Dot-product kernels is a large family of kernel functions based on dot-product between examples. A recent result states that any dot-product kernel can be decomposed as a non-negative linear combination of homogeneous polynomial kernels of different degrees, and it is possible to learn the coefficients of the combination by exploiting the Multiple Kernel Learning (MKL) paradigm. In this paper it is proved that, under mild conditions, any homogeneous polynomial kernel defined on binary valued data can be decomposed in a parametrized finite linear non-negative combination of monotone conjunctive kernels. MKL has been employed to learn the parameters of the combination. Furthermore, we show that our solution produces a deep kernel whose feature space consists of hierarchically organized features of increasing complexity. We also emphasize the connection between our solution and existing deep kernel learning frameworks. A wide empirical assessment is presented to evaluate the proposed framework, and to compare it against the baselines on several categorical and binary datasets.

点积内核是基于示例之间的点积的大量内核函数系列。最近的结果表明，任何点积核都可以分解为不同程度的齐次多项式核的非负线性组合，并且可以通过利用多核学习（MKL）范式来学习组合的系数。本文证明，在温和的条件下，在二进制值数据上定义的任何齐次多项式核都可以分解为单调联合核的参数化有限线性非负组合。MKL已被用来学习组合的参数。此外，我们证明了我们的解决方案产生了一个深层内核，其特征空间由层次结构化的，日益复杂的特征组成。我们还强调了我们的解决方案与现有的深度内核学习框架之间的联系。提出了广泛的经验评估，以评估所提出的框架，并将其与几个分类和二进制数据集上的基线进行比较。