、题目五(扩展):使用 numpy 编写逻辑回归算法,对 iris 数据进行多分类。 具体内容:输出决策函数的参数、预测值、分类准确率等。 提示: (1)可采用 OVR、OVO、ECOC 策略。 (2)可采用 CrossEntropy Loss + softmax 策略。 a)需将三个类别(如 0,1,2)进行 one-hot 编码。 b)每个线性分类器对应一组模型参数,3 个线性分类器对应 3 组模型参数。 c)可通过 softmax 回归计算多种类别的概率(K 种类别概率和为 1)。 d)通过最小化 CrossEntropy Loss 的梯度下降算法进行分类器参数寻优。
时间: 2024-02-29 08:52:59 浏览: 59
好的,以下是一个基于CrossEntropy Loss + softmax策略和OVR策略的多分类逻辑回归算法的Python代码示例:
```python
import numpy as np
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
# 加载iris数据集
iris = load_iris()
X = iris.data
y = iris.target
# 将三个类别进行one-hot编码
n_classes = 3
y_onehot = np.zeros((y.shape[0], n_classes))
y_onehot[np.arange(y.shape[0]), y] = 1
# 将数据集分成训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X, y_onehot, test_size=0.3)
# 初始化模型参数
n_features = X_train.shape[1]
n_epochs = 1000
learning_rate = 0.01
weights = np.zeros((n_features, n_classes))
bias = np.zeros((1, n_classes))
# 实现sigmoid函数和softmax函数
def sigmoid(x):
return 1 / (1 + np.exp(-x))
def softmax(x):
exp_x = np.exp(x)
return exp_x / np.sum(exp_x, axis=1, keepdims=True)
# 实现损失函数
def cross_entropy_loss(y, y_pred):
loss = -np.mean(y * np.log(y_pred + 1e-8))
return loss
# 实现梯度下降算法
def gradient_descent(X, y, y_pred):
dW = np.dot(X.T, (y_pred - y)) / X.shape[0]
db = np.mean(y_pred - y, axis=0, keepdims=True)
return dW, db
# 训练模型
for epoch in range(n_epochs):
# 计算线性分类器的输出值
z = np.dot(X_train, weights) + bias
# 计算线性分类器的sigmoid函数输出值
y_pred = sigmoid(z)
# 计算多个线性分类器的softmax函数输出值
y_pred = softmax(y_pred)
# 计算损失值
loss = cross_entropy_loss(y_train, y_pred)
# 计算梯度并更新模型参数
dW, db = gradient_descent(X_train, y_train, y_pred)
weights -= learning_rate * dW
bias -= learning_rate * db
# 输出损失值
print('Epoch %d, loss: %f' % (epoch, loss))
# 预测模型
z = np.dot(X_test, weights) + bias
y_pred = sigmoid(z)
y_pred = softmax(y_pred)
y_pred = np.argmax(y_pred, axis=1)
y_test = np.argmax(y_test, axis=1)
accuracy = np.mean(y_pred == y_test)
print('Accuracy: %f' % accuracy)
```
这段代码使用OVR策略来实现多分类逻辑回归算法,并使用CrossEntropy Loss + softmax策略来计算模型的损失值和多个线性分类器的输出值。在训练过程中,使用梯度下降算法来更新模型参数,并输出每个epoch的损失值。在预测过程中,使用softmax函数来计算多个线性分类器的输出值,并将其转换为类别标签,然后计算分类准确率。
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