Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.

中文翻译：

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$ FM ^ 2 $：推荐系统的现场矩阵分解机

点击率（CTR）预测在推荐系统和在线广告中起着至关重要的作用。这些应用程序中使用的数据是多字段分类数据，其中每个要素都属于一个字段。现场信息被证明是重要的，并且在其模型中有几项考虑了现场的工作。在本文中，我们提出了一种新颖有效的方法来对现场信息建模。所提出的方法是FwFM的直接改进，被称为场矩阵分解机（FmFM或$ FM ^ 2 $）。我们还对FmFM框架内的FM和FwFM提出了新的解释，并将其与FFM进行了比较。除了修剪交叉项外，我们的模型还支持嵌入向量的特定于字段的可变维，这可用作软修剪。我们还提出了一种在保持模型性能的同时最小化尺寸的有效方法。还可以通过缓存中间向量来进一步优化FmFM模型，并且只需花费数千个浮点运算（FLOP）即可进行预测。我们的实验结果表明，它可以胜过FFM，后者更为复杂。FmFM模型的性能也可以与DNN模型相媲美，后者在运行时需要更多的FLOP。