Block coordinate descent algorithms for large-scale sparse multiclass classification

• Published in: Machine learning Vol. 93; no. 1; pp. 31 - 52
• Main Authors: Blondel, Mathieu, Seki, Kazuhiro, Uehara, Kuniaki
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Boston Springer US 01.10.2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Blocking; Classification; Computer Science; Computer science; control theory; systems; Control; Data processing. List processing. Character string processing; Descent; Exact sciences and technology; Mathematical models; Mechatronics; Memory organisation. Data processing; Natural Language Processing (NLP); Regression; Regularization; Robotics; Simulation and Modeling; Software; Solvers; Group sparsity; Multiclass classification; Block coordinate descent; Data analysis; Coordinate system; Modeling; Optimization; Logistic regression; Multidimensional analysis; Descent method; Selection criterion; Sparse representation; Large scale; Document analysis; Multiple classification
• ISSN: 0885-6125; 1573-0565
• DOI: 10.1007/s10994-013-5367-2

Over the past decade, ℓ 1 regularization has emerged as a powerful way to learn classifiers with implicit feature selection. More recently, mixed-norm (e.g., ℓ 1 / ℓ 2 ) regularization has been utilized as a way to select entire groups of features. In this paper, we propose a novel direct multiclass formulation specifically designed for large-scale and high-dimensional problems such as document classification. Based on a multiclass extension of the squared hinge loss, our formulation employs ℓ 1 / ℓ 2 regularization so as to force weights corresponding to the same features to be zero across all classes, resulting in compact and fast-to-evaluate multiclass models. For optimization, we employ two globally-convergent variants of block coordinate descent, one with line search (Tseng and Yun in Math. Program. 117:387–423, 2009 ) and the other without (Richtárik and Takáč in Math. Program. 1–38, 2012a ; Tech. Rep. arXiv:1212.0873 , 2012b ). We present the two variants in a unified manner and develop the core components needed to efficiently solve our formulation. The end result is a couple of block coordinate descent algorithms specifically tailored to our multiclass formulation. Experimentally, we show that block coordinate descent performs favorably compared to other solvers such as FOBOS, FISTA and SpaRSA. Furthermore, we show that our formulation obtains very compact multiclass models and outperforms ℓ 1 / ℓ 2 -regularized multiclass logistic regression in terms of training speed, while achieving comparable test accuracy.