四元数分解机：复杂特征交互建模的轻量级解决方案
Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling
摘要：
作为一种成熟的方法，因子分解机（FM）能够自动学习特征之间的高阶交互来进行预测，而不需要手动特征工程。随着深度神经网络（DNN）的显著发展，最近有一种趋势是用DNN增强基于FM的模型的表达能力。然而，尽管使用基于DNN的FM变体可以获得更好的结果，但这种性能增益是通过在普通FM之上的大量（通常是数百万）过多模型参数来获得的。因此，大量的参数化阻碍了这些深度模型在现实生活中的实用性，特别是在资源受限的物联网和边缘设备上的有效部署。在本文中，我们超越了传统的实空间，其中大多数深FM为基础的模型定义，并寻求解决方案，从超复杂空间内的四元数表示。具体来说，我们提出了四元数因子分解机（QFM）和四元数神经因子分解机（QNFM），这是两种新的轻量级和内存高效的四元数值模型稀疏预测分析。通过引入一个全新的采取FM为基础的模型与四元数代数的概念，我们的模型不仅能够表达组件间的功能相互作用，但也显着减少了参数的大小，由于较低的自由度在超复杂的汉密尔顿产品相比，实值矩阵乘法。在三个大规模数据集上的大量实验结果表明，QFM在不引入任何额外参数的情况下，比普通FM性能提高了4.36%，而QNFM的性能优于所有基线，与最先进的同行方法相比，参数大小减少了两个数量级。
英文摘要：
As a well-established approach, factorization machine (FM) is capable of automatically learning high-order interactions among features to make predictions without the need for manual feature engineering. With the prominent development of deep neural networks (DNNs), there is a recent and ongoing trend of enhancing the expressiveness of FM-based models with DNNs. However, though better results are obtained with DNN-based FM variants, such performance gain is paid off by an enormous amount (usually millions) of excessive model parameters on top of the plain FM. Consequently, the heavy parameterization impedes the real-life practicality of those deep models, especially efficient deployment on resource-constrained IoT and edge devices. In this paper, we move beyond the traditional real space where most deep FM-based models are defined, and seek solutions from quaternion representations within the hypercomplex space. Specifically, we propose the quaternion factorization machine (QFM) and quaternion neural factorization machine (QNFM), which are two novel lightweight and memory-efficient quaternion-valued models for sparse predictive analytics. By introducing a brand new take on FM-based models with the notion of quaternion algebra, our models not only enable expressive inter-component feature interactions, but also significantly reduce the parameter size due to lower degrees of freedom in the hypercomplex Hamilton product compared with real-valued matrix multiplication. Extensive experimental results on three large-scale datasets demonstrate that QFM achieves 4.36% performance improvement over the plain FM without introducing any extra parameters, while QNFM outperforms all baselines with up to two magnitudes' parameter size reduction in comparison to state-of-the-art peer methods.
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