研究稀疏张量数据下秩一信号的估计性能，揭示信息丢失机制。
Performance of Rank-One Tensor Approximation on Incomplete Data
- 基于随机矩阵理论分析不完整张量的秩一逼近性能
- 发现删除随机部分数据会导致性能下降，且可定量描述
- 适合对张量压缩与信息损失敏感的研究者参考
我们关注在仅获得部分噪声观测（占比ε）的情况下，对秩一张量信号的估计问题。研究表明，该问题可转化为一个随机矩阵模型的谱分析，进而获得重构性能的理论刻画。这些结果揭示并量化了通过随机删减张量元素以降低内存开销所导致的性能损失，为张量压缩中的信息保留提供了理论依据。
原文摘要 · Abstract (English)
We are interested in the estimation of a rank-one tensor signal when only a portion $\varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral analysis gives access to the reconstruction performance. These results shed light on and specify the loss of performance induced by an artificial reduction of the memory cost of a tensor via the deletion of a random part of its entries.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。