论文标题
基础：批处理光谱嵌入空间
BASiS: Batch Aligned Spectral Embedding Space
论文作者
论文摘要
图是一种高度通用和多样的表示，几乎适用于任何数据处理问题。光谱图理论已显示出以实体线性代数理论为支持的强大算法。因此，设计具有光谱图特征的深网络构建块可能非常有用。例如，这样的网络允许设计用于某些任务的最佳图形或获得数据的规范性低维嵌入。解决此问题的最新尝试是基于最大程度地减少雷利（Rayleigh）质量型损失。我们提出了一种直接学习本特征的不同方法。在批处理学习中应用的直接方法的一个严重问题是将特征映射到不同批处理中特征空间坐标的不一致。我们使用批处理分析了学习此任务的自由度，并提出了一种稳定的对齐机制，该机制可以与批处理变化和图形变化一起使用。我们表明，与SOTA相比，在NMI，ACC，Grassman距离，正交性和分类精度方面，我们学到的光谱嵌入更好。此外，学习更加稳定。
Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely instrumental to design deep network building blocks with spectral graph characteristics. For instance, such a network allows the design of optimal graphs for certain tasks or obtaining a canonical orthogonal low-dimensional embedding of the data. Recent attempts to solve this problem were based on minimizing Rayleigh-quotient type losses. We propose a different approach of directly learning the eigensapce. A severe problem of the direct approach, applied in batch-learning, is the inconsistent mapping of features to eigenspace coordinates in different batches. We analyze the degrees of freedom of learning this task using batches and propose a stable alignment mechanism that can work both with batch changes and with graph-metric changes. We show that our learnt spectral embedding is better in terms of NMI, ACC, Grassman distance, orthogonality and classification accuracy, compared to SOTA. In addition, the learning is more stable.
