用数值方法将核函数映射到高维计算，提升模型准确率
Bridging the Gap Between Hyperdimensional Computing and Kernel Methods via the Nyström Method
- 基于奈斯特伦方法构建数据到高维空间的映射
- 在图与字符串数据上分别提升11%和17%分类准确率
- 可复用现有相似度函数，拓展高维计算应用场景
高维计算（HDC）是一种源自认知科学的数据处理方法，通过将数据表示为高维随机向量来完成信息处理任务。该方法具有严格的数学基础，且易于在能效高、高度并行的硬件（如FPGA和存算一体架构）上实现。HDC在机器学习中的表现很大程度上取决于原始数据如何映射到高维空间。本文提出NysHD，一种基于核近似文献中奈斯特伦方法的新映射构造方法。该方法提供了一种简单方案，可将任意用户定义的半正定相似度函数转化为等价的HDC映射。现有大量关于学习问题中相似度函数的设计研究，本方法使其可直接引入到HDC框架中，从而扩展了HDC可解决的问题类型。实证评估表明，相较于现有HDC编码方法，NysHD在图数据集和字符串数据集上平均分别获得11%和17%的分类准确率提升。
原文摘要 · Abstract (English)
Hyperdimensional computing (HDC) is an approach from the cognitive science literature for solving information processing tasks using data represented as high-dimensional random vectors. The technique has a rigorous mathematical backing, and is easy to implement in energy-efficient and highly parallel hardware like FPGAs and "processing-in-memory" architectures. The effectiveness of HDC in machine learning largely depends on how raw data is mapped to high-dimensional space. In this work, we propose NysHD, a new method for constructing this mapping that is based on the Nyström method from the literature on kernel approximation. Our approach provides a simple recipe to turn any user-defined positive-semidefinite similarity function into an equivalent mapping in HDC. There is a vast literature on the design of such functions for learning problems. Our approach provides a mechanism to import them into the HDC setting, expanding the types of problems that can be tackled using HDC. Empirical evaluation against existing HDC encoding methods shows that NysHD can achieve, on average, 11% and 17% better classification accuracy on graph and string datasets respectively.
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