Quantum-inspired canonical correlation analysis for exponentially large dimensional data
Quantum-inspired canonical correlation analysis for exponentially large dimensional data
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DOI：
10.1016/j.neunet.2020.11.019
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发表时间：
2021-03-01
期刊：
影响因子：
7.8
通讯作者：
Majima, Kei
中科院分区：
文献类型：
--
作者：
Koide-Majima, Naoko;Majima, Kei
典型相关分析（CCA）用于识别多变量数据对之间的统计依赖关系。然而，它的应用程序的高维数据是有限的，由于相当大的计算复杂性。作为一种替代传统的CCA方法，需要多项式的计算时间，我们提出了一种算法，近似CCA使用量子启发的计算与计算时间成正比的输入维数的对数。在合成数据集和真实的数据集上对量子CCA（qiCCA）算法的计算效率和性能进行了实验评估。此外，qiCCA提供的快速计算允许直接应用CCA，即使在将原始输入数据非线性映射到高维空间之后。所进行的实验表明，由于使用二阶单项式将原始输入数据映射到高维空间，与线性CCA相比，qiCCA提取了更多的相关性，并在多个数据集上实现了与最先进的CCA非线性变体相当的性能。这些结果证实了所提出的qiCCA的适当性以及量子启发计算在分析高维数据中的高潜力。(c)2020作者（S）由爱思唯尔有限公司出版。这是一篇开放获取的文章，使用CC BY许可证（http：//creativecommons.org/licenses/by/4.0/）。
Canonical correlation analysis (CCA) serves to identify statistical dependencies between pairs of multivariate data. However, its application to high-dimensional data is limited due to considerable computational complexity. As an alternative to the conventional CCA approach that requires polynomial computational time, we propose an algorithm that approximates CCA using quantum-inspired computations with computational time proportional to the logarithm of the input dimensionality. The computational efficiency and performance of the proposed quantum-inspired CCA (qiCCA) algorithm are experimentally evaluated on synthetic and real datasets. Furthermore, the fast computation provided by qiCCA allows directly applying CCA even after nonlinearly mapping raw input data into high-dimensional spaces. The conducted experiments demonstrate that, as a result of mapping raw input data into the high-dimensional spaces with the use of second-order monomials, qiCCA extracts more correlations compared with the linear CCA and achieves comparable performance with state-of-the-art nonlinear variants of CCA on several datasets. These results confirm the appropriateness of the proposed qiCCA and the high potential of quantum-inspired computations in analyzing high-dimensional data. (c) 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).