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.
In contrast to the above methods, we develop a pretreatment for those algorithms. The following three approaches are relevant to ours. Label Partitioning for Sub-linear Ranking (LPSR) follows a two-step approach. At the training stage, it clusters the training instances, and then assigns a fixed number of potential labels to each cluster. At the testing stage, a test instance is first put in one of the clusters, and its labels are predicted only from the labels attached to that cluster @cite_19 . While LPSR and our proposal stand on the same testing stage, three differences can be observed at the training stage. First, the optimized number of clusters in our method is selected by the algorithm, whereas the number in LPSR is predefined. Second, cardinality of our label clusters may vary across clusters, while the number of potential labels in each cluster in LPSR is fixed. Moreover, our instance and label clusters are updated via optimization, whereas assignment of training instances in LPSR solely depends on feature matrix. Consequently, our method permits more flexibility in cluster structure.
@cite_19
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Like other machine learning paradigms, multi-label learning also suffers from the curse of dimensionality problem. Multi-label dimensionality reduction can alleviate the problem but they generally ask for sufficient labeled samples. Nevertheless, we often may only have scarce labeled samples and abundant unlabeled samples. In this paper, we propose a @math emi-supervised @math ulti-label @math imensionality @math eduction based on @math ependence @math aximization approach (SMDRdm in short). SDMRdm assumes the semantic similarity and feature similarity of multi-label samples are inter-depended. SMDRdm first applies label propagation on a neighborhood graph composed with labeled and unlabeled samples to obtain the soft labels of unlabeled samples, and then measures the semantic similarity between all the training samples (including unlabeled ones) based on these soft labels and available labels of labeled samples. Next, it measures the feature similarity between samples in the subspace projected by the target projective matrix, instead of the original high-dimensional feature space. After that, it maximizes the dependence between these two types of similarities and incorporates the dependence into linear discriminant analysis to optimize the target projective matrix. Experiments on publicly accessible multi-label data sets demonstrate that SMDRdm achieves more prominent results than other related approaches across various evaluation metrics. In addition, the empirical study also shows the semantic similarity between samples derived from soft labels works better than that derived from scarce available labels. Supervised contour detection methods usually require many labeled training images to obtain satisfactory performance. However, a large set of annotated data might be unavailable or extremely labor intensive. In this paper, we investigate the usage of semi-supervised learning (SSL) to obtain competitive detection accuracy with very limited training data (three labeled images). Specifically, we propose a semi-supervised structured ensemble learning approach for contour detection built on structured random forests (SRF). To allow SRF to be applicable to unlabeled data, we present an effective sparse representation approach to capture inherent structure in image patches by finding a compact and discriminative low-dimensional subspace representation in an unsupervised manner, enabling the incorporation of abundant unlabeled patches with their estimated structured labels to help SRF perform better node splitting. We re-examine the role of sparsity and propose a novel and fast sparse coding algorithm to boost the overall learning efficiency. To the best of our knowledge, this is the first attempt to apply SSL for contour detection. Extensive experiments on the BSDS500 segmentation dataset and the NYU Depth dataset demonstrate the superiority of the proposed method. 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. 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.