(f"Total of predictions: {np.sum(prediction_p):0.3f}")

import warnings

warnings.simplefilter(action='ignore', category=FutureWarning)

# You do not need to modify anything in this cell

m, n = X.shape

fig, axes = plt.subplots(8,8, figsize=(5,5))

fig.tight_layout(pad=0.13,rect=[0, 0.03, 1, 0.91]) #[left, bottom, right, top]

widgvis(fig)

for i,ax in enumerate(axes.flat):

    # Select random indices

    random_index = np.random.randint(m)

    

    # Select rows corresponding to the random indices and

    # reshape the image

    X_random_reshaped = X[random_index].reshape((20,20)).T

    

    # Display the image

    ax.imshow(X_random_reshaped, cmap='gray')

    

    # Predict using the Neural Network

    prediction = model.predict(X[random_index].reshape(1,400))

    prediction_p = tf.nn.softmax(prediction)

    yhat = np.argmax(prediction_p)

    

    # Display the label above the image

    ax.set_title(f"{y[random_index,0]},{yhat}",fontsize=10)

    ax.set_axis_off()

fig.suptitle("Label, yhat", fontsize=14)

plt.show()

print( f"{display_errors(model,X,y)} errors out of {len(X)} images")