1. 支持向量机

1.1 可视化数据集1

  1.     data = load_mat_file('./data/ex6data1.mat')
  2.     X = data['X']
  3.     y = data['y']
  4.     plt.ion()
  5.     plt.figure()
  6.     plot_data(X, y)
  7.     plt.pause(1)
  8.     plt.close()
  10. def plot_data(x, y):
  11.     # 取出那些行中，列号为0的元素等于1的行号。返回的是一个元组，其中存在一个元素，类型为ndarray，使用[0]取出这个这个矩阵（一维向量）。
  12.     pos = np.where(y[:, 0] == 1)[0]
  13.     neg = np.where(y[:, 0] == 0)[0]
  14.     # pos代表那些正样本的行索引，列号为0代表横坐标。1代表那些正样本的纵坐标。
  15.     plt.scatter(x[pos, 0], x[pos, 1], marker='+')
  16.     plt.scatter(x[neg, 0], x[neg, 1], marker='o')

image.png

1.2 调用sklearn中的svm

  1.     C = 1
  2.     Classification = SVC(C=C, kernel='linear')
  3.     # fit(X, y, sample_weight=None), y : array-like, shape (n_samples,)
  4.     # y.raval返回y的一维向量形式，按照每行降维，返回的是一个视图，修改会影响原值。
  5.     Classification.fit(X, y.ravel())
  7.     plot_pad = 0.5
  8.     plot_x_min, plot_x_max = X[:, 0].min() - plot_pad, X[:, 0].max() + plot_pad
  9.     plot_y_min, plot_y_max = X[:, 1].min() - plot_pad, X[:, 1].max() + plot_pad
  11.     plot_step = 0.01
  12.     # 按照0.01的间隔生成min到max之间的一系列网格矩阵。
  13.     plot_x, plot_y = np.meshgrid(np.arange(plot_x_min, plot_x_max, plot_step),
  14.                                  np.arange(plot_y_min, plot_y_max, plot_step))
  15.     #np.c_，左右连接，要求行数相等
  16.     plot_z = Classification.predict(np.c_[plot_x.ravel(), plot_y.ravel()]).reshape(plot_x.shape)
  17.     #绘制等高线图,alpha代表透明度，1为完全透明
  18.     plt.contourf(plot_x, plot_y, plot_z, cmap="Wistia", alpha=0.2)
  19.     plt.pause(1)
  20.     plt.close()

image.png

有高斯核的SVM

高斯核实现

image.png
theta参数决定着，相似程度的下降速度。theta越大，高斯曲线越平缓，相似度下降度慢。反之，相似度下降越快。

  1. def gaussian_kernel(x1, x2, sigma):
  2.     #linalg.norm，求向量的2范数
  3.     return np.exp(-((linalg.norm(x1 - x2)) ** 2) / (2 * (sigma ** 2)))

可视化数据集2

image.png
RBF指的就是高斯核函数。当C为100时，产生过拟合，其表现为：决策边界强制区分正负样本。

  1. Classification = SVC(C=100, kernel='rbf', gamma=6)
  2.     # fit(X, y, sample_weight=None), y : array-like, shape (n_samples,)
  3.     Classification.fit(X, y.ravel())
  5.     plot_pad = 0.5
  6.     plot_x_min, plot_x_max = X[:, 0].min() - plot_pad, X[:, 0].max() + plot_pad
  7.     plot_y_min, plot_y_max = X[:, 1].min() - plot_pad, X[:, 1].max() + plot_pad
  9.     plot_step = 0.01
  10.     plot_x, plot_y = np.meshgrid(np.arange(plot_x_min, plot_x_max, plot_step),
  11.                                  np.arange(plot_y_min, plot_y_max, plot_step))
  12.     plot_z = Classification.predict(np.c_[plot_x.ravel(), plot_y.ravel()]).reshape(plot_x.shape)
  13.     plt.contourf(plot_x, plot_y, plot_z, cmap="Wistia", alpha=0.2)
  14.     plt.axis([-0.1, 1.1, 0.3, 1.05])
  15.     plt.pause(1)
  16.     plt.close()

image.png

可视化数据集3

image.png

  1. Classification = SVC(C=1, kernel='poly', degree=3, gamma=10)
  2.     # fit(X, y, sample_weight=None), y : array-like, shape (n_samples,)
  3.     Classification.fit(X, y.ravel())
  5.     plot_pad = 0.5
  6.     plot_x_min, plot_x_max = X[:, 0].min() - plot_pad, X[:, 0].max() + plot_pad
  7.     plot_y_min, plot_y_max = X[:, 1].min() - plot_pad, X[:, 1].max() + plot_pad
  9.     plot_step = 0.01
  10.     plot_x, plot_y = np.meshgrid(np.arange(plot_x_min, plot_x_max, plot_step),
  11.                                  np.arange(plot_y_min, plot_y_max, plot_step))
  12.     plot_z = Classification.predict(np.c_[plot_x.ravel(), plot_y.ravel()]).reshape(plot_x.shape)
  13.     plt.contourf(plot_x, plot_y, plot_z, cmap="Wistia", alpha=0.2)
  14.     plt.axis([-0.8, 0.4, -0.8, 0.8])
  15.     plt.pause(1)
  16.     plt.close()

image.png
当C=1时，SVM可以发现异常点。泛化能力较好。

垃圾邮件分类

邮件预处理

  1. def process_email(email_contents):
  2.     # Load Vocabulary
  3.     vocab_list = get_vocab_list()[:, 1]
  4.     word_indices = []
  5.     # ========================== Preprocess Email ===========================
  6.     # Lower case
  7.     email_contents = str(email_contents)
  8.     email_contents = email_contents.lower()
  10.     # Strip all HTML
  11.     # Looks for any expression that starts with < and ends with > and replace
  12.     # and does not have any < or > in the tag it with a space
  13.     # [^<>]表示除了<>的字符匹配1次或者多次
  14.     email_contents = re.sub(r'<[^<>]+>', ' ', email_contents)
  16.     # Handle Numbers
  17.     # Look for one or more characters between 0-9
  18.     email_contents = re.sub(r'[0-9]+', 'number', email_contents)
  20.     # Handle URLS
  21.     # Look for strings starting with http:// or https://
  22.     email_contents = re.sub(r'(http|https)://[^\s]*', 'httpaddr', email_contents)
  24.     # Handle Email Addresses
  25.     # Look for strings with @ in the middle
  26.     email_contents = re.sub(r'[^\s]+@[^\s]+', 'emailaddr', email_contents)
  28.     # Handle $ sign
  29.     email_contents = re.sub(r'[$]+', 'dollar', email_contents)
  31.     # ========================== Tokenize Email ===========================
  32.     # Output the email to screen as well
  33.     print('\n==== Processed Email ====\n\n')
  35.     # Process file
  36.     l_count = 0
  38.     # Tokenize and also get rid of any punctuation
  39.     partition_text = re.split(r'[ @$/#.-:&*+=\[\]?!(){},\'\">_<;%\n\f]', email_contents)
  41.     stemmer = PorterStemmer()
  43.     for one_word in partition_text:
  44.         if one_word != '':
  45.             # Remove any non alphanumeric characters
  46.             one_word = re.sub(r'[^a-zA-Z0-9]', '', one_word)
  48.             # Stem the word
  49.             # (the porterStemmer sometimes has issues, so we use a try catch block)
  50.             one_word = stemmer.stem(one_word)
  52.             # % Skip the word if it is too short.
  53.             if str == '':
  54.                 continue
  56.             temp = np.argwhere(vocab_list == one_word)
  57.             if temp.size == 1:
  58.                 word_indices.append(temp.min())
  60.             #    % Print to screen, ensuring that the output lines are not too long
  61.             if (l_count + len(one_word) + 1) > 78:
  62.                 print('\n')
  63.                 l_count = 0
  64.             print('%s' % one_word, end=' ')
  65.             l_count = l_count + len(one_word) + 1
  66.     print('\n')
  67.     # Print footer
  68.     print('\n\n=========================\n')
  69.     return np.array(word_indices)

特征提取

def email_features(word_indices):
    # Total number of words in the dictionary
    n = 1899

    # You need to return the following variables correctly.
    x = np.zeros((n, 1))
    for i in range(word_indices.size):
        x[word_indices[i]] = 1
    return x

为垃圾邮件分类训练SVM

     # =========== Part 3: Train Linear SVM for Spam Classification ========
    # In this section, you will train a linear classifier to determine if an
    # email is Spam or Not-Spam.

    # Load the Spam Email dataset
    data = load_mat_file('../data/spamTrain.mat')
    print('\nTraining Linear SVM (Spam Classification)\n')
    print('(this may take 1 to 2 minutes) ...\n')
    X = data['X']
    y = data['y'].ravel()
    C = 0.1
    Classification = SVC(C=C, kernel='linear')
    Classification.fit(X, y)
    p = Classification.predict(X)
    print('Training Accuracy: {:.2f}\n'.format((np.mean((p == y)) * 100)))
    print('Program paused. Press enter to continue.\n')
    # pause_func()

    # =================== Part 4: Test Spam Classification ================
    data = load_mat_file('../data/spamTest.mat')
    Xtest = data['Xtest']
    ytest = data['ytest'].ravel()
    p = Classification.predict(Xtest)
    print('Test Accuracy: {:.2f}\n'.format((np.mean((p == ytest)) * 100)))
    print('Program paused. Press enter to continue.\n')

测试

    # =================== Part 4: Test Spam Classification ================
    data = load_mat_file('../data/spamTest.mat')
    Xtest = data['Xtest']
    ytest = data['ytest'].ravel()
    p = Classification.predict(Xtest)
    print('Test Accuracy: {:.2f}\n'.format((np.mean((p == ytest)) * 100)))
    print('Program paused. Press enter to continue.\n')
    # pause_func()

    # ================= Part 5: Top Predictors of Spam ====================
    # np.argsort用于排序分类器的参数大小
    index_array = np.argsort(Classification.coef_).ravel()[::-1]
    vocab_list = get_vocab_list()[:, 1]
    for i in range(15):
        print(' %-15s (%f) \n' % (vocab_list[index_array[i]], Classification.coef_[:,             index_array[i]]))

    print('Program paused. Press enter to continue.\n')