python svm算法smo cifar_使用smo算法编写svm对CIFAR-10数据分类

SVM算法通过将数据映射到高维空间，将数据分为两个类别。SVM算法的目标是找到一个超平面，可以将数据分为两个类别。SMO算法是一种优化算法，用于求解SVM中的二次规划问题。下面介绍如何使用SMO算法编写SVM对CIFAR-10数据进行分类。

首先，我们需要加载CIFAR-10数据集。CIFAR-10数据集包含10个类别的60000个32x32彩色图像。每个类别包含6000个图像。我们将使用Python中的pickle模块来加载数据集。以下是加载数据集的代码：

import pickle
import numpy as np

def unpickle(file):
    with open(file, 'rb') as fo:
        dict = pickle.load(fo, encoding='bytes')
    return dict

def load_cifar10_data():
    xs = []
    ys = []
    for j in range(5):
        d = unpickle('cifar-10-batches-py/data_batch_%d' % (j + 1))
        x = d[b'data']
        y = d[b'labels']
        xs.append(x)
        ys.append(y)
    d = unpickle('cifar-10-batches-py/test_batch')
    xs.append(d[b'data'])
    ys.append(d[b'labels'])
    x = np.concatenate(xs) / np.float32(255)
    y = np.concatenate(ys)
    return x.reshape((len(x), -1)), np.array(y)

接下来，我们将使用SMO算法来训练SVM模型。以下是使用SMO算法训练SVM模型的代码：

class SVM:
    def __init__(self, C, toler, kernel_opt=('linear', 0)):
        self.C = C
        self.toler = toler
        self.kernel_opt = kernel_opt

    def fit(self, X, y):
        n_samples, n_features = X.shape
        alpha = np.zeros(n_samples)
        b = 0
        kernel = kernel_set[self.kernel_opt[0]]
        K = np.zeros((n_samples, n_samples))
        for i in range(n_samples):
            K[:, i] = kernel(X, X[i], self.kernel_opt[1])
        iter = 0
        while iter < max_iter:
            num_changed_alphas = 0
            for i in range(n_samples):
                Ei = np.dot(alpha * y, K[:, i]) + b - y[i]
                if (y[i] * Ei < -self.toler and alpha[i] < self.C) or \
                        (y[i] * Ei > self.toler and alpha[i] > 0):
                    j = np.random.choice([x for x in range(n_samples) if x != i])
                    Ej = np.dot(alpha * y, K[:, j]) + b - y[j]
                    alpha_i_old, alpha_j_old = alpha[i], alpha[j]
                    if y[i] != y[j]:
                        L = max(0, alpha[j] - alpha[i])
                        H = min(self.C, self.C + alpha[j] - alpha[i])
                    else:
                        L = max(0, alpha[i] + alpha[j] - self.C)
                        H = min(self.C, alpha[i] + alpha[j])
                    if L == H:
                        continue
                    eta = 2.0 * K[i, j] - K[i, i] - K[j, j]
                    if eta >= 0:
                        continue
                    alpha[j] -= y[j] * (Ei - Ej) / eta
                    alpha[j] = min(alpha[j], H)
                    alpha[j] = max(alpha[j], L)
                    if abs(alpha[j] - alpha_j_old) < 1e-5:
                        continue
                    alpha[i] += y[i] * y[j] * (alpha_j_old - alpha[j])
                    b1 = b - Ei - y[i] * (alpha[i] - alpha_i_old) * K[i, i] - \
                         y[j] * (alpha[j] - alpha_j_old) * K[i, j]
                    b2 = b - Ej - y[i] * (alpha[i] - alpha_i_old) * K[i, j] - \
                         y[j] * (alpha[j] - alpha_j_old) * K[j, j]
                    if 0 < alpha[i] < self.C:
                        b = b1
                    elif 0 < alpha[j] < self.C:
                        b = b2
                    else:
                        b = (b1 + b2) / 2
                    num_changed_alphas += 1
            if num_changed_alphas == 0:
                iter += 1
            else:
                iter = 0
        self.X = X
        self.y = y
        self.kernel = kernel
        self.alpha = alpha
        self.b = b

    def predict(self, X):
        n_samples, n_features = X.shape
        K = np.zeros((n_samples, len(self.X)))
        for i in range(n_samples):
            K[i, :] = self.kernel(self.X, X[i], self.kernel_opt[1])
        y_pred = np.dot(self.alpha * self.y, K) + self.b
        return np.sign(y_pred)

最后，我们使用以下代码来加载数据集并使用SMO算法训练SVM模型：

X, y = load_cifar10_data()
y[y == 0] = -1
X_train, X_test = X[:50000], X[50000:]
y_train, y_test = y[:50000], y[50000:]
svm = SVM(C=1.0, toler=0.001, kernel_opt=('rbf', 1))
svm.fit(X_train, y_train)
y_pred_train = svm.predict(X_train)
y_pred_test = svm.predict(X_test)
train_acc = np.mean(y_train == y_pred_train)
test_acc = np.mean(y_test == y_pred_test)
print('train_acc:', train_acc)
print('test_acc:', test_acc)

这样我们就使用SMO算法编写了SVM对CIFAR-10数据进行分类的代码。