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\(\langle (x_1, Y_1), \cdots, (x_m, Y_m) \rangle\),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sparkboostscikit-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.

posted @ 2018-10-17 17:29  Treant  阅读(...)  评论(...编辑  收藏