python实现多层感知机
什么是多层感知机？
多层感知机（MLP，Multilayer Perceptron）也叫人工神经网络（ANN，Artificial Neural Network），除了输入输出层，它中间可以有多个隐层，最简单的MLP只含一个隐层，即三层的结构，如下图：
上图可以看到，多层感知机层与层之间是全连接的。多层感知机最底层是输入层，中间是隐藏层，最后是输出层。
参考：https://blog.csdn.net/fg13821267836/article/details/93405572
多层感知机和感知机的区别？
我们来看下感知机是什么样的：
从上述内容更可以看出，感知机是一个线性的二分类器，但不能对非线性的数据并不能进行有效的分类。因此便有了对网络层次的加深，理论上，多层感知机可以模拟任何复杂的函数。
多层感知机的前向传播过程？
这里以输入层、一个隐含层，输出层为例：
结合之前定义的字母标记，对于第二层的三个神经元的输出则有：
将上述的式子转换为矩阵表达式：
将第二层的前向传播计算过程推广到网络中的任意一层，则:
多层感知机的反向传播过程？
可参考：https://blog.csdn.net/xholes/article/details/78461164
下面是实现代码：代码来源：https://github.com/eriklindernoren/ML-From-Scratch
from __future__ import print_function, division
import numpy as np
import math
from sklearn import datasets
from mlfromscratch.utils import train_test_split, to_categorical, normalize, accuracy_score, Plot
from mlfromscratch.deep_learning.activation_functions import Sigmoid, Softmax
from mlfromscratch.deep_learning.loss_functions import CrossEntropy
class MultilayerPerceptron():
"""Multilayer Perceptron classifier. A fully-connected neural network with one hidden layer.
Unrolled to display the whole forward and backward pass.
Parameters:
-----------
n_hidden: int:
The number of processing nodes (neurons) in the hidden layer.
n_iterations: float
The number of training iterations the algorithm will tune the weights for.
learning_rate: float
The step length that will be used when updating the weights.
"""
def __init__(self, n_hidden, n_iterations=3000, learning_rate=0.01):
self.n_hidden = n_hidden
self.n_iterations = n_iterations
self.learning_rate = learning_rate
self.hidden_activation = Sigmoid()
self.output_activation = Softmax()
self.loss = CrossEntropy()
def _initialize_weights(self, X, y):
n_samples, n_features = X.shape
_, n_outputs = y.shape
# Hidden layer
limit = 1 / math.sqrt(n_features)
self.W = np.random.uniform(-limit, limit, (n_features, self.n_hidden))
self.w0 = np.zeros((1, self.n_hidden))
# Output layer
limit = 1 / math.sqrt(self.n_hidden)
self.V = np.random.uniform(-limit, limit, (self.n_hidden, n_outputs))
self.v0 = np.zeros((1, n_outputs))
def fit(self, X, y):
self._initialize_weights(X, y)
for i in range(self.n_iterations):
# ..............
# Forward Pass
# ..............
# HIDDEN LAYER
hidden_input = X.dot(self.W) + self.w0
hidden_output = self.hidden_activation(hidden_input)
# OUTPUT LAYER
output_layer_input = hidden_output.dot(self.V) + self.v0
y_pred = self.output_activation(output_layer_input)
# ...............
# Backward Pass
# ...............
# OUTPUT LAYER
# Grad. w.r.t input of output layer
grad_wrt_out_l_input = self.loss.gradient(y, y_pred) * self.output_activation.gradient(output_layer_input)
grad_v = hidden_output.T.dot(grad_wrt_out_l_input)
grad_v0 = np.sum(grad_wrt_out_l_input, axis=0, keepdims=True)
# HIDDEN LAYER
# Grad. w.r.t input of hidden layer
grad_wrt_hidden_l_input = grad_wrt_out_l_input.dot(self.V.T) * self.hidden_activation.gradient(hidden_input)
grad_w = X.T.dot(grad_wrt_hidden_l_input)
grad_w0 = np.sum(grad_wrt_hidden_l_input, axis=0, keepdims=True)
# Update weights (by gradient descent)
# Move against the gradient to minimize loss
self.V -= self.learning_rate * grad_v
self.v0 -= self.learning_rate * grad_v0
self.W -= self.learning_rate * grad_w
self.w0 -= self.learning_rate * grad_w0
# Use the trained model to predict labels of X
def predict(self, X):
# Forward pass:
hidden_input = X.dot(self.W) + self.w0
hidden_output = self.hidden_activation(hidden_input)
output_layer_input = hidden_output.dot(self.V) + self.v0
y_pred = self.output_activation(output_layer_input)
return y_pred
def main():
data = datasets.load_digits()
X = normalize(data.data)
y = data.target
# Convert the nominal y values to binary
y = to_categorical(y)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, seed=1)
# MLP
clf = MultilayerPerceptron(n_hidden=16,
n_iterations=1000,
learning_rate=0.01)
clf.fit(X_train, y_train)
y_pred = np.argmax(clf.predict(X_test), axis=1)
y_test = np.argmax(y_test, axis=1)
accuracy = accuracy_score(y_test, y_pred)
print ("Accuracy:", accuracy)
# Reduce dimension to two using PCA and plot the results
Plot().plot_in_2d(X_test, y_pred, title="Multilayer Perceptron", accuracy=accuracy, legend_labels=np.unique(y))
if __name__ == "__main__":
main()运行结果：
Accuracy: 0.967966573816156
另外的一种实现是使用卷积神经网络中的全连接层实现：
from __future__ import print_function
from sklearn import datasets
import matplotlib.pyplot as plt
import numpy as np
import sys
sys.path.append("/content/drive/My Drive/learn/ML-From-Scratch/")
# Import helper functions
from mlfromscratch.deep_learning import NeuralNetwork
from mlfromscratch.utils import train_test_split, to_categorical, normalize, Plot
from mlfromscratch.utils import get_random_subsets, shuffle_data, accuracy_score
from mlfromscratch.deep_learning.optimizers import StochasticGradientDescent, Adam, RMSprop, Adagrad, Adadelta
from mlfromscratch.deep_learning.loss_functions import CrossEntropy
from mlfromscratch.utils.misc import bar_widgets
from mlfromscratch.deep_learning.layers import Dense, Dropout, Activation
def main():
optimizer = Adam()
#-----
# MLP
#-----
data = datasets.load_digits()
X = data.data
y = data.target
# Convert to one-hot encoding
y = to_categorical(y.astype("int"))
n_samples, n_features = X.shape
n_hidden = 512
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4, seed=1)
clf = NeuralNetwork(optimizer=optimizer,
loss=CrossEntropy,
validation_data=(X_test, y_test))
clf.add(Dense(n_hidden, input_shape=(n_features,)))
clf.add(Activation(‘leaky_relu‘))
clf.add(Dense(n_hidden))
clf.add(Activation(‘leaky_relu‘))
clf.add(Dropout(0.25))
clf.add(Dense(n_hidden))
clf.add(Activation(‘leaky_relu‘))
clf.add(Dropout(0.25))
clf.add(Dense(n_hidden))
clf.add(Activation(‘leaky_relu‘))
clf.add(Dropout(0.25))
clf.add(Dense(10))
clf.add(Activation(‘softmax‘))
print ()
clf.summary(name="MLP")
train_err, val_err = clf.fit(X_train, y_train, n_epochs=50, batch_size=256)
# Training and validation error plot
n = len(train_err)
training, = plt.plot(range(n), train_err, label="Training Error")
validation, = plt.plot(range(n), val_err, label="Validation Error")
plt.legend(handles=[training, validation])
plt.title("Error Plot")
plt.ylabel(‘Error‘)
plt.xlabel(‘Iterations‘)
plt.show()
_, accuracy = clf.test_on_batch(X_test, y_test)
print ("Accuracy:", accuracy)
# Reduce dimension to 2D using PCA and plot the results
y_pred = np.argmax(clf.predict(X_test), axis=1)
Plot().plot_in_2d(X_test, y_pred, title="Multilayer Perceptron", accuracy=accuracy, legend_labels=range(10))
if __name__ == "__main__":
main()运行结果：
+-----+ | MLP | +-----+ Input Shape: (64,) +------------------------+------------+--------------+ | Layer Type | Parameters | Output Shape | +------------------------+------------+--------------+ | Dense | 33280 | (512,) | | Activation (LeakyReLU) | 0 | (512,) | | Dense | 262656 | (512,) | | Activation (LeakyReLU) | 0 | (512,) | | Dropout | 0 | (512,) | | Dense | 262656 | (512,) | | Activation (LeakyReLU) | 0 | (512,) | | Dropout | 0 | (512,) | | Dense | 262656 | (512,) | | Activation (LeakyReLU) | 0 | (512,) | | Dropout | 0 | (512,) | | Dense | 5130 | (10,) | | Activation (Softmax) | 0 | (10,) | +------------------------+------------+--------------+ Total Parameters: 826378 Training: 100% [------------------------------------------------] Time: 0:00:29
Accuracy: 0.9763231197771588
