多标签分类

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mllibX。

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) angle)，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 otin Y} cr } } ight. ]

(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sparkboost，scikit-multilearn实现ML-KNN算法。我在siam-competition2007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，Mulan提供了众多数据集，Kaggle也有多标签分类的比赛WISE 2014。

实验部分代码如下：

import numpy as np
from sklearn import metrics
from sklearn.datasets import load_svmlight_file
from sklearn.linear_model import LogisticRegression
from sklearn.multiclass import OneVsRestClassifier
from sklearn.preprocessing import MultiLabelBinarizer

# load svm file
X_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 matrix
mb = MultiLabelBinarizer()
y_train = mb.fit_transform(y_train)
y_test = mb.fit_transform(y_test)

# LR + OvR
clf = OneVsRestClassifier(LogisticRegression(), n_jobs=10)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)

# multilabel classification metrics
loss = 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 MLkNN

clf = MLkNN(k=15)
clf.fit(X_train, y_train)
y_pred = clf.predict(X_test)

// AdaBoost.MH for multilabel classification
val labels0Based = true
val binaryProblem = false

val learner = new AdaBoostMHLearner(sc)
learner.setNumIterations(params.numIterations) // 500 iter
learner.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] 基于PredictionIO的推荐引擎打造，及大规模多标签分类探索.