平衡展开的诱导电张器核规范,用于高阶电张器完成
IEEE transactions on neural networks and learning systems
|April 24, 2024
概括
这项研究引入了新的张量核规范 (TNNs) 用于张量完成,增强了多维的低管级结构捕获. 提出的方法在完成现实世界张量数据方面提供了卓越的性能.
科学领域:
- 多维数据分析数据分析.
- 张量分解的张量分解
- 机器学习 机器学习
背景情况:
- 张量数据的完整性对于现实世界的应用程序至关重要.
- 现有的张量管排列方法在捕捉多维结构方面存在局限性.
- 第三种模式通常是当前方法中的固定转换方向.
研究的目的:
- 为了引入新的展开诱导的张量核规范 (TNNs) 用于张量完成.
- 为了将张量管排的概念扩展到高阶数据.
- 解决现有方法在捕捉多维低管级结构方面的局限性.
主要方法:
- 两个TNN的发展:重叠的TNN (OTNN) 和隐藏的TNN (LTNN).
- 使用一种新的平衡展开策略来捕捉多维的低管级结构.
- 提出了两个高效的张量完成模型,使用统一的非对称上限提供理论保证.
- 采用交替方向方法的乘数 (ADMM) 基于算法进行优化.
主要成果:
- 展开的张量管等级和现有的张量网络等级 (CP,Tucker,TR) 之间的证明关系.
- 拟议的模型在张量完成任务中表现出卓越的性能.
- 在合成和现实世界的张量数据 (面部图像,光场图像,视频序列) 上进行实验验证.
结论:
- 拟议的OTNN和LTNN有效地捕捉了多维的低管级结构.
- 新的TNN为高阶数据提供了有效的延伸张量管等级.
- 开发的张量完成模型为处理复杂的张量数据提供了一个有希望的方法.
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