用python写一个线性分类器

好的，以下是一个简单的线性分类器的 Python 代码示例：

import numpy as np

class LinearClassifier:
    def __init__(self):
        self.weights = None
        self.bias = None
        
    def train(self, X_train, y_train, lr=0.01, epochs=1000):
        num_samples, num_features = X_train.shape
        num_classes = np.max(y_train) + 1
        
        # initialize weights and bias
        self.weights = np.zeros((num_features, num_classes))
        self.bias = np.zeros(num_classes)
        
        # one-hot encode the labels
        y_onehot = np.zeros((num_samples, num_classes))
        y_onehot[np.arange(num_samples), y_train] = 1
        
        # gradient descent
        for i in range(epochs):
            scores = np.dot(X_train, self.weights) + self.bias
            exp_scores = np.exp(scores)
            probs = exp_scores / np.sum(exp_scores, axis=1, keepdims=True)
            
            # compute loss and gradient
            loss = -np.mean(y_onehot * np.log(probs))
            d_scores = probs - y_onehot
            d_weights = np.dot(X_train.T, d_scores)
            d_bias = np.sum(d_scores, axis=0)
            
            # update weights and bias
            self.weights -= lr * d_weights
            self.bias -= lr * d_bias
            
            if i % 100 == 0:
                print(f"Epoch {i}, Loss: {loss:.4f}")
        
    def predict(self, X_test):
        scores = np.dot(X_test, self.weights) + self.bias
        return np.argmax(scores, axis=1)

这个线性分类器使用梯度下降来训练权重和偏差，并且使用 softmax 函数来计算每个类别的概率得分。在训练期间，损失会被记录下来，以便我们可以查看模型的性能如何随时间而变化。在预测时，我们简单地计算每个样本的得分，并返回得分最高的类别。