Orthogonal Connectivity Factorization: Interpretable Decomposition of Variability in Correlation Matrices
Orthogonal Connectivity Factorization: Interpretable Decomposition of Variability in Correlation Matrices
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DOI：
10.1162/neco_a_00810
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发表时间：
2016-03-01
影响因子：
2.9
通讯作者：
Kawanabe, Motoaki
中科院分区：
文献类型：
--
作者：
Hyvarinen, Aapo;Hirayama, Jun-ichiro;Kawanabe, Motoaki
在许多多变量时间序列中，相关结构是非平稳的，也就是说，它随时间而变化。相关性结构还可以作为其他辅因子的函数而改变，例如，生物医学数据中的受试者的身份。分析此类数据的基本方法是在短时间窗口内或针对不同主题分别估计相关性结构（连通性），并使用现有的机器学习方法（如主成分分析（PCA））来总结或可视化连通性的变化。然而，这样一个简单的PCA的可视化是有问题的，因为随之而来的连接模式是更复杂的对象比，比如说，空间模式。在这里，我们开发了一个新的框架，分析变异的连接使用PCA方法作为起点。首先，我们展示了如何分析和可视化的连接矩阵的主成分的量身定制的秩2矩阵近似，其中我们使用两个正交向量的外积。这导致了一种新的特征向量变换，特别适合于此目的，并且通常可以将主成分解释为两组变量之间的连接。其次，我们展示了如何将正交性和秩二约束的PCA本身的估计，以改善结果。我们进一步提供了一个解释这些方法的概率生成模型相关的盲分离的依赖源的估计。对脑成像数据的实验给出了非常有希望的结果。
In many multivariate time series, the correlation structure is nonstationary, that is, it changes over time. The correlation structure may also change as a function of other cofactors, for example, the identity of the subject in biomedical data. A fundamental approach for the analysis of such data is to estimate the correlation structure (connectivities) separately in short timewindows or for different subjects and use existing machine learning methods, such as principal component analysis (PCA), to summarize or visualize the changes in connectivity. However, the visualization of such a straightforward PCA is problematic because the ensuing connectivity patterns are much more complex objects than, say, spatial patterns. Here, we develop a new framework for analyzing variability in connectivities using the PCA approach as the starting point. First, we show how to analyze and visualize the principal components of connectivity matrices by a tailor-made rank-two matrix approximation in which we use the outer product of two orthogonal vectors. This leads to a new kind of transformation of eigenvectors that is particularly suited for this purpose and often enables interpretation of the principal component as connectivity between two groups of variables. Second, we show how to incorporate the orthogonality and the rank-two constraint in the estimation of PCA itself to improve the results. We further provide an interpretation of these methods in terms of estimation of a probabilistic generative model related to blind separation of dependent sources. Experiments on brain imaging data give very promising results.