论文标题
几何布尔张量分解
Geometric All-Way Boolean Tensor Decomposition
论文作者
论文摘要
布尔张量已广泛用于表示在空间，时间和/或其他关系域收集的高维逻辑数据。布尔张量分解（BTD）将二进制张量分配到多个级别1张量的布尔总和中，这是一个NP硬化问题。现有的BTD方法受其高计算成本的限制，在大规模或高阶张量的应用中。在这项工作中，我们介绍了一种计算有效的BTD算法，即\ textIt {全阶张量分解}（GETF）的几何扩展}（GETF），从几何学角度依次识别张量的rank-1基基组件。我们对GETF分解全阶张量的有效性以及算法效率进行了严格的理论分析。对合成和现实世界数据的实验表明，GETF在重建精度，潜在结构的提取方面的性能显着提高，并且比其他最新方法要快的阶数。
Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely \textit{Geometric Expansion for all-order Tensor Factorization} (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.
