4 ms·
For example: you measure concentrations of `p` gases at `n` different places. You collect the results in a matrix A where A_ij is the concentration (a value bet
by stabbles 8y ago
For example: you measure concentrations of `p` gases at `n` different places. You collect the results in a matrix A where A_ij is the concentration (a value between 0 and 1) of gas `i` at station `j`.
Now you factorize A ≈ B * C in the sense that ||A - B * C|| is small in your favourite matrix norm. Here B is of size `p × k` with normalized columns and C is `k × n` and of course k is very small.
Then the columns of B form an approximate basis for the column space of A -- so B compresses the data of A well.
Now, if also B is element-wise positive, you might interpret the columns as concentrations (values between 0 and 1 due to normalization). And you could plot them.
It's not mathematical, but it's also not a crazy interpretation.