Support matrix machine (SMM) is an efficient matrix classification method that can leverage the structure information within the matrix to improve the classification performance. However, its computational and storage costs are still expensive for high-dimensional data. To address these problems, in this paper, we consider a 2D compressed learning paradigm to learn the SMM classifier in some compressed data domain. Specifically, we use the Kronecker compressed sensing (KCS) to obtain the compressive measurements and learn the SMM classifier. We show that the Kronecker product measurement matrices used by KCS satisfies the restricted isometry property (RIP), which is a property to ensure the learnability of the compressed data. We further give a lower bound on the number of measurements required for KCS. Though this lower bound shows that KCS requires more measurements than the regular CS to satisfy the same RIP condition, KCS itself still enjoys lower computational and storage complexities. Then, using the RIP condition, we verify that the learned SMM classifier in the compressed domain can perform almost as well as the best linear classifier in the original uncompressed domain. Finally, our experimental results also demonstrate the feasibility of 2D compressed learning.

中文翻译：

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2D 压缩学习：支持带有双线性随机投影的矩阵机

支持矩阵机（SMM）是一种有效的矩阵分类方法，可以利用矩阵内的结构信息来提高分类性能。然而，它的计算和存储成本对于高维数据来说仍然很昂贵。为了解决这些问题，在本文中，我们考虑了一种二维压缩学习范式来学习某些压缩数据域中的 SMM 分类器。具体来说，我们使用 Kronecker 压缩感知 (KCS) 来获取压缩测量值并学习 SMM 分类器。我们表明 KCS 使用的 Kronecker 乘积测量矩阵满足受限等距特性 (RIP)，这是确保压缩数据的可学习性的特性。我们进一步给出了 KCS 所需测量次数的下限。尽管这个下限表明 KCS 比常规 CS 需要更多的测量才能满足相同的 RIP 条件，但 KCS 本身的计算和存储复杂性仍然较低。然后，使用 RIP 条件，我们验证了在压缩域中学习的 SMM 分类器的性能几乎与原始未压缩域中的最佳线性分类器一样好。最后，我们的实验结果也证明了二维压缩学习的可行性。