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As a well-established approach, factorization machine (FM) is capable ofautomatically learning high-order interactions among features to makepredictions without the need for manual feature engineering. With the prominentdevelopment of deep neural networks (DNNs), there is a recent and ongoing trendof enhancing the expressiveness of FM-based models with DNNs. However, thoughbetter results are obtained with DNN-based FM variants, such performance gainis paid off by an enormous amount (usually millions) of excessive modelparameters on top of the plain FM. Consequently, the heavy parameterizationimpedes the real-life practicality of those deep models, especially efficientdeployment on resource-constrained IoT and edge devices. In this paper, we movebeyond the traditional real space where most deep FM-based models are defined,and seek solutions from quaternion representations within the hypercomplexspace. Specifically, we propose the quaternion factorization machine (QFM) andquaternion neural factorization machine (QNFM), which are two novel lightweightand memory-efficient quaternion-valued models for sparse predictive analytics.By introducing a brand new take on FM-based models with the notion ofquaternion algebra, our models not only enable expressive inter-componentfeature interactions, but also significantly reduce the parameter size due tolower degrees of freedom in the hypercomplex Hamilton product compared withreal-valued matrix multiplication. Extensive experimental results on threelarge-scale datasets demonstrate that QFM achieves 4.36% performanceimprovement over the plain FM without introducing any extra parameters, whileQNFM outperforms all baselines with up to two magnitudes' parameter sizereduction in comparison to state-of-the-art peer methods.

Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling