Support Matrix Machines
Support Matrix Machines
复制标题
DOI：
--
复制
发表时间：
2015-07
期刊：
影响因子：
--
通讯作者：
Luo Luo-Luo;Yubo Xie;Zhihua Zhang;Wu-Jun Li
中科院分区：
文献类型：
--
作者：
Luo Luo-Luo;Yubo Xie;Zhihua Zhang;Wu-Jun Li
在许多分类问题中，如脑电（EEG）分类和图像分类，输入的特征自然表示为矩阵，而不是矢量或标量。通常，原始特征矩阵的结构信息对于诸如分类的数据分析任务是有用的和信息丰富的。一个典型的结构信息是特征矩阵中列或行之间的相关性。为了利用这种结构信息，我们提出了一种新的分类方法，我们称之为支持矩阵机（SMM）。具体地说，SMM被定义为铰链损失加上所谓的谱弹性网惩罚，这是一个传统的弹性网在矩阵上的谱扩展。谱弹性网具有分组效应的性质，即，强相关的列或行倾向于一起被选择或不被选择。由于SMM的优化问题是凸的，这促使我们设计一个交替方向的乘法器（ADMM）算法来解决这个问题。在EEG和图像分类数据上的实验结果表明，该模型比现有的方法具有更好的鲁棒性和有效性。
In many classification problems such as electroencephalogram (EEG) classification and image classification, the input features are naturally represented as matrices rather than vectors or scalars. In general, the structure information of the original feature matrix is useful and informative for data analysis tasks such as classification. One typical structure information is the correlation between columns or rows in the feature matrix. To leverage this kind of structure information, we propose a new classification method that we call support matrix machine (SMM). Specifically, SMM is defined as a hinge loss plus a so-called spectral elastic net penalty which is a spectral extension of the conventional elastic net over a matrix. The spectral elastic net enjoys a property of grouping effect, i.e., strongly correlated columns or rows tend to be selected altogether or not. Since the optimization problem for SMM is convex, this encourages us to devise an alternating direction method of multipliers (ADMM) algorithm for solving the problem. Experimental results on EEG and image classification data show that our model is more robust and efficient than the state-of-the-art methods.