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I need good sources of gene expression data in the form of 3rd order tensors. Typically the commonly available datasets are in the form of a matrix, for instance, $sample \times gene$ or $gene \times time$. I need good sources for 3-dimensional data, for example $gene \times sample \times tissue$ or $gene \times sample \times time$ ... etc.

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    $\begingroup$ Analysis packages rarely use that format for analysis, so find a nice time course dataset (there won't be many matching your needs) and reshape the matrix for it into the correct dimensions. As a aside, it's rarely useful to refer to a 3D matrix or 3 factor experiment as a "3rd order tensor" outside of machine learning. $\endgroup$
    – Devon Ryan
    Jun 22 '18 at 7:33
  • $\begingroup$ I am working on tensor decomposition. I am interested in testing an idea on gene expression 3-d dataset. The papers who have worked on such gene expression dataset haven't made their data public. So... $\endgroup$
    – Satwik
    Jun 22 '18 at 7:58
  • $\begingroup$ @Satwik, you can ask them for the data and do a collaboration (if they and you wish). $\endgroup$
    – llrs
    Jun 22 '18 at 14:10
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I familiar with the inflammatory bowel disease which is quite complicated: It affects multiple sites and depending on when it appears it is different. So you can look at the GEO for microarrays and RNA-seq data of this disease and I'm sure you'll find datasets from the same patients from several tissues or time.

In this disease there is a multi'omics project that fits your needs. You can find (and download) data of high dimensionality: there are samples for the same time, tissue (but different locations), gene, over a period of time and for several omics (not only expression data).
The only problem is that there are some mistakes on the metadata.

However, I don't think they are usually described as 3rd order tensors and I doubt you'll find enough data to train a machine learning method.

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