Low-Rank Bilinear Classification: Efficient Convex Optimization and Extensions
Low-Rank Bilinear Classification: Efficient Convex Optimization and Extensions
复制标题
DOI：
10.1007/s11263-014-0709-5
复制
发表时间：
2014-12
影响因子：
19.5
通讯作者：
Takumi Kobayashi
中科院分区：
文献类型：
--
作者：
Takumi Kobayashi
在模式分类中，不仅需要有效地处理特征向量，还需要有效地处理定义为双向数据的特征矩阵，同时保留诸如时空关系等双向结构。特征矩阵的分类器通常以双线性形式表示，由行权重和列权重组成，它们共同产生矩阵权重。从泛化性能和计算成本的角度来看，矩阵的秩应该较低。为此，我们提出了一种基于高效凸优化的低秩双线性分类器。在所提出的方法中，通过最小化分类器（矩阵）的迹范数来优化分类器，以降低秩，而对其没有任何硬约束。我们以易于处理的凸形式表述优化问题，并提供通过全局最优有效解决该问题的程序。此外，我们在多核学习和跨模态学习方面提出了双线性分类器的两种新颖的扩展。通过对双线性方法进行核化，我们自然地引入了一种新颖的多核学习。该方法使用双线性模型以统一的方式将异构再生核希尔伯特空间（RKHS）之间的互核和各个RKHS内的普通核集成为新的判别核。此外，对于跨模态学习，我们考虑将多模态特征映射到公共空间，然后在该空间中进行分类。我们证明了投影和分类由双线性模型共同表示，然后提出了在双线性框架中同时优化两者的方法。在各种视觉分类任务的实验中，所提出的方法与其他方法相比表现出了良好的性能。
In pattern classification, it is needed to efficiently treat not only feature vectors but also feature matrices defined as two-way data, while preserving the two-way structure such as spatio-temporal relationships. The classifier for the feature matrix is generally formulated in a bilinear form composed of row and column weights which jointly result in a matrix weight. The rank of the matrix 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 convex optimization. In the proposed method, the classifier is optimized by minimizing the trace norm of the classifier (matrix) to reduce the rank without any hard constraint on it. We formulate the optimization problem in a tractable convex form and provide the procedure to solve it efficiently with the global optimum. In addition, we propose two novel extensions of the bilinear classifier in terms of multiple kernel learning and cross-modal learning. Through kernelizing the bilinear method, we naturally induce a novel multiple kernel learning. The method integrates both the inter kernels between heterogeneous reproducing kernel Hilbert spaces (RKHSs) and the ordinary kernels within respective RKHSs into a new discriminative kernel in a unified manner using the bilinear model. Besides, for cross-modal learning, we consider to map into the common space the multi-modal features which are subsequently classified in that space. We show that the projection and the classification are jointly represented by the bilinear model, and then propose the method to optimize both of them simultaneously in the bilinear framework. In the experiments on various visual classification tasks, the proposed methods exhibit favorable performances compared to the other methods.