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Abstract:
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Co-inertia analysis (CIA) is a multivariate analysis method that can assess relationships and trends in two sets of data. CIA has been used for integrative analysis of two high-dimensional -omics data sets. In addition, penalized CIA methods have been proposed to enhance interpretability. However, to apply existing CIA or sparse CIA methods to the integrative analysis of genomics data and imaging data that are represented by multi-dimensional array also known as a tensor, one needs to vectorize the tensor data. The resulting vector for imaging data is of ultra-high dimension, which presents challenges in fitting CIA or penalized CIA. More importantly, the inherent spatial information is lost in the vectorized data, which is important to preserve for some research areas, e.g., brain connectivity study. To address these challenges, we propose a sparse tensor CIA method which uses a low-dimensional representation of loading tensors through tensor decomposition and also imposes a sparsity constraint on the model parameters. This method allows us to preserve the spatial structure of multi-dimensional imaging data while alleviating the challenge of the ultra-high dimensionality.
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