吴恩达机器学习系列作业目录
1 Support Vector Machines
1.1 Example Dataset 1
%matplotlib inlineimport numpy as npimport pandas as pdimport matplotlib.pyplot as pltimport seaborn as sbfrom scipy.io import loadmatfrom sklearn import svm
大多数SVM的库会自动帮你添加额外的特征 x0x_0x0 已经 θ0\theta_0θ0，所以无需手动添加。
mat = loadmat('./data/ex6data1.mat')print(mat.keys())# dict_keys(['__header__', '__version__', '__globals__', 'X', 'y'])X = mat['X']y = mat['y']
def plotData(X, y):plt.figure(figsize=(8,5))plt.scatter(X[:,0], X[:,1], c=y.flatten(), cmap='rainbow')plt.xlabel('X1')plt.ylabel('X2')plt.legend() plotData(X, y)
def plotBoundary(clf, X):'''plot decision bondary'''x_min, x_max = X[:,0].min()*1.2, X[:,0].max()*1.1y_min, y_max = X[:,1].min()*1.1,X[:,1].max()*1.1xx, yy = np.meshgrid(np.linspace(x_min, x_max, 500),np.linspace(y_min, y_max, 500))Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])Z = Z.reshape(xx.shape)plt.contour(xx, yy, Z)
models = [svm.SVC(C, kernel='linear') for C in [1, 100]]clfs = [model.fit(X, y.ravel()) for model in models]
title = ['SVM Decision Boundary with C = {} (Example Dataset 1'.format(C) for C in [1, 100]]for model,title in zip(clfs,title):plt.figure(figsize=(8,5))plotData(X, y)plotBoundary(model, X)plt.title(title)
可以从上图看到，当C比较小时模型对误分类的惩罚增大，比较严格，误分类少，间隔比较狭窄。
当C比较大时模型对误分类的惩罚增大，比较宽松，允许一定的误分类存在，间隔较大。
1.2 SVM with Gaussian Kernels
这部分，使用SVM做非线性分类。我们将使用高斯核函数。
为了用SVM找出一个非线性的决策边界，我们首先要实现高斯核函数。我可以把高斯核函数想象成一个相似度函数，用来测量一对样本的距离，(x(i),y(j))(x^{(i)}, y^{(j)})(x(i),y(j)) 。
这里我们用sklearn自带的svm中的核函数即可。
1.2.1 Gaussian Kernel
def gaussKernel(x1, x2, sigma):return np.exp(- ((x1 - x2) ** 2).sum() / (2 * sigma ** 2))gaussKernel(np.array([1, 2, 1]),np.array([0, 4, -1]), 2.) # 0.32465246735834974
1.2.2 Example Dataset 2
mat = loadmat('./data/ex6data2.mat')X2 = mat['X']y2 = mat['y']
plotData(X2, y2)
sigma = 0.1gamma = np.power(sigma,-2.)/2clf = svm.SVC(C=1, kernel='rbf', gamma=gamma)modle = clf.fit(X2, y2.flatten())plotData(X2, y2)plotBoundary(modle, X2)
1.2.3 Example Dataset 3
mat3 = loadmat('data/ex6data3.mat')X3, y3 = mat3['X'], mat3['y']Xval, yval = mat3['Xval'], mat3['yval']plotData(X3, y3)
Cvalues = (0.01, 0.03, 0.1, 0.3, 1., 3., 10., 30.)sigmavalues = Cvaluesbest_pair, best_score = (0, 0), 0for C in Cvalues:for sigma in sigmavalues:gamma = np.power(sigma,-2.)/2model = svm.SVC(C=C,kernel='rbf',gamma=gamma)model.fit(X3, y3.flatten())this_score = model.score(Xval, yval)if this_score > best_score:best_score = this_scorebest_pair = (C, sigma)print('best_pair={}, best_score={}'.format(best_pair, best_score))# best_pair=(1.0, 0.1), best_score=0.965
model = svm.SVC(C=1., kernel='rbf', gamma = np.power(.1, -2.)/2)model.fit(X3, y3.flatten())plotData(X3, y3)plotBoundary(model, X3)
# 这我的一个练习画图的，和作业无关，给个画图的参考。import numpy as npimport matplotlib.pyplot as pltfrom sklearn import svm# we create 40 separable pointsnp.random.seed(0)X = np.array([[3,3],[4,3],[1,1]])Y = np.array([1,1,-1])# fit the modelclf = svm.SVC(kernel='linear')clf.fit(X, Y)# get the separating hyperplanew = clf.coef_[0]a = -w[0] / w[1]xx = np.linspace(-5, 5)yy = a * xx - (clf.intercept_[0]) / w[1]# plot the parallels to the separating hyperplane that pass through the# support vectorsb = clf.support_vectors_[0]yy_down = a * xx + (b[1] - a * b[0])b = clf.support_vectors_[-1]yy_up = a * xx + (b[1] - a * b[0])# plot the line, the points, and the nearest vectors to the planeplt.figure(figsize=(8,5))plt.plot(xx, yy, 'k-')plt.plot(xx, yy_down, 'k--')plt.plot(xx, yy_up, 'k--')# 圈出支持向量plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],s=150, facecolors='none', edgecolors='k', linewidths=1.5)plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.rainbow)plt.axis('tight')plt.show()print(clf.decision_function(X))
[ 1. 1.5 -1. ]
2 Spam Classification
2.1 Preprocessing Emails
这部分用SVM建立一个垃圾邮件分类器。你需要将每个email变成一个n维的特征向量，这个分类器将判断给定一个邮件x是垃圾邮件(y=1)或不是垃圾邮件(y=0)。
take a look at examples from the dataset
with open('data/emailSample1.txt', 'r') as f:email = f.read()print(email)
> Anyone knows how much it costs to host a web portal ?>Well, it depends on how many visitors you're expecting.This can be anywhere from less than 10 bucks a month to a couple of $100. You should checkout / or perhaps Amazon EC2 if youre running something big..To unsubscribe yourself from this mailing list, send an email to:groupname-unsubscribe@
可以看到，邮件内容包含 a URL, an email address(at the end), numbers, and dollar amounts. 很多邮件都会包含这些元素，但是每封邮件的具体内容可能会不一样。因此，处理邮件经常采用的方法是标准化这些数据，把所有URL当作一样，所有数字看作一样。
例如，我们用唯一的一个字符串‘httpaddr’来替换所有的URL，来表示邮件包含URL，而不要求具体的URL内容。这通常会提高垃圾邮件分类器的性能，因为垃圾邮件发送者通常会随机化URL，因此在新的垃圾邮件中再次看到任何特定URL的几率非常小。
我们可以做如下处理：
1. Lower-casing: 把整封邮件转化为小写。2. Stripping HTML: 移除所有HTML标签，只保留内容。3. Normalizing URLs: 将所有的URL替换为字符串 “httpaddr”.4. Normalizing Email Addresses: 所有的地址替换为 “emailaddr”5. Normalizing Dollars: 所有dollar符号($)替换为“dollar”.6. Normalizing Numbers: 所有数字替换为“number”7. Word Stemming(词干提取): 将所有单词还原为词源。例如，“discount”, “discounts”, “discounted” and “discounting”都替换为“discount”。8. Removal of non-words: 移除所有非文字类型，所有的空格(tabs, newlines, spaces)调整为一个空格.
%matplotlib inlineimport numpy as npimport matplotlib.pyplot as pltfrom scipy.io import loadmatfrom sklearn import svmimport re #regular expression for e-mail processing# 这是一个可用的英文分词算法(Porter stemmer)from stemming.porter2 import stem# 这个英文算法似乎更符合作业里面所用的代码，与上面效果差不多import nltk, nltk.stem.porter
def processEmail(email):"""做除了Word Stemming和Removal of non-words的所有处理"""email = email.lower()email = re.sub('<[^<>]>', ' ', email) # 匹配<开头，然后所有不是< ,> 的内容，知道>结尾，相当于匹配<...>email = re.sub('(http|https)://[^\s]*', 'httpaddr', email ) # 匹配//后面不是空白字符的内容，遇到空白字符则停止email = re.sub('[^\s]+@[^\s]+', 'emailaddr', email)email = re.sub('[\$]+', 'dollar', email)email = re.sub('[\d]+', 'number', email) return email
接下来就是提取词干，以及去除非字符内容。
def email2TokenList(email):"""预处理数据，返回一个干净的单词列表"""# I'll use the NLTK stemmer because it more accurately duplicates the# performance of the OCTAVE implementation in the assignmentstemmer = nltk.stem.porter.PorterStemmer()email = preProcess(email)# 将邮件分割为单个单词，re.split() 可以设置多种分隔符tokens = re.split('[ \@\$\/\#\.\-\:\&\*\+\=\[\]\?\!\(\)\{\}\,\'\"\>\_\<\;\%]', email)# 遍历每个分割出来的内容tokenlist = []for token in tokens:# 删除任何非字母数字的字符token = re.sub('[^a-zA-Z0-9]', '', token);# Use the Porter stemmer to 提取词根stemmed = stemmer.stem(token)# 去除空字符串‘’，里面不含任何字符if not len(token): continuetokenlist.append(stemmed)return tokenlist
2.1.1 Vocabulary List(词汇表)
在对邮件进行预处理之后，我们有一个处理后的单词列表。下一步是选择我们想在分类器中使用哪些词，我们需要去除哪些词。
我们有一个词汇表vocab.txt，里面存储了在实际中经常使用的单词，共1899个。
我们要算出处理后的email中含有多少vocab.txt中的单词，并返回在vocab.txt中的index，这就我们想要的训练单词的索引。
def email2VocabIndices(email, vocab):"""提取存在单词的索引"""token = email2TokenList(email)index = [i for i in range(len(vocab)) if vocab[i] in token ]return index
2.2 Extracting Features from Emails
def email2FeatureVector(email):"""将email转化为词向量，n是vocab的长度。存在单词的相应位置的值置为1，其余为0"""df = pd.read_table('data/vocab.txt',names=['words'])vocab = df.as_matrix() # return arrayvector = np.zeros(len(vocab)) # init vectorvocab_indices = email2VocabIndices(email, vocab) # 返回含有单词的索引# 将有单词的索引置为1for i in vocab_indices:vector[i] = 1return vector
vector = email2FeatureVector(email)print('length of vector = {}\nnum of non-zero = {}'.format(len(vector), int(vector.sum())))
length of vector = 1899num of non-zero = 45
2.3 Training SVM for Spam Classification
读取已经训提取好的特征向量以及相应的标签。分训练集和测试集。
# Training setmat1 = loadmat('data/spamTrain.mat')X, y = mat1['X'], mat1['y']# Test setmat2 = scipy.io.loadmat('data/spamTest.mat')Xtest, ytest = mat2['Xtest'], mat2['ytest']
clf = svm.SVC(C=0.1, kernel='linear')clf.fit(X, y)
2.4 Top Predictors for Spam
predTrain = clf.score(X, y)predTest = clf.score(Xtest, ytest)predTrain, predTest
(0.99825, 0.989)
