多距离支持矩阵机
Multi-distance Support Matrix Machines
摘要：
真实世界的数据，如数字图像，MRI扫描和脑电图信号，自然表示为具有结构信息的矩阵。大多数现有的分类器旨在通过将回归矩阵正则化为低秩或稀疏来捕获这些结构。其他一些方法引入因子分解技术来探索核空间中矩阵数据的非线性关系。在本文中，我们提出了一个多距离支持矩阵机（MDSMM），它提供了一个原则性的方法来解决矩阵分类问题。引入多距离，通过输入数据的行和列中的内在信息来捕获矩阵数据内的相关性。在这些值上建立复超平面以分离不同的类。进一步研究了独立同分布的泛化界。过程和非i.i.d.基于SVM和SMM分类器的过程。对于矩阵范数受限的典型假设类，MDSMM实现了比传统分类器更快的学习速度。我们还为没有先验知识的样本提供了一种更通用的方法。我们证明了所提出的方法的优点进行详尽的实验模拟研究和一些真实的字数据集。
英文摘要：
Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression matrix to be low-rank or sparse. Some other methodologies introduce factorization technique to explore nonlinear relationships of matrix data in kernel space. In this paper, we propose a multi-distance support matrix machine (MDSMM), which provides a principled way of solving matrix classification problems. The multi-distance is introduced to capture the correlation within matrix data, by means of intrinsic information in rows and columns of input data. A complex hyperplane is established upon these values to separate distinct classes. We further study the generalization bounds for i.i.d. processes and non i.i.d. process based on both SVM and SMM classifiers. For typical hypothesis classes where matrix norms are constrained, MDSMM achieves a faster learning rate than traditional classifiers. We also provide a more general approach for samples without prior knowledge. We demonstrate the merits of the proposed method by conducting exhaustive experiments on both simulation study and a number of real-word datasets.
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