Robust multicategory support matrix machines
Robust multicategory support matrix machines
复制标题
强大的多类别支持矩阵机器
DOI：
10.1007/s10107-019-01386-z
复制
发表时间：
2019
影响因子：
2.7
通讯作者：
Liu, Yufeng
中科院分区：
文献类型：
--
作者：
Qian, Chengde;Tran-Dinh, Quoc;Fu, Sheng;Zou, Changliang;Liu, Yufeng
我们考虑的分类问题时，输入功能表示为矩阵，而不是向量。为了保留用于分类的固有结构，一种成功的方法是Luo等人（在：Proceedings of the 32 nd international conference on machine learning，里尔，法国，第1期，第938-947页，2015年）中的支持矩阵机（SMM），其利用铰链损失加上所谓的谱弹性网罚分来优化目标函数。然而，将SMM扩展到多类别分类的问题仍然存在。此外，在实践中，经常会看到训练数据被离群观测值污染，这会影响现有矩阵分类方法的鲁棒性。在本文中，我们解决这些问题，通过引入一个强大的角度为基础的分类器，它归结为一个统一的框架，二进制和多类别的问题。受益于截断铰链损失函数的使用，该分类器实现了一定的鲁棒性离群值。底层的优化模型变得非凸，但承认一个自然的DC（两个凸函数的差异）表示。我们开发了一个新的和有效的算法，结合DC算法和原始对偶一阶方法。建议的DC算法自适应地选择在每次迭代的子问题的精度，同时保证算法的整体收敛性。原始对偶方法的使用消除了子问题中线性算子的自然复杂性，并使我们能够使用目标函数的近似算子和矩阵向量运算。这种优势使我们能够有效地解决大规模问题。理论和数值结果表明，对于具有潜在离群点的问题，我们的方法可以在现有的方法中具有很强的竞争力。
We consider the classification problem when the input features are represented as matrices rather than vectors. To preserve the intrinsic structures for classification, a successful method is the support matrix machine (SMM) in Luo et al. (in: Proceedings of the 32nd international conference on machine learning, Lille, France, no 1, pp 938–947, 2015), which optimizes an objective function with a hinge loss plus a so-called spectral elastic net penalty. However, the issues of extending SMM to multicategory classification still remain. Moreover, in practice, it is common to see the training data contaminated by outlying observations, which can affect the robustness of existing matrix classification methods. In this paper, we address these issues by introducing a robust angle-based classifier, which boils down binary and multicategory problems to a unified framework. Benefitting from the use of truncated hinge loss functions, the proposed classifier achieves certain robustness to outliers. The underlying optimization model becomes nonconvex, but admits a natural DC (difference of two convex functions) representation. We develop a new and efficient algorithm by incorporating the DC algorithm and primal–dual first-order methods together. The proposed DC algorithm adaptively chooses the accuracy of the subproblem at each iteration while guaranteeing the overall convergence of the algorithm. The use of primal–dual methods removes a natural complexity of the linear operator in the subproblems and enables us to use the proximal operator of the objective functions, and matrix–vector operations. This advantage allows us to solve large-scale problems efficiently. Theoretical and numerical results indicate that for problems with potential outliers, our method can be highly competitive among existing methods.
DOI：
10.1016/b978-0-12-386908-1.00037-9
发表时间：
2018-11
期刊：
Wiley Series in Probability and Statistics
影响因子：
--
作者：
Bruce E. Blaine
通讯作者：
Bruce E. Blaine
影响因子：
2.2
作者：
Quoc Tran-Dinh
通讯作者：
Quoc Tran-Dinh