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基于组稀疏的张量cp分解模型与算法及其在化学计量学中的应用
首发时间：2024-05-09
摘要：在化学计量学领域中, 在复杂体系下存在未知干扰的对感兴趣目标物质浓度进行准确定量问题是一个重要的研究方向. 如何寻找一种对分析系统中既对化学成分数量(化学秩)不敏感, 又对噪音数据不敏感的方法是一个相当有趣的问题. 在本文中, 基于此问题我们提出了一个带有列单位约束和组稀疏约束的cp分解模型(cpd\_cus). 由于该问题是一个具有三块可分离变量的非凸非光滑问题, 我们提出了一种apg加速格式的块坐标下降算法(apgbcd). 其中将前两个子问题使用交替近端梯度法进行有限步数迭代求解, 第三个子问题由于组稀疏不可分离性, 采用矩阵求解并进行多步迭代. 最后对合成张量数据、两成分和三成分的化学数据分别进行数值实验, 将本文提出的cpd\_cus模型与其他模型和算法进行比较, 通过平均回收率, rmesep, 时间和准确率证明了 cpd\_cus 模型的有效性和鲁棒性, 解决了化学计量学组分分离问题中对秩敏感和噪音敏感的问题.
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tensor cp decomposition model and algorithm based on group sparsity and its application in chemometrics
abstract：it is an inmportant problem in chemometrics to measure the concentration of target substances of interest with unknown interference in complex systems. it is quite an interesting problem to devise a method that is insensitive to both the number of chemical components (chemical rank) and noise data in the analysis system. in this paper, based on this problem, we propose a cp decomposition model with column unit constraints and group sparse constraints (cpd\_cus). since this problem is a non-convex and non-smooth problem with three separable variables, we propose an apg-accelerated block coordinate descent algorithm (apgbcd). the first two subproblems are solved by alternating proximal gradient method with finite number of steps, and the third sub-problem is solved by matrix and multi-step iteration due to the sparse inseparability of the group. finally, numerical experiments are conducted on synthetic tensor data as well as chemical data with two and three component datasets. the proposed cpd\_cus model is compared with other models and algorithms. the effectiveness and robustness of the cpd\_cus model is proven through average recovery rate, rmesep, time and accuracy. this approach effectively addresses the sensitivity to rank and sensitivity to noise in the component separation problem in chemometrics.
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基于组稀疏的张量cp分解模型与算法及其在化学计量学中的应用
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