论文标题
通过张量产物和大约正规代码的图形嵌入
Graph Embeddings via Tensor Products and Approximately Orthonormal Codes
论文作者
论文摘要
我们提出了一种动态图表示方法，展示其丰富的表示能力并建立其一些理论属性。我们的表示属于高维计算（HDC）中的结合和-AM方法，我们表明张量产物是尊重HDC中使用的叠加原理的最通用的结合操作。我们还建立了一些表征我们方法行为的精确结果，包括记忆与大小分析我们的表示形式的大小必须与边缘数量进行扩展，以保留准确的图形操作。与其HDC根相称，我们还将图形表示与HADAMARD-RADEMACHER方案的另一个典型HDC表示形式进行了比较，这表明这两个图表示具有相同的内存可容量缩放。我们建立了与邻接矩阵的链接，表明我们的方法是邻接矩阵的伪正交概括。鉴于此，我们简要讨论了其针对大型稀疏图的动态压缩表示的应用。
We propose a dynamic graph representation method, showcasing its rich representational capacity and establishing some of its theoretical properties. Our representation falls under the bind-and-sum approach in hyperdimensional computing (HDC), and we show that the tensor product is the most general binding operation that respects the superposition principle employed in HDC. We also establish some precise results characterizing the behavior of our method, including a memory vs. size analysis of how our representation's size must scale with the number of edges in order to retain accurate graph operations. True to its HDC roots, we also compare our graph representation to another typical HDC representation, the Hadamard-Rademacher scheme, showing that these two graph representations have the same memory-capacity scaling. We establish a link to adjacency matrices, showing that our method is a pseudo-orthogonal generalization of adjacency matrices. In light of this, we briefly discuss its applications toward a dynamic compressed representation of large sparse graphs.
