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Nov 10, 2022 at 10:06 history bounty ended CommunityBot
Nov 6, 2022 at 17:33 vote accept Sam
Nov 6, 2022 at 17:29 history edited EdM CC BY-SA 4.0
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Nov 6, 2022 at 16:40 comment added EdM @Sam yes, in this application the number of linearly-independent columns in $M_{b,\cdot}$ is limiting. For the general matrix equation shown, the number of linearly-independent rows in $B$ could be limiting instead. You might be able to find a solution with a rank-1 expression matrix (just 1 linearly independent column) like you constructed with the pseudo-replicates, but there is no unique solution and what you are fitting with added noise is essentially the noise. I'll add a bit to the answer now that I know you are limiting to 2 cell types.
Nov 6, 2022 at 12:26 comment added Sam Even a more trivial check : I've seen that it is possible to de-convolute 1 single sample with CibersortX to get its proportions (using a signature matrix of 9 cell-types). Should not this be impossible according to what you say (the limiting step being getting the list of fractions )? Perhaps I mistunderstand something
Nov 6, 2022 at 11:06 comment added Sam Not sure your explanation is correct.I've created an artificial mixture which consists of one sample and 19 pseudo-replicates (not introducing any noise,just copied the sample values 19 times). I've also created a signature matrix with 9 cell types (by averaging the values of the different cell-types in the signature matrix ). I have managed to run CibersortX and get the cell-types fraction matrix F (not using CibersortX batch correction). The number of linearly independent samples is 1 and the number of cell types is 9, so this should not have been mathematically possible by your explanation.
Nov 6, 2022 at 9:24 comment added Sam You say The first problem is that you can't solve that equation uniquely for any more cell types c than you have linearly independent columns in Mb,or _rows in B_ The latter part seems incorrect - the number of rows in B is the number of genes (which is not the limiting factor).
Nov 6, 2022 at 8:21 vote accept Sam
Nov 6, 2022 at 14:46
Nov 4, 2022 at 16:08 history answered EdM CC BY-SA 4.0