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arXiv 2210.02590cs.LGcs.NAmath.NA
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用于数据融合和迁移学习的星图多模态匹配分量分析

Star-Graph Multimodal Matching Component Analysis for Data Fusion and Transfer Learning

University of Dayton Research Institute(戴顿大学研究院)

Nick Lorenzo

摘要:

先前的匹配分量分析(MCA)技术将两个数据域映射到公共域以用于在数据融合和迁移学习上下文中进一步处理。在本文中,我们将这些技术扩展到星图多模态(SGM)的情况下,其中一个特定的数据域连接到$m$他人通过一个目标函数。我们提供了一个特定的可行点的轨迹最大化问题的封闭形式和算法的计算和迭代改进,导致我们的主要结果,SGM地图。我们还提供了数值例子证明,SGM是能够编码到它的地图比MCA的信息时,很少的训练点。此外,我们开发了一个进一步推广的MCA协方差约束,消除了以前的可行性条件,并允许更大的值的规定协方差矩阵的秩。

英文摘要:

Previous matching component analysis (MCA) techniques map two data domains to a common domain for further processing in data fusion and transfer learning contexts. In this paper, we extend these techniques to the star-graph multimodal (SGM) case in which one particular data domain is connected to $m$ others via an objective function. We provide a particular feasible point for the resulting trace maximization problem in closed form and algorithms for its computation and iterative improvement, leading to our main result, the SGM maps. We also provide numerical examples demonstrating that SGM is capable of encoding into its maps more information than MCA when few training points are available. In addition, we develop a further generalization of the MCA covariance constraint, eliminating a previous feasibility condition and allowing larger values of the rank of the prescribed covariance matrix.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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