Extreme multi-label classification aims to learn a classifier that annotates an instance with a relevant subset of labels from an extremely large label set. Many existing solutions embed the label matrix to a low-dimensional linear subspace, or examine the relevance of a test instance to every label via a linear scan. In practice, however, those approaches can be computationally exorbitant. To alleviate this drawback, we propose a Block-wise Partitioning (BP) pretreatment that divides all instances into disjoint clusters, to each of which the most frequently tagged label subset is attached. One multi-label classifier is trained on one pair of instance and label clusters, and the label set of a test instance is predicted by first delivering it to the most appropriate instance cluster. Experiments on benchmark multi-label data sets reveal that BP pretreatment significantly reduces prediction time, and retains almost the same level of prediction accuracy.
Most state-of-the-art methods for extreme multi-label classification can be trichotomized to tree-based, embedding-based and polished one-versus-all approaches. The first branch learns a hierarchical structure of the full label set by recursively dividing feature or label spaces. For instance, FastXML @cite_14 searches for a sparse linear separator to split each node by optimizing an nDCG based loss function. The second branch reduces the effective number of labels under the low-rank assumption. For example, LEML @cite_13 directly optimizes for the decompression matrices using a regularized least square objective function in a generic empirical risk minimization framework. PD-Sparse @cite_4 and DiSMEC @cite_11 are two methods in the third trend that attract considerable attention in the literature. PD-Sparse makes use of both primal and dual sparsity by margin-maximizing loss with @math and @math penalties. DiSMEC revisits one-versus-all paradigm and provides prominent boosts in prediction accuracy and prediction time by explicitly inducing sparsity and doubly parallel training.
@cite_14 @cite_13 @cite_4 @cite_11
2068074736 2461743311 2520348554 2743021690
The objective in extreme multi-label classification is to learn a classifier that can automatically tag a data point with the most relevant subset of labels from a large label set. Extreme multi-label classification is an important research problem since not only does it enable the tackling of applications with many labels but it also allows the reformulation of ranking problems with certain advantages over existing formulations. Our objective, in this paper, is to develop an extreme multi-label classifier that is faster to train and more accurate at prediction than the state-of-the-art Multi-label Random Forest (MLRF) algorithm [2] and the Label Partitioning for Sub-linear Ranking (LPSR) algorithm [35]. MLRF and LPSR learn a hierarchy to deal with the large number of labels but optimize task independent measures, such as the Gini index or clustering error, in order to learn the hierarchy. Our proposed FastXML algorithm achieves significantly higher accuracies by directly optimizing an nDCG based ranking loss function. We also develop an alternating minimization algorithm for efficiently optimizing the proposed formulation. Experiments reveal that FastXML can be trained on problems with more than a million labels on a standard desktop in eight hours using a single core and in an hour using multiple cores. We consider Multiclass and Multilabel classification with extremely large number of classes, of which only few are labeled to each instance. In such setting, standard methods that have training, prediction cost linear to the number of classes become intractable. State-of-the-art methods thus aim to reduce the complexity by exploiting correlation between labels under assumption that the similarity between labels can be captured by structures such as low-rank matrix or balanced tree. However, as the diversity of labels increases in the feature space, structural assumption can be easily violated, which leads to degrade in the testing performance. In this work, we show that a margin-maximizing loss with l1 penalty, in case of Extreme Classification, yields extremely sparse solution both in primal and in dual without sacrificing the expressive power of predictor. We thus propose a Fully-Corrective Block-Coordinate Frank-Wolfe (FC-BCFW) algorithm that exploits both primal and dual sparsity to achieve a complexity sublinear to the number of primal and dual variables. A bi-stochastic search method is proposed to further improve the efficiency. In our experiments on both Multiclass and Multilabel problems, the proposed method achieves significant higher accuracy than existing approaches of Extreme Classification with very competitive training and prediction time. Extreme multi-label classification refers to supervised multi-label learning involving hundreds of thousands or even millions of labels. Datasets in extreme classification exhibit fit to power-law distribution, i.e. a large fraction of labels have very few positive instances in the data distribution. Most state-of-the-art approaches for extreme multi-label classification attempt to capture correlation among labels by embedding the label matrix to a low-dimensional linear sub-space. However, in the presence of power-law distributed extremely large and diverse label spaces, structural assumptions such as low rank can be easily violated. In this work, we present DiSMEC, which is a large-scale distributed framework for learning one-versus-rest linear classifiers coupled with explicit capacity control to control model size. Unlike most state-of-the-art methods, DiSMEC does not make any low rank assumptions on the label matrix. Using double layer of parallelization, DiSMEC can learn classifiers for datasets consisting hundreds of thousands labels within few hours. The explicit capacity control mechanism filters out spurious parameters which keep the model compact in size, without losing prediction accuracy. We conduct extensive empirical evaluation on publicly available real-world datasets consisting upto 670,000 labels. We compare DiSMEC with recent state-of-the-art approaches, including - SLEEC which is a leading approach for learning sparse local embeddings, and FastXML which is a tree-based approach optimizing ranking based loss function. On some of the datasets, DiSMEC can significantly boost prediction accuracies - 10 better compared to SLECC and 15 better compared to FastXML, in absolute terms. Extreme Classification comprises multi-class or multi-label prediction where there is a large number of classes, and is increasingly relevant to many real-world applications such as text and image tagging. In this setting, standard classification methods, with complexity linear in the number of classes, become intractable, while enforcing structural constraints among classes (such as low-rank or tree-structure) to reduce complexity often sacrifices accuracy for efficiency. The recent PD-Sparse method addresses this via an algorithm that is sub-linear in the number of variables, by exploiting primal-dual sparsity inherent in a specific loss function, namely the max-margin loss. In this work, we extend PD-Sparse to be efficiently parallelized in large-scale distributed settings. By introducing separable loss functions, we can scale out the training, with network communication and space efficiency comparable to those in one-versus-all approaches while maintaining an overall complexity sub-linear in the number of classes. On several large-scale benchmarks our proposed method achieves accuracy competitive to the state-of-the-art while reducing the training time from days to tens of minutes compared with existing parallel or sparse methods on a cluster of 100 cores.