1. 算法

多标签分类的适用场景较为常见，比如，一份歌单可能既属于标签旅行也属于标签驾车。有别于多分类分类，多标签分类中每个标签不是互斥的。多标签分类算法大概有两类流派：

• 采用One-vs-Rest（或其他方法）组合多个二分类基分类器；
• 改造经典的单分类器，比如，AdaBoost-MH与ML-KNN。

One-vs-Rest

基本思想：为每一个标签\(y_i\)构造一个二分类器，正样本为含有标签\(y_i\)的实例，负样本为不含有标签\(y_i\)的实例；最后组合N个二分类器结果得到N维向量，可视作为在多标签上的得分。我实现一个Spark版本MultiLabelOneVsRest，源代码见。

AdaBoost-MH

AdaBoost-MH算法是由Schapire（AdaBoost算法作者）与Singer提出，基本思想与AdaBoost算法类似：自适应地调整样本-类别的分布权重。对于训练样本\(\langle (x_1, Y_1), \cdots, (x_m, Y_m) \rangle\)，任意一个实例 \(x_i \in \mathcal{X}\)，标签类别\(Y_i \subseteq \mathcal{Y}\)，算法流程如下：

其中，\(D_t(i, \ell)\)表示在t次迭代实例\(x_i\)对应标签\(\ell\)的权重，\(Y[\ell]\)标识标签\(\ell\)是否属于实例\((x, Y)\)，若属于则为+1，反之为-1（增加样本标签的权重）；即

\[ Y[\ell] = \left \{ { \matrix { {+1} & {\ell \in Y} \cr {-1} & {\ell \notin Y} \cr } } \right. \]

\(Z_t\)为每一次迭代的归一化因子，保证权重分布矩阵\(D\)的所有权重之和为1，

\[ Z_t = \sum_{i=1}^{m} \sum_{\ell \in \mathcal{Y}} D_{t}(i, \ell) \exp \large{(}-\alpha_{t} Y_i[\ell] h_t(x_i, \ell) \large{)} \]

ML-KNN

ML-KNN (multi-label K nearest neighbor)基于KNN算法，已知K近邻的标签信息，通过最大后验概率（Maximum A Posteriori）估计实例\(t\)是否应打上标签\(\ell\)，

\[ y_t(\ell) = \mathop{ \arg \max}_{b \in \{0,1\}} P(H_b^{\ell} | E_{C_t(\ell)}^{\ell} ) \]

其中，\(H_0^{\ell}\)表示实例\(t\)不应打上标签\(\ell\)，\(H_1^{\ell}\)则表示应被打上；\(E_{C_t(\ell)}^{\ell}\) 表示实例\(t\)的K近邻中拥有标签\(\ell\)的实例数为\(C_t(\ell)\)。上述式子可有贝叶斯定理求解：

\[ y_t(\ell) = \mathop{ \arg \max}_{b \in \{0,1\}} P(H_b^{\ell}) P(E_{C_t(\ell)}^{\ell} | H_b^{\ell} ) \]

上面两项计算细节见论文[2].

2. 实验

AdaBoost.MH算法Spark实现见，实现ML-KNN算法。我在数据集上做了几个算法的对比实验，结果如下：

算法	Hamming loss	Precision	Recall	F1 Measure
LR+OvR	0.0569	0.6252	0.5586	0.5563
AdaBoost.MH	0.0587	0.6280	0.6082	0.5837
ML-KNN	0.0652	0.6204	0.6535	0.5977

此外，提供了众多数据集，Kaggle也有多标签分类的比赛。

实验部分代码如下：

import numpy as npfrom sklearn import metricsfrom sklearn.datasets import load_svmlight_filefrom sklearn.linear_model import LogisticRegressionfrom sklearn.multiclass import OneVsRestClassifierfrom sklearn.preprocessing import MultiLabelBinarizer# load svm fileX_train, y_train = load_svmlight_file('tmc2007_train.svm', dtype=np.float64, multilabel=True)X_test, y_test = load_svmlight_file('tmc2007_test.svm', dtype=np.float64, multilabel=True)# convert multi labels to binary matrixmb = MultiLabelBinarizer()y_train = mb.fit_transform(y_train)y_test = mb.fit_transform(y_test)# LR + OvRclf = OneVsRestClassifier(LogisticRegression(), n_jobs=10)clf.fit(X_train, y_train)y_pred = clf.predict(X_test)# multilabel classification metricsloss = metrics.hamming_loss(y_test, y_pred)prf = metrics.precision_recall_fscore_support(y_test, y_pred, average='samples')"""ML-KNN for multilabel classification"""from skmultilearn.adapt import MLkNNclf = MLkNN(k=15)clf.fit(X_train, y_train)y_pred = clf.predict(X_test)

// AdaBoost.MH for multilabel classificationval labels0Based = trueval binaryProblem = falseval learner = new AdaBoostMHLearner(sc)learner.setNumIterations(params.numIterations) // 500 iterlearner.setNumDocumentsPartitions(params.numDocumentsPartitions)learner.setNumFeaturesPartitions(params.numFeaturesPartitions)learner.setNumLabelsPartitions(params.numLabelsPartitions)val classifier = learner.buildModel(params.input, labels0Based, binaryProblem)val testPath = "./tmc2007_test.svm"val numRows = DataUtils.getNumRowsFromLibSvmFile(sc, testPath)val testRdd = DataUtils.loadLibSvmFileFormatDataAsList(sc, testPath, labels0Based, binaryProblem, 0, numRows, -1);val results = classifier.classifyWithResults(sc, testRdd, 20)val predAndLabels = sc.parallelize(predLabels.zip(goldLabels)  .map(t => {    (t._1.map(e => e.toDouble), t._2.map(e => e.toDouble))  }))val metrics = new MultilabelMetrics(predAndLabels)

3. 参考文献

[1] Schapire, Robert E., and Yoram Singer. "BoosTexter: A boosting-based system for text categorization." Machine learning 39.2-3 (2000): 135-168.

[2] Zhang, Min-Ling, and Zhi-Hua Zhou. "ML-KNN: A lazy learning approach to multi-label learning." Pattern recognition 40.7 (2007): 2038-2048.

[3] .