Using distance on the Riemannian manifold to compare representations in brain and in models
Using distance on the Riemannian manifold to compare representations in brain and in models
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DOI：
10.1016/j.neuroimage.2021.118271
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发表时间：
2021-06-28
期刊：
影响因子：
5.7
通讯作者：
Nili, Hamed
中科院分区：
文献类型：
--
作者：
Shahbazi, Mahdiyar;Shirali, Ali;Nili, Hamed
代表性相似性分析 (RSA) 将一组实验条件的活动模式总结为由活动模式之间的成对比较组成的矩阵。此类矩阵的两个示例是逐个条件的内积和相关矩阵。这些表征矩阵位于半正定矩阵流形上，称为黎曼流形。我们假设通过考虑表征矩阵的基础流形可以更准确地量化表征相似性。因此，我们引入黎曼流形上的距离作为比较表示的度量。分析模拟和真实的功能磁共振成像数据并考虑广泛的指标，我们表明黎曼距离最不受采样偏差的影响，导致更大的受试者内可靠性，并提供具有高灵敏度和特异性的探照灯映射。此外，我们表明黎曼距离可用于测量多维连通性。与最先进的测量方法相比，该测量方法捕获了单变量和多变量的连通性，并且对非线性区域相互作用更加敏感。将我们提出的度量应用于自然图像的神经网络表示，我们证明它在量化模型相似性方面也具有出色的性能。总而言之，我们的结果证明了 RSA 应该考虑表征矩阵的多样性来总结大脑和模型中的反应模式的主张。
Representational similarity analysis (RSA) summarizes activity patterns for a set of experimental conditions into a matrix composed of pairwise comparisons between activity patterns. Two examples of such matrices are the condition-by-condition inner product and correlation matrix. These representational matrices reside on the manifold of positive semidefinite matrices, called the Riemannian manifold. We hypothesize that representational similarities would be more accurately quantified by considering the underlying manifold of the representational matrices. Thus, we introduce the distance on the Riemannian manifold as a metric for comparing representations. Analyzing simulated and real fMRI data and considering a wide range of metrics, we show that the Riemannian distance is least susceptible to sampling bias, results in larger intra-subject reliability, and affords searchlight mapping with high sensitivity and specificity. Furthermore, we show that the Riemannian distance can be used for measuring multi-dimensional connectivity. This measure captures both univariate and multivariate connectivity and is also more sensitive to nonlinear regional interactions compared to the state-of-the-art measures. Applying our proposed metric to neural network representations of natural images, we demonstrate that it also possesses outstanding performance in quantifying similarity in models. Taken together, our results lend credence to the proposition that RSA should consider the manifold of the representational matrices to summarize response patterns in the brain and in models.