jupyternotebok采用BP神经网络模型将鸢尾花数据二分类。

首先，加载鸢尾花数据集并进行预处理：

import numpy as np
from sklearn import datasets

iris = datasets.load_iris()
X = iris.data
y = iris.target

# 将标签转换为0和1
y[y != 0] = 1

# 标准化特征值
X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)

然后，我们定义BP神经网络模型。在这个例子中，我们使用一个具有两个隐藏层的神经网络，每个隐藏层有10个神经元。我们使用sigmoid作为激活函数，二元交叉熵作为损失函数，批量梯度下降作为优化算法。

class BPNeuralNetwork:
    def __init__(self, n_input, n_hidden1, n_hidden2, n_output):
        self.n_input = n_input
        self.n_hidden1 = n_hidden1
        self.n_hidden2 = n_hidden2
        self.n_output = n_output

        # 初始化权重和偏置
        self.weights1 = np.random.randn(self.n_input, self.n_hidden1)
        self.bias1 = np.zeros((1, self.n_hidden1))
        self.weights2 = np.random.randn(self.n_hidden1, self.n_hidden2)
        self.bias2 = np.zeros((1, self.n_hidden2))
        self.weights3 = np.random.randn(self.n_hidden2, self.n_output)
        self.bias3 = np.zeros((1, self.n_output))

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def sigmoid_derivative(self, x):
        return x * (1 - x)

    def forward(self, X):
        self.z1 = np.dot(X, self.weights1) + self.bias1
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        self.a2 = self.sigmoid(self.z2)
        self.z3 = np.dot(self.a2, self.weights3) + self.bias3
        self.y_hat = self.sigmoid(self.z3)
        return self.y_hat

    def backward(self, X, y, y_hat, learning_rate):
        # 计算输出层误差
        self.output_error = y - y_hat
        self.output_delta = self.output_error * self.sigmoid_derivative(y_hat)

        # 计算隐藏层2误差
        self.hidden2_error = np.dot(self.output_delta, self.weights3.T)
        self.hidden2_delta = self.hidden2_error * self.sigmoid_derivative(self.a2)

        # 计算隐藏层1误差
        self.hidden1_error = np.dot(self.hidden2_delta, self.weights2.T)
        self.hidden1_delta = self.hidden1_error * self.sigmoid_derivative(self.a1)

        # 更新权重和偏置
        self.weights1 += learning_rate * np.dot(X.T, self.hidden1_delta)
        self.bias1 += learning_rate * np.sum(self.hidden1_delta, axis=0, keepdims=True)
        self.weights2 += learning_rate * np.dot(self.a1.T, self.hidden2_delta)
        self.bias2 += learning_rate * np.sum(self.hidden2_delta, axis=0, keepdims=True)
        self.weights3 += learning_rate * np.dot(self.a2.T, self.output_delta)
        self.bias3 += learning_rate * np.sum(self.output_delta, axis=0, keepdims=True)

    def train(self, X, y, learning_rate=0.1, n_epochs=1000):
        for i in range(n_epochs):
            y_hat = self.forward(X)
            self.backward(X, y, y_hat, learning_rate)

    def predict(self, X):
        y_hat = self.forward(X)
        predictions = np.round(y_hat)
        return predictions

接下来，我们将数据集分为训练集和测试集，并训练模型。

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

bpnn = BPNeuralNetwork(n_input=4, n_hidden1=10, n_hidden2=10, n_output=1)
bpnn.train(X_train, y_train, learning_rate=0.1, n_epochs=1000)

最后，我们使用测试集评估模型。

from sklearn.metrics import accuracy_score

predictions = bpnn.predict(X_test)
accuracy = accuracy_score(y_test, predictions)
print("Accuracy:", accuracy)

完整代码如下：

import numpy as np
from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score


class BPNeuralNetwork:
    def __init__(self, n_input, n_hidden1, n_hidden2, n_output):
        self.n_input = n_input
        self.n_hidden1 = n_hidden1
        self.n_hidden2 = n_hidden2
        self.n_output = n_output

        # 初始化权重和偏置
        self.weights1 = np.random.randn(self.n_input, self.n_hidden1)
        self.bias1 = np.zeros((1, self.n_hidden1))
        self.weights2 = np.random.randn(self.n_hidden1, self.n_hidden2)
        self.bias2 = np.zeros((1, self.n_hidden2))
        self.weights3 = np.random.randn(self.n_hidden2, self.n_output)
        self.bias3 = np.zeros((1, self.n_output))

    def sigmoid(self, x):
        return 1 / (1 + np.exp(-x))

    def sigmoid_derivative(self, x):
        return x * (1 - x)

    def forward(self, X):
        self.z1 = np.dot(X, self.weights1) + self.bias1
        self.a1 = self.sigmoid(self.z1)
        self.z2 = np.dot(self.a1, self.weights2) + self.bias2
        self.a2 = self.sigmoid(self.z2)
        self.z3 = np.dot(self.a2, self.weights3) + self.bias3
        self.y_hat = self.sigmoid(self.z3)
        return self.y_hat

    def backward(self, X, y, y_hat, learning_rate):
        # 计算输出层误差
        self.output_error = y - y_hat
        self.output_delta = self.output_error * self.sigmoid_derivative(y_hat)

        # 计算隐藏层2误差
        self.hidden2_error = np.dot(self.output_delta, self.weights3.T)
        self.hidden2_delta = self.hidden2_error * self.sigmoid_derivative(self.a2)

        # 计算隐藏层1误差
        self.hidden1_error = np.dot(self.hidden2_delta, self.weights2.T)
        self.hidden1_delta = self.hidden1_error * self.sigmoid_derivative(self.a1)

        # 更新权重和偏置
        self.weights1 += learning_rate * np.dot(X.T, self.hidden1_delta)
        self.bias1 += learning_rate * np.sum(self.hidden1_delta, axis=0, keepdims=True)
        self.weights2 += learning_rate * np.dot(self.a1.T, self.hidden2_delta)
        self.bias2 += learning_rate * np.sum(self.hidden2_delta, axis=0, keepdims=True)
        self.weights3 += learning_rate * np.dot(self.a2.T, self.output_delta)
        self.bias3 += learning_rate * np.sum(self.output_delta, axis=0, keepdims=True)

    def train(self, X, y, learning_rate=0.1, n_epochs=1000):
        for i in range(n_epochs):
            y_hat = self.forward(X)
            self.backward(X, y, y_hat, learning_rate)

    def predict(self, X):
        y_hat = self.forward(X)
        predictions = np.round(y_hat)
        return predictions


iris = datasets.load_iris()
X = iris.data
y = iris.target

# 将标签转换为0和1
y[y != 0] = 1

# 标准化特征值
X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

bpnn = BPNeuralNetwork(n_input=4, n_hidden1=10, n_hidden2=10, n_output=1)
bpnn.train(X_train, y_train, learning_rate=0.1, n_epochs=1000)

predictions = bpnn.predict(X_test)
accuracy = accuracy_score(y_test, predictions)
print("Accuracy:", accuracy)

注：这只是一个简单的示例，实际应用中需要进行更多的数据预处理和模型调优。