D-GCCA:基于分解的多视角高维数据广义典范相关分析。

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2022-01-01
Hai Shu, Zhe Qu, Hongtu Zhu
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引用次数: 0

摘要

现代生物医学研究经常收集多视图数据,即对同一组对象测量的多种类型数据。高维多视图数据分析中的一种流行模型是将每个视图的数据矩阵分解为由所有数据视图中共同的潜在因子生成的低阶共源矩阵、与每个视图相对应的低阶独特源矩阵以及加性噪声矩阵。我们为此模型提出了一种新颖的分解方法,称为基于分解的广义典型相关分析(D-GCCA)。与大多数现有方法使用的欧几里得点积空间不同,D-GCCA 在随机变量的 L 2 空间上严格定义了分解,因此能为低阶矩阵恢复提供估计一致性。此外,为了很好地校准共同潜因,我们对不同的潜因施加了理想的正交性约束。然而,现有的方法没有充分考虑到这种正交性,因此可能会导致大量未检测到的共源变异损失。我们的 D-GCCA 比广义典型相关分析更进了一步,它在典型变量中分离了共同成分和独特成分,同时从主成分分析的角度进行了有吸引力的解释。此外,我们还建议使用由共同或独特潜在因素解释的信号方差的变量级比例来选择受影响最大的变量。我们的 D-GCCA 方法建立了一致的估计值,具有良好的有限样本数值性能,并且具有闭式表达式,特别适合大规模数据的高效计算。模拟和实际数据实例也证实了 D-GCCA 方法优于最先进的方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

D-GCCA: Decomposition-based Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data.

D-GCCA: Decomposition-based Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data.

Modern biomedical studies often collect multi-view data, that is, multiple types of data measured on the same set of objects. A popular model in high-dimensional multi-view data analysis is to decompose each view's data matrix into a low-rank common-source matrix generated by latent factors common across all data views, a low-rank distinctive-source matrix corresponding to each view, and an additive noise matrix. We propose a novel decomposition method for this model, called decomposition-based generalized canonical correlation analysis (D-GCCA). The D-GCCA rigorously defines the decomposition on the L 2 space of random variables in contrast to the Euclidean dot product space used by most existing methods, thereby being able to provide the estimation consistency for the low-rank matrix recovery. Moreover, to well calibrate common latent factors, we impose a desirable orthogonality constraint on distinctive latent factors. Existing methods, however, inadequately consider such orthogonality and may thus suffer from substantial loss of undetected common-source variation. Our D-GCCA takes one step further than generalized canonical correlation analysis by separating common and distinctive components among canonical variables, while enjoying an appealing interpretation from the perspective of principal component analysis. Furthermore, we propose to use the variable-level proportion of signal variance explained by common or distinctive latent factors for selecting the variables most influenced. Consistent estimators of our D-GCCA method are established with good finite-sample numerical performance, and have closed-form expressions leading to efficient computation especially for large-scale data. The superiority of D-GCCA over state-of-the-art methods is also corroborated in simulations and real-world data examples.

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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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