svm linear

支持向量机（Support Vector Machine, SVM）是一种二分类模型，它的基本模型是定义在特征空间上的间隔最大的线性分类器。而SVM Linear则是SVM的一种线性分类器，它通过寻找一个最优的超平面（超平面可以看作是多维空间中的一个n-1维的子空间），使得两个不同类别的数据点到这个超平面的距离最大，从而实现线性分类。SVM Linear还有一个特点是它的求解方法非常高效，可以处理大规模数据集。

相关问题

from sklearn import svm linear_svm = svm.SVC(C=0.5, #惩罚参数 kernel='linear') gauss_svm = svm.SVC(C=0.5,#高斯核 kernel='rbf') linear_svm.fit(x,y) y_pred = linear_svm.predict(x)

这段代码是使用Scikit-learn库中的SVM算法来进行分类任务。其中，C是惩罚因子，用于控制模型的过拟合程度，kernel参数用于选择SVM算法的核函数类型，这里linear表示线性核函数，rbf表示高斯核函数。

接下来，我们使用linear_svm.fit()来对模型进行训练，其中x是训练集的特征数据，y是训练集的标签数据。

最后，使用linear_svm.predict()来对训练集的特征数据进行预测，得到预测结果y_pred。

在SVM中，linear_svm.py、linear_classifier.py和svm.ipynb中相应的代码

linear_svm.py:

import numpy as np


class LinearSVM:
    def __init__(self, lr=0.01, reg=0.01, num_iters=1000, batch_size=32):
        self.lr = lr
        self.reg = reg
        self.num_iters = num_iters
        self.batch_size = batch_size
        self.W = None
        self.b = None

    def train(self, X, y):
        num_train, dim = X.shape
        num_classes = np.max(y) + 1
        if self.W is None:
            self.W = 0.001 * np.random.randn(dim, num_classes)
            self.b = np.zeros((1, num_classes))

        loss_history = []
        for i in range(self.num_iters):
            batch_idx = np.random.choice(num_train, self.batch_size)
            X_batch = X[batch_idx]
            y_batch = y[batch_idx]
            loss, grad_W, grad_b = self.loss(X_batch, y_batch)
            loss_history.append(loss)
            self.W -= self.lr * grad_W
            self.b -= self.lr * grad_b

        return loss_history

    def predict(self, X):
        scores = X.dot(self.W) + self.b
        y_pred = np.argmax(scores, axis=1)
        return y_pred

    def loss(self, X_batch, y_batch):
        num_train = X_batch.shape[0]
        scores = X_batch.dot(self.W) + self.b
        correct_scores = scores[range(num_train), y_batch]
        margins = np.maximum(0, scores - correct_scores[:, np.newaxis] + 1)
        margins[range(num_train), y_batch] = 0
        loss = np.sum(margins) / num_train + 0.5 * self.reg * np.sum(self.W * self.W)
        num_pos = np.sum(margins > 0, axis=1)
        dscores = np.zeros_like(scores)
        dscores[margins > 0] = 1
        dscores[range(num_train), y_batch] -= num_pos
        dscores /= num_train
        grad_W = np.dot(X_batch.T, dscores) + self.reg * self.W
        grad_b = np.sum(dscores, axis=0, keepdims=True)
        return loss, grad_W, grad_b

linear_classifier.py:

import numpy as np


class LinearClassifier:
    def __init__(self, lr=0.01, reg=0.01, num_iters=1000, batch_size=32):
        self.lr = lr
        self.reg = reg
        self.num_iters = num_iters
        self.batch_size = batch_size
        self.W = None
        self.b = None

    def train(self, X, y):
        num_train, dim = X.shape
        num_classes = np.max(y) + 1
        if self.W is None:
            self.W = 0.001 * np.random.randn(dim, num_classes)
            self.b = np.zeros((1, num_classes))

        loss_history = []
        for i in range(self.num_iters):
            batch_idx = np.random.choice(num_train, self.batch_size)
            X_batch = X[batch_idx]
            y_batch = y[batch_idx]
            loss, grad_W, grad_b = self.loss(X_batch, y_batch)
            loss_history.append(loss)
            self.W -= self.lr * grad_W
            self.b -= self.lr * grad_b

        return loss_history

    def predict(self, X):
        scores = X.dot(self.W) + self.b
        y_pred = np.argmax(scores, axis=1)
        return y_pred

    def loss(self, X_batch, y_batch):
        num_train = X_batch.shape[0]
        scores = X_batch.dot(self.W) + self.b
        correct_scores = scores[range(num_train), y_batch]
        margins = np.maximum(0, scores - correct_scores[:, np.newaxis] + 1)
        margins[range(num_train), y_batch] = 0
        loss = np.sum(margins) / num_train + 0.5 * self.reg * np.sum(self.W * self.W)
        num_pos = np.sum(margins > 0, axis=1)
        dscores = np.zeros_like(scores)
        dscores[margins > 0] = 1
        dscores[range(num_train), y_batch] -= num_pos
        dscores /= num_train
        grad_W = np.dot(X_batch.T, dscores) + self.reg * self.W
        grad_b = np.sum(dscores, axis=0, keepdims=True)
        return loss, grad_W, grad_b

svm.ipynb:

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs, make_moons
from sklearn.model_selection import train_test_split
from linear_classifier import LinearClassifier


def plot_data(X, y, title):
    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu)
    plt.title(title)
    plt.xlabel('Feature 1')
    plt.ylabel('Feature 2')
    plt.show()


def plot_decision_boundary(clf, X, y, title):
    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu)
    ax = plt.gca()
    xlim = ax.get_xlim()
    ylim = ax.get_ylim()

    xx = np.linspace(xlim[0], xlim[1], 100)
    yy = np.linspace(ylim[0], ylim[1], 100)
    XX, YY = np.meshgrid(xx, yy)
    xy = np.vstack([XX.ravel(), YY.ravel()]).T
    Z = clf.predict(xy).reshape(XX.shape)

    plt.contour(XX, YY, Z, levels=[0], colors='k', linestyles='-')
    plt.title(title)
    plt.xlabel('Feature 1')
    plt.ylabel('Feature 2')
    plt.show()


def main():
    X, y = make_blobs(n_samples=200, centers=2, random_state=42)
    plot_data(X, y, 'Linearly Separable Data')

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

    clf = LinearClassifier()
    loss_history = clf.train(X_train, y_train)

    train_acc = np.mean(clf.predict(X_train) == y_train)
    test_acc = np.mean(clf.predict(X_test) == y_test)
    print('Train accuracy: {:.3f}, Test accuracy: {:.3f}'.format(train_acc, test_acc))

    plot_decision_boundary(clf, X, y, 'Linear SVM')


if __name__ == '__main__':
    main()

以上的代码实现了一个简单的线性 SVM，可以用于二分类问题。在 `svm.ipynb` 文件中，我们使用 `make_blobs` 生成了一个线性可分的数据集，然后将其拆分为训练集和测试集。接着，我们使用 `LinearClassifier` 对训练集进行训练，并在测试集上评估模型性能。最后，我们绘制了模型的决策边界。