Efficient Optimization for Low-Rank Integrated Bilinear Classifiers
Efficient Optimization for Low-Rank Integrated Bilinear Classifiers
复制标题
DOI：
10.1007/978-3-642-33709-3_34
复制
发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
Takumi Kobayashi;N. Otsu
中科院分区：
文献类型：
--
作者：
Takumi Kobayashi;N. Otsu
在模式分类中，需要有效地处理双向数据（特征矩阵），同时保持双向结构（如时空关系等）。特征矩阵的分类器通常由多个双线性形式组成，从而得到一个矩阵。矩阵的秩，即。从泛化性能和计算成本的角度来看，双线性形式的数量应该较少。为此，我们提出了一种基于高效优化的低秩双线性分类器。在该方法中，通过最小化分类器的迹范数（矩阵）来优化分类器，这有助于在没有任何等级硬约束的情况下实现高效分类器的降阶。将优化问题化为可处理的凸形式，并给出了全局最优的有效求解方法。此外，通过考虑双线性方法的基于核的扩展，我们引入了一种新的多核学习（MKL），称为异构MKL。该方法利用双线性模型，将异质特征之间的内部核和同质特征内部的普通核统一地组合成一个新的判别核。在使用特征阵列、共现特征矩阵和多核的各种分类问题的实验中，与其他方法相比，该方法表现出良好的性能。
In pattern classification, it is needed to efficiently treat two-way data (feature matrices) while preserving the two-way structure such as spatio-temporal relationships,etc. The classifier for the feature matrix is generally formulated by multiple bilinear forms which result in a matrix. The rank of the matrix,i.e., the number of bilinear forms, should be low from the viewpoint of generalization performance and computational cost. For that purpose, we propose a low-rank bilinear classifier based on the efficient optimization. In the proposed method, the classifier is optimized by minimizing the trace norm of the classifier (matrix), which contributes to the rank reduction for an efficient classifier without any hard constraint on the rank. We formulate the optimization problem in a tractable convex form and propose the procedure to solve it efficiently with the global optimum. In addition, by considering a kernel-based extension of the bilinear method, we induce a novel multiple kernel learning (MKL), called heterogeneous MKL. The method combines both inter kernels between heterogeneous types of features and the ordinary kernels within homogeneous features into a new discriminative kernel in a unified manner using the bilinear model. In the experiments on various classification problems using feature arrays, co-occurrence feature matrices, and multiple kernels, the proposed method exhibits favorable performances compared to the other methods.