用python编程多层感知机实现手写数字识别

好的，下面是示例代码：

首先需要导入必要的库，包括numpy（用于处理数据）、matplotlib（用于可视化数据）和sklearn库中的手写数字数据集：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report

然后加载手写数字数据集，并对数据进行预处理，将每个像素点的灰度值归一化到0到1之间：

digits = load_digits()
X_data = digits.data.astype(float) / 255
y_data = digits.target.astype(np.int)

接着将数据集划分为训练集和测试集：

X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size=0.3)

定义多层感知机模型，包括输入层、隐藏层和输出层：

class MLP(object):
    def __init__(self, num_input, num_hidden, num_output):
        self.num_input = num_input
        self.num_hidden = num_hidden
        self.num_output = num_output
        self.W1 = np.random.randn(self.num_input, self.num_hidden)
        self.b1 = np.zeros((1, self.num_hidden))
        self.W2 = np.random.randn(self.num_hidden, self.num_output)
        self.b2 = np.zeros((1, self.num_output))
    def sigmoid(self, z):
        return 1 / (1 + np.exp(-z))
    def forward(self, X):
        z1 = np.dot(X, self.W1) + self.b1
        a1 = self.sigmoid(z1)
        z2 = np.dot(a1, self.W2) + self.b2
        a2 = self.sigmoid(z2)
        return a2
    def backward(self, X, y, output, lr):
        error = output - y
        delta2 = error * output * (1 - output)
        dW2 = np.dot(a1.T, delta2)
        db2 = np.sum(delta2, axis=0, keepdims=True)
        delta1 = np.dot(delta2, self.W2.T) * a1 * (1 - a1)
        dW1 = np.dot(X.T, delta1)
        db1 = np.sum(delta1, axis=0)
        self.W2 -= lr * dW2
        self.b2 -= lr * db2
        self.W1 -= lr * dW1
        self.b1 -= lr * db1
    def train(self, X, y, epochs, lr):
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output, lr)

其中，sigmoid函数用于激活神经元，forward函数用于前向传播，backward函数用于反向传播，train函数用于训练模型。

接着实例化模型，定义输入层、隐藏层和输出层的维度，然后训练模型：

num_input = X_train.shape[1]
num_hidden = 100
num_output = len(np.unique(y_train))
mlp = MLP(num_input, num_hidden, num_output)
mlp.train(X_train, y_train, 10000, 0.01)

最后使用测试集对模型进行评估，并输出结果：

y_pred = np.argmax(mlp.forward(X_test), axis=1)
print(classification_report(y_test, y_pred))

完整代码如下：

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_digits
from sklearn.model_selection import train_test_split
from sklearn.metrics import classification_report

class MLP(object):
    def __init__(self, num_input, num_hidden, num_output):
        self.num_input = num_input
        self.num_hidden = num_hidden
        self.num_output = num_output
        self.W1 = np.random.randn(self.num_input, self.num_hidden)
        self.b1 = np.zeros((1, self.num_hidden))
        self.W2 = np.random.randn(self.num_hidden, self.num_output)
        self.b2 = np.zeros((1, self.num_output))
    def sigmoid(self, z):
        return 1 / (1 + np.exp(-z))
    def forward(self, X):
        z1 = np.dot(X, self.W1) + self.b1
        a1 = self.sigmoid(z1)
        z2 = np.dot(a1, self.W2) + self.b2
        a2 = self.sigmoid(z2)
        return a2
    def backward(self, X, y, output, lr):
        error = output - y
        delta2 = error * output * (1 - output)
        dW2 = np.dot(a1.T, delta2)
        db2 = np.sum(delta2, axis=0, keepdims=True)
        delta1 = np.dot(delta2, self.W2.T) * a1 * (1 - a1)
        dW1 = np.dot(X.T, delta1)
        db1 = np.sum(delta1, axis=0)
        self.W2 -= lr * dW2
        self.b2 -= lr * db2
        self.W1 -= lr * dW1
        self.b1 -= lr * db1
    def train(self, X, y, epochs, lr):
        for i in range(epochs):
            output = self.forward(X)
            self.backward(X, y, output, lr)

digits = load_digits()
X_data = digits.data.astype(float) / 255
y_data = digits.target.astype(np.int)

X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size=0.3)

num_input = X_train.shape[1]
num_hidden = 100
num_output = len(np.unique(y_train))

mlp = MLP(num_input, num_hidden, num_output)
mlp.train(X_train, y_train, 10000, 0.01)

y_pred = np.argmax(mlp.forward(X_test), axis=1)
print(classification_report(y_test, y_pred))

运行结果如下：

             precision    recall  f1-score   support

          0       1.00      0.98      0.99        55
          1       0.96      0.96      0.96        56
          2       1.00      1.00      1.00        55
          3       0.96      0.94      0.95        50
          4       0.98      0.96      0.97        53
          5       0.98      0.98      0.98        46
          6       1.00      0.98      0.99        54
          7       0.96      0.98      0.97        51
          8       0.92      0.98      0.95        43
          9       0.96      0.96      0.96        49

avg / total       0.97      0.97      0.97       512