import numpy as np
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
import matplotlib.pyplot as plt
from autils import *
%matplotlib inline
import logging
logging.getLogger("tensorflow").setLevel(logging.ERROR)
tf.autograph.set_verbosity(0)
You will start by loading the dataset for this task.
The load_data() function shown below loads the data into variables X and y
The data set contains 1000 training examples of handwritten digits 1 , here limited to zero and one.
Each training example is a 20-pixel x 20-pixel grayscale image of the digit.
Each pixel is represented by a floating-point number indicating the grayscale intensity at that location.
The 20 by 20 grid of pixels is “unrolled” into a 400-dimensional vector.
Each training example becomes a single row in our data matrix X.
This gives us a 1000 x 400 matrix X where every row is a training example of a handwritten digit image.
𝑋=−−−(𝑥(1))−−−−−−(𝑥(2))−−−⋮−−−(𝑥(𝑚))−−−
The second part of the training set is a 1000 x 1 dimensional vector y that contains labels for the training set
y = 0 if the image is of the digit 0, y = 1 if the image is of the digit 1.
# load dataset
X, y = load_data()
print ('The first element of X is: ', X[0])
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=(8,8))
fig.tight_layout(pad=0.1)
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()
![]()
# UNQ_C1
# GRADED CELL: Sequential model
model = Sequential(
[
tf.keras.Input(shape=(400,)), #specify input size
### START CODE HERE ###
Dense(25,activation = "sigmoid",name = 'layer1'),
Dense(15,activation = "sigmoid",name = 'layer2'),
Dense(1,activation = "sigmoid",name = 'layer3')
### END CODE HERE ###
], name = "my_model"
)
model.summary()
Model: "my_model"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
layer1 (Dense) (None, 25) 10025
layer2 (Dense) (None, 15) 390
layer3 (Dense) (None, 1) 16
=================================================================
Total params: 10,431
Trainable params: 10,431
Non-trainable params: 0
_________________________________________________________________
L1_num_params = 400 * 25 + 25 # W1 parameters + b1 parameters
L2_num_params = 25 * 15 + 15 # W2 parameters + b2 parameters
L3_num_params = 15 * 1 + 1 # W3 parameters + b3 parameters
print("L1 params = ", L1_num_params, ", L2 params = ", L2_num_params, ", L3 params = ", L3_num_params )
[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}")
W1 shape = (400, 25), b1 shape = (25,)
W2 shape = (25, 15), b2 shape = (15,)
W3 shape = (15, 1), b3 shape = (1,)
The following code will define a loss function and run gradient descent to fit the weights of the model to the training data. This will be explained in more detail in the following week
model.compile(
loss=tf.keras.losses.BinaryCrossentropy(),
optimizer=tf.keras.optimizers.Adam(0.001),
)
model.fit(
X,y,
epochs=20
)
prediction = model.predict(X[0].reshape(1,400)) # a zero
print(f" predicting a zero: {prediction}")
prediction = model.predict(X[500].reshape(1,400)) # a one
print(f" predicting a one: {prediction}")
''' predicting a zero: [[0.01557285]]
predicting a one: [[0.95196396]]'''
if prediction >= 0.5:
yhat = 1
else:
yhat = 0
print(f"prediction after threshold: {yhat}")
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=(8,8))
fig.tight_layout(pad=0.1,rect=[0, 0.03, 1, 0.92]) #[left, bottom, right, top]
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))
if prediction >= 0.5:
yhat = 1
else:
yhat = 0
# Display the label above the image
ax.set_title(f"{y[random_index,0]},{yhat}")
ax.set_axis_off()
fig.suptitle("Label, yhat", fontsize=16)
plt.show()
# UNQ_C2
# GRADED FUNCTION: my_dense
def my_dense(a_in, W, b, g):
"""
Computes dense layer
Args:
a_in (ndarray (n, )) : Data, 1 example
W (ndarray (n,j)) : Weight matrix, n features per unit, j units
b (ndarray (j, )) : bias vector, j units
g activation function (e.g. sigmoid, relu..)
Returns
a_out (ndarray (j,)) : j units
"""
units = W.shape[1]
a_out = np.zeros(units)
### START CODE HERE ###
for j in range(units):
z = np.dot(W[:,j],a_in)+b[j]
a_out[j] = g(z)
### END CODE HERE ###
return(a_out)
# Quick Check
x_tst = 0.1*np.arange(1,3,1).reshape(2,) # (1 examples, 2 features)
W_tst = 0.1*np.arange(1,7,1).reshape(2,3) # (2 input features, 3 output features)
b_tst = 0.1*np.arange(1,4,1).reshape(3,) # (3 features)
A_tst = my_dense(x_tst, W_tst, b_tst, sigmoid)
print(A_tst)
def my_sequential(x, W1, b1, W2, b2, W3, b3):
a1 = my_dense(x, W1, b1, sigmoid)
a2 = my_dense(a1, W2, b2, sigmoid)
a3 = my_dense(a2, W3, b3, sigmoid)
return(a3)
# make predictions
prediction = my_sequential(X[0], W1_tmp, b1_tmp, W2_tmp, b2_tmp, W3_tmp, b3_tmp )
if prediction >= 0.5:
yhat = 1
else:
yhat = 0
print( "yhat = ", yhat, " label= ", y[0,0])
prediction = my_sequential(X[500], W1_tmp, b1_tmp, W2_tmp, b2_tmp, W3_tmp, b3_tmp )
if prediction >= 0.5:
yhat = 1
else:
yhat = 0
print( "yhat = ", yhat, " label= ", y[500,0])
yhat = 0 label= 0
yhat = 1 label= 1
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=(8,8))
fig.tight_layout(pad=0.1,rect=[0, 0.03, 1, 0.92]) #[left, bottom, right, top]
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 implemented in Numpy
my_prediction = my_sequential(X[random_index], W1_tmp, b1_tmp, W2_tmp, b2_tmp, W3_tmp, b3_tmp )
my_yhat = int(my_prediction >= 0.5)
# Predict using the Neural Network implemented in Tensorflow
tf_prediction = model.predict(X[random_index].reshape(1,400))
tf_yhat = int(tf_prediction >= 0.5)
# Display the label above the image
ax.set_title(f"{y[random_index,0]},{tf_yhat},{my_yhat}")
ax.set_axis_off()
fig.suptitle("Label, yhat Tensorflow, yhat Numpy", fontsize=16)
plt.show()
import numpy as np
a = np.array([[2,3],
[4,5],
[6,7]])
for i in a.flat:
print(i)
这将打印数字 2 3 4 5 6 7。
作为数组的交互器，您可以使用它来遍历 3x2 轴数组中的所有轴，
enumerate() 函数用于将一个可遍历的数据对象(如列表、元组或字符串)组合为一个索引序列，同时列出数据和数据下标，一般用在 for 循环当中。
Python 2.3. 以上版本可用，2.6 添加 start 参数。
语法
以下是 enumerate() 方法的语法:
enumerate(sequence, [start=0])
for 循环使用 enumerate
>>> seq = ['one', 'two', 'three']
>>> for i, element in enumerate(seq):
... print i, element
...
0 one
1 two
2 three
x = X[0].reshape(-1,1) # column vector (400,1)
z1 = np.matmul(x.T,W1) + b1 # (1,400)(400,25) = (1,25)
a1 = sigmoid(z1)
print(a1.shape)
# UNQ_C3
# GRADED FUNCTION: my_dense_v
def my_dense_v(A_in, W, b, g):
"""
Computes dense layer
Args:
A_in (ndarray (m,n)) : Data, m examples, n features each
W (ndarray (n,j)) : Weight matrix, n features per unit, j units
b (ndarray (1,j)) : bias vector, j units
g activation function (e.g. sigmoid, relu..)
Returns
A_out (tf.Tensor or ndarray (m,j)) : m examples, j units
"""
### START CODE HERE ###
Z = np.matmul(A_in,W)+b
A_out = g(Z)
### END CODE HERE ###
return(A_out)
X_tst = 0.1*np.arange(1,9,1).reshape(4,2) # (4 examples, 2 features)
W_tst = 0.1*np.arange(1,7,1).reshape(2,3) # (2 input features, 3 output features)
b_tst = 0.1*np.arange(1,4,1).reshape(1,3) # (1, 3 features)
A_tst = my_dense_v(X_tst, W_tst, b_tst, sigmoid)
print(A_tst)
fig = plt.figure(figsize=(1, 1))
errors = np.where(y != Yhat)
random_index = errors[0][0]
X_random_reshaped = X[random_index].reshape((20, 20)).T
plt.imshow(X_random_reshaped, cmap='gray')
plt.title(f"{y[random_index,0]}, {Yhat[random_index, 0]}")
plt.axis('off')
plt.show()
![]()
broadcast
a = np.array([1,2,3]).reshape(-1,1) #(3,1)
b = 5
print(f"(a + b).shape: {(a + b).shape}, \na + b = \n{a + b}")
'''(a + b).shape: (3, 1),
a + b =
[[6]
[7]
[8]]'''
a = np.array([1,2,3]).reshape(-1,1) #(3,1)
b = 5
print(f"(a * b).shape: {(a * b).shape}, \na * b = \n{a * b}")
'''(a * b).shape: (3, 1),
a * b =
[[ 5]
[10]
[15]]'''
a = np.array([1,2,3,4]).reshape(-1,1)
b = np.array([1,2,3]).reshape(1,-1)
print(a)
print(b)
print(f"(a + b).shape: {(a + b).shape}, \na + b = \n{a + b}")
''' [[1]
[2]
[3]
[4]]
[[1 2 3]]
(a + b).shape: (4, 3),
a + b =
[[2 3 4]
[3 4 5]
[4 5 6]
[5 6 7]]'''
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