I am trying to work on a project on MALDI-TOF MS dataset.

The dataset contains mass-spectrometry data of pure samples (1 bacterium species) and mixed samples (mixtures in known proportions of 2 bacteria species).

The topic I'd like to explore is to use mixture observations to train a classifier for predicting the pure ones. Say we have altogether 5 species (actually we have 20, just for an example). The labels of the training set are like $(\frac{2}{3},0,\frac{1}{3},0,0),(0,0,0,0,1),$ or $(0,0,0,\frac{1}{2},\frac{1}{2})$, which may contain one or two positive elements that sum up to $1$. However, we have the prior knowledge that the labels of the tests can only be like $(1,0,0,0,0),(0,0,0,1,0),$ or $(0,0,1,0,0)$, which stand for pure samples.

I am looking for appropriate algorithms to deal with it. Any suggestions would be highly appreciated. Or, maybe my research topic is not well-formulated?


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