吳恩達深度學習：1.3樣例用一個隱含層神經網路對資料進行分類
coding: utf-8
# Planar data classification with one hidden layer
用一個隱含層神經網路對資料進行分類
Welcome to your week 3 programming assignment. It’s time to build your first neural network,
which will have a hidden layer. You will see a big difference between this model and the one
you implemented using logistic regression.
**You will learn how to:
- (1)Implement a 2-class classification neural network with a single hidden layer
- (2)Use units with a non-linear activation function, such as tanh
- (3)Compute the cross entropy loss 計算交叉熵損失
- (4)Implement forward and backward propagation
## 1 - Packages
1、準備對應的包
Let’s first import all the packages that you will need during this assignment.
- numpy is the fundamental package for scientific computing with Python.
- sklearn provides simple and efficient tools for data mining and data analysis.
- matplotlib is a library for plotting graphs in Python.
- testCases provides some test examples to assess the correctness of your functions
- planar_utils provide various useful functions used in this assignment
Package imports
import numpy as np
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets
np.random.seed(1) # set a seed so that the results are consistent
## 2 - Dataset ##檢視資料
2.1準備資料集
First, let’s get the dataset you will work on. The following code will load a “flower” 2-class
dataset into variables X and Y.
X, Y = load_planar_dataset()
Visualize the dataset using matplotlib. The data looks like a “flower” with some red (label y=0)
and some blue (y=1) points. Your goal is to build a model to fit this data.
2.2顯示資料
Visualize the data:
plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral)
plt.show()
You have:
- a numpy-array (matrix) X that contains your features (x1, x2)
- a numpy-array (vector) Y that contains your labels (red:0, blue:1).
Lets first get a better sense of what our data is like.
How many training examples do you have? In addition, what is the shape of the variables X and Y?
How do you get the shape of a numpy array?
2.3輸出資料的維度
shape_X = X.shape#X.shape是2*400
shape_Y = Y.shape#Y.shape是1*400
m = shape_X[1] # training set size
print(‘The shape of X is: ’ + str(shape_X))#(2,400)
print(‘The shape of Y is: ’ + str(shape_Y))#(1,400)
print(‘I have m = %d training examples!’ % (m))#m=400
## 3 - Simple Logistic Regression
用簡單的分類器進行分類
Before building a full neural network, lets first see how logistic regression performs on this problem.
You can use sklearn’s built-in functions to do that. Run the code below to train a logistic regression
classifier on the dataset.
Train the logistic regression classifier
clf = sklearn.linear_model.LogisticRegressionCV()
clf.fit(X.T, Y.T)
You can now plot the decision boundary of these models. Run the code below.
Plot the decision boundary for logistic regression
plot_decision_boundary(lambda x: clf.predict(x), X, Y)
plt.title(“Logistic Regression”)
Print accuracy
LR_predictions = clf.predict(X.T)#所有預測的結果400個行向量
print(‘Accuracy of logistic regression: %d ’ % float(
(np.dot(Y, LR_predictions) + np.dot(1 - Y, 1 - LR_predictions)) / float(Y.size) * 100) +
‘% ’ + “(percentage of correctly labelled datapoints)”)
np.dot(Y, LR_predictions)是LR_predictions是預測為1的正確的數量，
np.dot(1 - Y, 1 - LR_predictions)是預測為0正確的數量
Interpretation: The dataset is not linearly separable, so logistic regression
doesn’t perform well.Hopefully a neural network will do better. Let’s try this now!
## 4 - Neural Network model
4、用神經網路模型來處理資料
Logistic regression did not work well on the “flower dataset”. You are going to
train a Neural Network with a single hidden layer.
Reminder: The general methodology to build a Neural Network is to:
(1.) Define the neural network structure ( # of input units, # of hidden units, etc).
(2.) Initialize the model’s parameters
(3.)Loop:
- Implement forward propagation
- Compute loss
- Implement backward propagation to get the gradients
- Update parameters (gradient descent)
You often build helper functions to compute steps 1-3 and then merge them into one
function we call nn_model(). Once you’ve built nn_model() and learnt the right
parameters, you can make predictions on new data.
### 4.1 - Defining the neural network structure
4.1 構建神經網路結構
Exercise: Define three variables:
- n_x: the size of the input layer
- n_h: the size of the hidden layer (set this to 4)
- n_y: the size of the output layer
Use shapes of X and Y to find n_x and n_y. Also, hard code the hidden layer size to be 4.
def layer_sizes(X, Y):
“””
Arguments:
X – input dataset of shape (input size, number of examples)
Y – labels of shape (output size, number of examples)
Returns:
n_x -- the size of the input layer
n_h -- the size of the hidden layer
n_y -- the size of the output layer
"""
n_x = X.shape[0] # size of input layer
n_h = 4
n_y = Y.shape[0] # size of output layer
return (n_x, n_h, n_y)
用一個輸入層5、隱含層4和輸出層2的維數去測試
X_assess, Y_assess = layer_sizes_test_case()#X_assess(5, 3)，Y_assess(2, 3)
(n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)
print(“The size of the input layer is: n_x = ” + str(n_x))#n_x=5
print(“The size of the hidden layer is: n_h = ” + str(n_h))#n_h=4
print(“The size of the output layer is: n_y = ” + str(n_y))#n_y=2
these are not the sizes you will use for your network, they are just used to
assess the function you’ve just coded).
### 4.2 - Initialize the model’s parameters
4.2初始化模型引數
Exercise: Implement the function initialize_parameters().
Instructions:
- Make sure your parameters’ sizes are right. Refer to the neural network figure above if needed.
- You will initialize the weights matrices with random values.
- Use: np.random.randn(a,b) * 0.01 to randomly initialize a matrix of shape (a,b).
- You will initialize the bias vectors as zeros.
- Use: np.zeros((a,b)) to initialize a matrix of shape (a,b) with zeros.
def initialize_parameters(n_x, n_h, n_y):
“””
Argument:
n_x – size of the input layer
n_h – size of the hidden layer
n_y – size of the output layer
Returns:
params -- python dictionary containing your parameters:
W1 -- weight matrix of shape (n_h, n_x)
b1 -- bias vector of shape (n_h, 1)
W2 -- weight matrix of shape (n_y, n_h)
b2 -- bias vector of shape (n_y, 1)
"""
np.random.seed(2) # we set up a seed so that your output matches ours although
# the initialization is random.
W1 = np.random.randn(n_h, n_x) * 0.01#當n_h為4時W1為(4,2)
b1 = np.zeros((n_h, 1))#當n_h為4時b1為(4,1)
W2 = np.random.randn(n_y, n_h) * 0.01#當n_h為4時W2為(1,4)
b2 = np.zeros((n_y, 1))#b2為(1,1)
assert (W1.shape == (n_h, n_x))
assert (b1.shape == (n_h, 1))
assert (W2.shape == (n_y, n_h))
assert (b2.shape == (n_y, 1))
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}
return parameters
n_x, n_h, n_y = initialize_parameters_test_case()
parameters = initialize_parameters(n_x, n_h, n_y)#值為2,4,1
print(“W1 = ” + str(parameters[“W1”]))
W1 = [[-0.00416758 -0.00056267]
# [-0.02136196 0.01640271]
# [-0.01793436 -0.00841747]
[ 0.00502881 -0.01245288]]
print(“b1 = ” + str(parameters[“b1”]))
b1 = [[ 0.]
# [ 0.]
# [ 0.]
# [ 0.]]
print(“W2 = ” + str(parameters[“W2”]))
W2 = [[-0.01057952 -0.00909008 0.00551454 0.02292208]]
print(“b2 = ” + str(parameters[“b2”]))
b2 = [[ 0.]]
4.3 Implement forward_propagation().
4.3 實現前向傳播函式
Instructions:
- Look above at the mathematical representation of your classifier.
- You can use the function sigmoid(). It is built-in (imported) in the notebook.
- You can use the function np.tanh(). It is part of the numpy library.
- The steps you have to implement are:
(1.)Retrieve each parameter from the dictionary “parameters” (which is the output
of initialize_parameters()) by using parameters[".."].
(2.)Implement Forward Propagation. Compute Z[1],A[1],Z[2]and A[2](the vector of
all your predictions on all the examples in the training set).
- Values needed in the backpropagation are stored in “cache“. The cache will
be given as an input to the backpropagation function.
def forward_propagation(X, parameters):
“””
Argument:
X – input data of size (n_x, m)
parameters – python dictionary containing your parameters (output of initialization function)
Returns:
A2 -- The sigmoid output of the second activation
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
"""
# Retrieve each parameter from the dictionary "parameters"
W1 = parameters["W1"]#和之前的W1資料一致
b1 = parameters["b1"]#和之前的b1資料一致
W2 = parameters["W2"]#和之前的W2資料一致
b2 = parameters["b2"]#和之前的b2資料一致
# Implement Forward Propagation to calculate A2 (probabilities)
Z1 = np.dot(W1, X) + b1#Z1是4*3
A1 = np.tanh(Z1)#A1也是4*3
Z2 = np.dot(W2, A1) + b2#Z2是1*3=(0.000922809273968,-0.000566778795347,0.000958531874256)
A2 = sigmoid(Z2)#A2是1*3=(0.500230702302,0.499858305305,0.50023963295)
assert (A2.shape == (1, X.shape[1]))
cache = {"Z1": Z1,
"A1": A1,
"Z2": Z2,
"A2": A2}
return A2, cache
X_assess, parameters = forward_propagation_test_case()
X_assess的值為[1.62434536366,-0.61175641365,-0.528171752263]
#[-1.0729682216,0.865407629325,-2.30153869688]
“”“forward_propagation_test_case初始化的值和initialize_parameters一致
parameters = {
‘W1’: np.array([[-0.00416758, -0.00056267],
[-0.02136196, 0.01640271],
[-0.01793436, -0.00841747],
[ 0.00502881, -0.01245288]]),
‘W2’: np.array([[-0.01057952, -0.00909008, 0.00551454, 0.02292208]]),
‘b1’: np.array([[ 0.],
[ 0.],
[ 0.],
[ 0.]]),
‘b2’: np.array([[ 0.]])}
“””
A2, cache = forward_propagation(X_assess, parameters)
Note: we use the mean here just to make sure that your output matches ours.
print(np.mean(cache[‘Z1’]), np.mean(cache[‘A1’]), np.mean(cache[‘Z2’]),
np.mean(cache[‘A2’]))
Now that you have computed A[2](in the Python variable A2`), which contains a2
for every example, you can compute the cost function as follows:
Exercise: Implement compute_cost() to compute the value of the cost
logprobs = np.multiply(np.log(A2),Y)
cost = - np.sum(logprobs),no need to use a for loop!
(you can use either np.multiply() and then np.sum() or directly np.dot()).
4.4計算損失函式
def compute_cost(A2, Y, parameters):
“””
Computes the cross-entropy cost given in equation (13)
Arguments:
A2 -- The sigmoid output of the second activation, of shape (1, number of examples)
Y -- "true" labels vector of shape (1, number of examples)
parameters -- python dictionary containing your parameters W1, b1, W2 and b2
Returns:
cost -- cross-entropy cost given equation (13)
"""
m = Y.shape[1] # number of example
# Compute the cross-entropy cost
logprobs = Y * np.log(A2) + (1 - Y) * np.log(1 - A2)#logprobs是1*3為[-0.69210974103]
cost = -1 / m * np.sum(logprobs)#cost值為0.692919893776
cost = np.squeeze(cost) # makes sure cost is the dimension we expect.#cost值為0.692919893776
#把1維的元素去掉
assert (isinstance(cost, float))#判斷物件是否是已知型別
return cost
A2, Y_assess, parameters = compute_cost_test_case()
print(“cost = ” + str(compute_cost(A2, Y_assess, parameters)))
cost = 0.692919893776
Using the cache computed during forward propagation, you can now implement
backward propagation.
Implement the function backward_propagation().
4.5實現反向傳播函式
Backpropagation is usually the hardest (most mathematical) part in deep learning.
To help you, here again is the slide from the lecture on backpropagation. You’ll want
to use the six equations on the right of this slide, since you are building a
vectorized implementation.
def backward_propagation(parameters, cache, X, Y):
“””
Implement the backward propagation using the instructions above.
Arguments:
parameters -- python dictionary containing our parameters
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
X -- input data of shape (2, number of examples)
Y -- "true" labels vector of shape (1, number of examples)
Returns:
grads -- python dictionary containing your gradients with respect to different parameters
"""
m = X.shape[1]
#(1)retrieve W1 and W2 from the dictionary "parameters".
W1 = parameters["W1"]
W2 = parameters["W2"]
#(2)Retrieve also A1 and A2 from dictionary "cache".
A1 = cache["A1"]
A2 = cache["A2"]
#(3)Backward propagation: calculate dW1, db1, dW2, db2.書上有公式
dZ2 = A2 - Y
dW2 = 1 / m * np.dot(dZ2, A1.T)
db2 = 1 / m * np.sum(dZ2, axis=1, keepdims=True)
dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))
dW1 = 1 / m * np.dot(dZ1, X.T)
db1 = 1 / m * np.sum(dZ1, axis=1, keepdims=True)
grads = {"dW1": dW1,
"db1": db1,
"dW2": dW2,
"db2": db2}
return grads
parameters, cache, X_assess, Y_assess = backward_propagation_test_case()
grads = backward_propagation(parameters, cache, X_assess, Y_assess)
print(“dW1 = ” + str(grads[“dW1”]))
“””
dW1 = [[ 0.01018708 -0.00708701]
[ 0.00873447 -0.0060768 ]
[-0.00530847 0.00369379]
[-0.02206365 0.01535126]]
“””
print(“db1 = ” + str(grads[“db1”]))
“””
db1 = [[-0.00069728]
[-0.00060606]
[ 0.000364 ]
[ 0.00151207]]
“””
print(“dW2 = ” + str(grads[“dW2”]))
dW2 = [[ 0.00363613 0.03153604 0.01162914 -0.01318316]]
print(“db2 = ” + str(grads[“db2”]))
db2 = [[ 0.06589489]]
Question: Implement the update rule. Use gradient descent. You have to use
(dW1, db1, dW2, db2) in order to update (W1, b1, W2, b2).
Illustration: The gradient descent algorithm with a good learning rate
(converging) and a bad learning rate (diverging). Images courtesy of Adam Harley.
GRADED FUNCTION: 4.6 update_parameters
4.6更新引數
def update_parameters(parameters, grads, learning_rate=1.2):
“””
Updates parameters using the gradient descent update rule given above
Arguments:
parameters – python dictionary containing your parameters
grads – python dictionary containing your gradients
Returns:
parameters -- python dictionary containing your updated parameters
"""
# Retrieve each parameter from the dictionary "parameters"
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Retrieve each gradient from the dictionary "grads"
dW1 = grads["dW1"]
db1 = grads["db1"]
dW2 = grads["dW2"]
db2 = grads["db2"]
# Update rule for each parameter
W1 = W1 - learning_rate * dW1
b1 = b1 - learning_rate * db1
W2 = W2 - learning_rate * dW2
b2 = b2 - learning_rate * db2
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}
return parameters
parameters, grads = update_parameters_test_case()
parameters = update_parameters(parameters, grads)
“””
parameters = {‘W1’: np.array([[-0.00615039, 0.0169021 ],
[-0.02311792, 0.03137121],
[-0.0169217 , -0.01752545],
[ 0.00935436, -0.05018221]]),
‘W2’: np.array([[-0.0104319 , -0.04019007, 0.01607211, 0.04440255]]),
‘b1’: np.array([[ -8.97523455e-07],
[ 8.15562092e-06],
[ 6.04810633e-07],
[ -2.54560700e-06]]),
‘b2’: np.array([[ 9.14954378e-05]])}
“”“
“””
grads = {‘dW1’: np.array([[ 0.00023322, -0.00205423],
[ 0.00082222, -0.00700776],
[-0.00031831, 0.0028636 ],
[-0.00092857, 0.00809933]]),
‘dW2’: np.array([[ -1.75740039e-05, 3.70231337e-03, -1.25683095e-03,
-2.55715317e-03]]),
‘db1’: np.array([[ 1.05570087e-07],
[ -3.81814487e-06],
[ -1.90155145e-07],
[ 5.46467802e-07]]),
‘db2’: np.array([[ -1.08923140e-05]])}
“”“
print(“W1 = ” + str(parameters[“W1”]))
“””
W1 = [[-0.00643025 0.01936718]
[-0.02410458 0.03978052]
[-0.01653973 -0.02096177]
[ 0.01046864 -0.05990141]]
“”“
print(“b1 = ” + str(parameters[“b1”]))
“”“b1 = [[ -1.02420756e-06]
[ 1.27373948e-05]
[ 8.32996807e-07]
[ -3.20136836e-06]]
“”“
print(“W2 = ” + str(parameters[“W2”]))
W2 = [[-0.01041081 -0.04463285 0.01758031 0.04747113]]
print(“b2 = ” + str(parameters[“b2”]))
b2 = [[ 0.00010457]]
5、Build your neural network model in nn_model().
5、構建你自己的神經網路模型
The neural network model has to use the previous functions in the right order.
GRADED FUNCTION: 5.1 nn_model
5.1構建模型並用梯度下降法
def nn_model(X, Y, n_h, num_iterations=10000, print_cost=False):
“””
Arguments:
X – dataset of shape (2, number of examples)
Y – labels of shape (1, number of examples)
n_h – size of the hidden layer
num_iterations – Number of iterations in gradient descent loop
print_cost – if True, print the cost every 1000 iterations
Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""
np.random.seed(3)
n_x = layer_sizes(X, Y)[0]
n_y = layer_sizes(X, Y)[2]
# Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y".
# Outputs = "W1, b1, W2, b2, parameters".
parameters = initialize_parameters(n_x, n_h, n_y)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
"""parameters
'W1': np.array([[-0.00416758, -0.00056267],
[-0.02136196, 0.01640271],
[-0.01793436, -0.00841747],
[0.00502881, -0.01245288]]),
'W2': np.array([[-0.01057952, -0.00909008, 0.00551454, 0.02292208]]),
'b1': np.array([[0.],
[0.],
[0.],
[0.]]),
'b2': np.array([[0.]])
"""
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".
A2, cache = forward_propagation(X, parameters)
#A2是1 * 3 = (0.500230702302, 0.499858305305, 0.50023963295)
# Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".
cost = compute_cost(A2, Y, parameters)
#cost=0.692583903568
# Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".
grads = backward_propagation(parameters, cache, X, Y)
# Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".
parameters = update_parameters(parameters, grads)
# Print the cost every 1000 iterations
if print_cost and i % 1000 == 0:
print("Cost after iteration %i: %f" % (i, cost))
return parameters
5.2 輸出預測後的值
X_assess, Y_assess = nn_model_test_case()
X_assess為2*3:[1.62434536366,-0.61175641365,-0.528171752263]
# [-1.07296862216,0.865407629325,-2.30153869688]
Y_assess為1*3：[1.74481176422,-0.761206900895,0.319039096057]
parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=False)
print(“W1 = ” + str(parameters[“W1”]))
“””
W1 = [[-4.18494482 5.33220319]
[-7.52989354 1.24306197]
[-4.19295428 5.32631786]
[ 7.52983748 -1.24309404]]
“”“
print(“b1 = ” + str(parameters[“b1”]))
“””
b1 = [[ 2.32926815]
[ 3.7945905 ]
[ 2.33002544]
[-3.79468791]]
“”“
print(“W2 = ” + str(parameters[“W2”]))
W2 = [[-6033.83672179 -6008.12981272 -6033.10095329 6008.06636901]]
print(“b2 = ” + str(parameters[“b2”]))
b2 = [[-52.66607704]]
###6、Predictions
6、預測結果
Question: Use your model to predict by building predict().
Use forward propagation to predict results.
As an example, if you would like to set the entries of a matrix X to 0 and 1
based on a threshold you would do: X_new = (X > threshold)
def predict(parameters, X):
“””
Using the learned parameters, predicts a class for each example in X
Arguments:
parameters -- python dictionary containing your parameters
X -- input data of size (n_x, m)
Returns：
predictions -- vector of predictions of our model (red: 0 / blue: 1)
"""
#(1)Computes probabilities using forward propagation, and classifies to 0/1
# using 0.5 as the threshold.
A2, cache = forward_propagation(X, parameters)
predictions = np.round(A2)#四捨五入
#(1)python 2中如果距離兩端一樣遠，則保留到離0遠的一邊。所以
# round(0.5)會近似到1，而round(-0.5)會近似到-1。
#(2)python3中如果距離兩邊一樣遠，會保留到偶數的一邊。比如
# round(0.5)和round(-0.5)都會保留到0，而round(1.5)會保留到2
return predictions
parameters, X_assess = predict_test_case()
“””
X_assess = np.random.randn(2, 3)
parameters =
{‘W1’: np.array([[-0.00615039, 0.0169021 ],
[-0.02311792, 0.03137121],
[-0.0169217 , -0.01752545],
[ 0.00935436, -0.05018221]]),
‘W2’: np.array([[-0.0104319 , -0.04019007, 0.01607211, 0.04440255]]),
‘b1’: np.array([[ -8.97523455e-07],
[ 8.15562092e-06],
[ 6.04810633e-07],
[ -2.54560700e-06]]),
‘b2’: np.array([[ 9.14954378e-05]])}
“”“
predictions = predict(parameters, X_assess)
print(“predictions mean = ” + str(np.mean(predictions)))
“””
上面的內容都是測試你的模型，輸入的資料比較小X為2*3，W1為4*2，W1為1*4
b1為4*1，b2為1*1
“”“
7、輸入實際的資料進行驗證模型
It is time to run the model and see how it performs on a planar dataset. Run the
following code to test your model with a single hidden layer of hidden units.
7.1Build a model with a n_h-dimensionalhidden layer
parameters = nn_model(X, Y, n_h=4, num_iterations=10000, print_cost=True)
7.2Plot the decision boundary
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title(“Decision Boundary for hidden layer size ” + str(4))
7.3Print accuracy
predictions = predict(parameters, X)
print(‘Accuracy: %d’ % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T))
/ float(Y.size) * 100) + ‘%’)
Accuracy is really high compared to Logistic Regression. The model has learnt
the leaf patterns of the flower! Neural networks are able to learn even highly
non-linear decision boundaries, unlike logistic regression.
Now, let’s try out several hidden layer sizes.
### Tuning hidden layer size (optional/ungraded exercise)
8、改變隱含層數去測試
Run the following code. It may take 1-2 minutes. You will observe different behaviors
of the model for various hidden layer sizes.
This may take about 2 minutes to run
plt.figure(figsize=(16, 32))
hidden_layer_sizes = [1, 2, 3, 4, 5, 10, 20]
for i, n_h in enumerate(hidden_layer_sizes):
plt.subplot(5, 2, i + 1)
plt.title(‘Hidden Layer of size %d’ % n_h)
parameters = nn_model(X, Y, n_h, num_iterations=5000)
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
predictions = predict(parameters, X)
accuracy = float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100)
print(“Accuracy for {} hidden units: {} %”.format(n_h, accuracy))
Interpretation:
-(1)The larger models (with more hidden units) are able to fit the training set better,
until eventually the largest models overfit the data.
-(2)The best hidden layer size seems to be around n_h = 5. Indeed, a value around here
seems to fits the data well without also incurring noticable overfitting.
-(3)You will also learn later about regularization, which lets you use very large models
(such as n_h = 50) without much overfitting.
Optional questions:
Note: Remember to submit the assignment but clicking the blue “Submit Assignment”
button at the upper-right.
Some optional/ungraded questions that you can explore if you wish:
- (1)What happens when you change the tanh activation for a sigmoid activation or a ReLU activation?
- (2)Play with the learning_rate. What happens?
- (3)What if we change the dataset? (See part 5 below!)
You’ve learnt to:
- (1)Build a complete neural network with a hidden layer
- (2)Make a good use of a non-linear unit
- (3)Implemented forward propagation and backpropagation, and trained a neural network
- (4)See the impact of varying the hidden layer size, including overfitting.
## 8、Performance on other datasets
8、在別的資料集表現
If you want, you can rerun the whole notebook (minus the dataset part) for each
of the following datasets.
Datasets
noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()
datasets = {“noisy_circles”: noisy_circles,
“noisy_moons”: noisy_moons,
“blobs”: blobs,
“gaussian_quantiles”: gaussian_quantiles}
dataset = “gaussian_quantiles”
X, Y = datasets[dataset]#X是2*200資料,Ya是1*200標籤
X, Y = X.T, Y.reshape(1, Y.shape[0])
make blobs binary
if dataset == “blobs”:
Y = Y % 2
Visualize the data
plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral);
plt.show()