A machine learning (ML) feature network is a graph that connects ML features in learning tasks based on their similarity. This network representation allows us to view feature vectors as functions on the network. By leveraging function operations from Fourier analysis and from functional analysis, one can easily generate new and novel features, making use of the graph structure imposed on the feature vectors. Such network structures have previously been studied implicitly in image processing and computational biology. We thus describe feature networks as graph structures imposed on feature vectors, and provide applications in machine learning. One application involves graph-based generalizations of convolutional neural networks, involving structured deep learning with hierarchical representations of features that have varying depth or complexity. This extends also to learning algorithms that are able to generate useful new multilevel features. Additionally, we discuss the use of feature networks to engineer new features, which can enhance the expressiveness of the model. We give a specific example of a deep tree-structured feature network, where hierarchical connections are formed through feature clustering and feed-forward learning. This results in low learning complexity and computational efficiency. Unlike "standard" neural features which are limited to modulated (thresholded) linear combinations of adjacent ones, feature networks offer more general feedforward dependencies among features. For example, radial basis functions or graph structure-based dependencies between features can be utilized.

翻译：机器学习(ML)特征网络是一个基于特征相似性连接学习任务中ML特征的图结构。这种网络表示允许我们将特征向量视为网络上的函数。通过利用傅里叶分析和泛函分析中的函数运算，可以基于施加在特征向量上的图结构轻松生成新颖特征。此类网络结构此前已在图像处理和计算生物学领域被隐性研究。因此，我们将特征网络描述为施加在特征向量上的图结构，并提供其在机器学习中的应用。一项应用涉及卷积神经网络的图基泛化，通过具有不同深度或复杂度的特征分层表示实现结构化深度学习。该应用还可扩展至能够生成有用新型多层次特征的学习算法。此外，我们讨论了利用特征网络设计新特征以增强模型表达能力的方法。我们给出一个深度树状结构特征网络的具体实例，其中通过特征聚类和前馈学习形成层次连接，从而实现低学习复杂度和高计算效率。与局限于相邻特征调制(阈值化)线性组合的"标准"神经特征不同，特征网络支持特征间更通用的前馈依赖关系。例如，可利用径向基函数或基于图结构的特征依赖关系。