cs231n-学习笔记-02线性分类(续)

关于多分类SVM和Softmax代码实现

本文根据cs231n作业1整理而来。

本次作业可以学到：

① 实现一个全向量化的softmax分类器损失函数

② 实现全向量化的分析梯度表达式

③ 用数字梯度进行梯度检查

④ 使用验证集调整学习率和正则化系数

⑤ 使用随机梯度下降的算法优化损失函数

⑥ 可视化最终习得的权重

1 softmax分类器

1.1 softmax分类器循环实现

#  Softmax损失函数, 循环实现
def softmax_loss_naive(W, X, y, reg):
  """
  输入:
  - W: （维度总数，种类）
  - X: （样本批数，维度总数）
  - y: （维度总数，）
  - reg: (float)正则化系数
  输入:
  - 损失函数值
  - 期望的梯度值W，（维度总数，）
  """
  # 初始化损失值以及W的梯度值为0
  loss = 0.0
  dW = np.zeros_like(W)

  num_classes = W.shape[1]
  num_train = X.shape[0]

  scores = np.dot(X, W)

  #  为每一批计算损失值和梯度
  for ii in range(num_train):
    current_scores = scores[ii, :]
    #  通过从得分向量中减去最大值来修复数值稳定性。
    shift_scores = current_scores - np.max(current_scores)
    #  为本例计算损失值
    loss_ii = -shift_scores[y[ii]] + np.log(np.sum(np.exp(shift_scores)))
    loss += loss_ii

    for jj in range(num_classes):
        softmax_score = np.exp(shift_scores[jj]) / np.sum(np.exp(shift_scores))

        #  计算梯度
        if jj == y[ii]:
            dW[:, jj] += (-1 + softmax_score) * X[ii]
        else:
            dW[:, jj] += softmax_score * X[ii]

  #  在批上求平均，以及添加正则化系数项
  loss /= num_train
  loss += reg * np.sum(W*W)

  #  在批上求平均，以及添加正则化系数项的导数
  dW /= num_train
  loss += 2 * reg * W

  return loss, dW

1.2 softmax分类器向量化实现

#  Softmax损失函数, 向量化实现
def softmax_loss_vectorized(W, X, y, reg):
  # 初始化损失值以及W的梯度值为0
  loss = 0.0
  dW = np.zeros_like(W)

  num_train = X.shape[0]
  #  计算得分，并修正数值
  scores = np.dot(X, W)
  shift_scores = scores - np.max(scores, axis=1)[..., np.newaxis]

  #  计算softmax得分
  softmax_scores = np.exp(shift_scores)/np.sum(np.exp(shift_scores), axis=1)[..., np.newaxis]

  #  计算dScore
  dScore = softmax_scores
  dScore[range(num_train), y] = dScore[range(num_train),y] - 1

  dW = np.dot(X.T, dScore)
  dW /= num_train
  dW += 2 * reg * W

  #  计算交叉熵损失函数
  correct_class_scores = np.choose(y, shift_scores.T)
  loss = -correct_class_scores + np.log(np.sum(np.exp(shift_scores), axis=1))
  loss = np.num(loss)

  #  平均损失函数值，并且正则化
  loss /= num_train
  loss += reg * np.sum(W*W)

  return loss, dW

2 使用验证集调整超参数

#  使用验证集调整超参数（正则化系数和学习率）。试验不同的正则化系数和学习率，
#  我们在验证集上分类的精确度应该超过0.35
from cs231n.classifiers import Softmax

results = {}
best_val = -1
best_softmax = None
learning_rates = [1e-7, 5e-7]
regularization_strengths = [2.5e4, 5e4]

num_splt_lr = 3
num_splt_rs = 8
for i in range(num_splt_lr):
    for j in range(num_splt_rs):
        learning_rate_ij = learning_rates[0] + i * (learning_rates[1] - learning_rates[0]) / num_splt_lr
        reg_ij = regularization_strengths[0] + j * (regularization_strengths[1] - regularization_strengths[0])/ num_splt_rs
        softmax = Softmax()
        loss_hist = softmax.train(X_train, y_train, learning_rate=learning_rate_ij, reg=reg_ij,
                              num_iters=1500, verbose=False)

        y_train_pred = softmax.predict(X_train)
        accuracy_train = np.mean(y_train == y_train_pred)
        y_val_pred = softmax.predict(X_val)
        accuracy_val = np.mean(y_val == y_val_pred)

        results[(learning_rate_ij, reg_ij)] = (accuracy_train, accuracy_val)

        if accuracy_val > best_val:
            best_val = accuracy_val
            best_softmax = softmax

#  输出结果
for lr, reg in sorted(results):
    train_accuacy, val_accuracy = results[(lr, reg)]
    print('lr %e reg %e train accuracy: %f val accuracy:%f' % (lr, reg, train_accuacy, val_accuracy))

print('best validation accuracy achieved during cross-validation:%f' % best_val)

3 测试集评估

#  利用测试集评估
y_test_pred = best_softmax.predict(X_test)
test_accuracy = np.mean(y_test == y_test_pred)
print('softmax on raw pixels final test set accuracy:%f' % (test_accuracy,))
#  softmax on raw pixels final test set accuracy:0.344000

4 习得结果可视化

#  使每个类别学习的权重可视化
w = best_softmax.W[:-1,:]  #  剔除偏置
w = w.reshape(32, 32, 3, 10)

w_min, w_max = np.min(w), np.max(w)

classes = ['plane', 'car', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck']
for i in range(10):
    plt.subplot(2, 5, i+1)

    #  约束权值在0-255之间
    wimg = 255.0 * (w[:, :, :, i].squeeze() - w_min) / (w_max - w_min)
    plt.imshow(wimg.astype('uint8'))
    plt.axis('off')
    plt.title(classes[i])

最终输出结果如下图所示：