Commit d8839946 authored by Ying-Qiu Zheng's avatar Ying-Qiu Zheng
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Update 2021JUL21.md

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![diagram](/figs/2021JUL21/diagram-20210721.png)
### Model formulation
Suppose $`\mathbf{X}^{H}, \mathbf{X}^{L}`$ are $`N \times V`$ feature matrices (e.g. connectivity between $`N`$ thalamus voxels and $`V`$ whole brain voxels). Note that they can have different dimensions in practice. To keep notations uncluttered, we suppose the number of voxels in high- and low-quality images are the same for a given subject. Now we assume $`\mathbf{X}^{H}, \mathbf{X}^{L}`$ share the same latent variable $`Z`$, which is a $`N \times K`$ binary matrix representing the voxels' classes.
Suppose $`\mathbf{X}^{H}, \mathbf{X}^{L}`$ are $`N \times V`$ feature matrices (e.g. connectivity between $`N`$ thalamus voxels and $`V`$ whole brain voxels). Note that they can have different dimensions in practice. To keep notations uncluttered, we suppose the number of voxels in high- and low-quality images are the same for a given subject. Now we assume $`\mathbf{X}^{H}, \mathbf{X}^{L}`$ share the same latent variable $`Y`$, which is a $`N \times K`$ binary matrix representing the voxels' classes.
For a single voxel, suppose $`\mathbf{y}_{n} \sim \text{multinomial}(\mathcal{\pi})`$, and $`p(\mathbf{x}^{L}_{n}|y_{nk}=1) = \mathcal{N}(\mu_{k}, \Sigma_{k}^{L})`$.
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