A Tensor SVD-based Classification Algorithm Applied to fMRI Data
A Tensor SVD-based Classification Algorithm Applied to fMRI Data
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DOI：
10.1137/21s1456522
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发表时间：
2021-10
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通讯作者：
K. Keegan;T. Vishwanath;Yihua Xu
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作者：
K. Keegan;T. Vishwanath;Yihua Xu
为了分析丰富的多维数据，开发了基于张量的框架。传统上，矩阵奇异值分解 (SVD) 用于从包含矢量化数据的矩阵中提取最主要的特征。虽然 SVD 对于可以适当表示为矩阵的数据非常有用，但矢量化的这一步会导致我们失去数据固有的高维关系。为了促进高效的多维特征提取，我们利用基于投影的分类算法，该算法使用 t-SVDM（矩阵 SVD 的张量模拟）。我们的工作将 t-SVDM 框架和分类算法（最初都是针对 3 阶张量提出）扩展到任意数量的维度。然后，我们使用 StarPlus fMRI 数据集将此算法应用于分类任务。我们的数值实验表明，存在一种基于张量的 fMRI 分类方法，优于最佳的等效基于矩阵的方法。我们的结果说明了我们选择的张量框架的优势，提供了对参数的有益选择的深入了解，并且可以进一步开发用于更复杂的成像数据的分类。我们在 https://github.com/elizabethnewman/tensor-fmri 提供了 Python 实现。
To analyze the abundance of multidimensional data, tensor-based frameworks have been developed. Traditionally, the matrix singular value decomposition (SVD) is used to extract the most dominant features from a matrix containing the vectorized data. While the SVD is highly useful for data that can be appropriately represented as a matrix, this step of vectorization causes us to lose the high-dimensional relationships intrinsic to the data. To facilitate efficient multidimensional feature extraction, we utilize a projection-based classification algorithm using the t-SVDM, a tensor analog of the matrix SVD. Our work extends the t-SVDM framework and the classification algorithm, both initially proposed for tensors of order 3, to any number of dimensions. We then apply this algorithm to a classification task using the StarPlus fMRI dataset. Our numerical experiments demonstrate that there exists a superior tensor-based approach to fMRI classification than the best possible equivalent matrix-based approach. Our results illustrate the advantages of our chosen tensor framework, provide insight into beneficial choices of parameters, and could be further developed for classification of more complex imaging data. We provide our Python implementation at https://github.com/elizabethnewman/tensor-fmri.