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Question: What are some instances of polythetic datasets in biology? In particular, I am looking for a dataset to benchmark a machine learning algorithm optimized via episodic training.


On polythetic classification

The conventional definition of a conceptual or monothetic class is that its members must possess certain properties in common [1]. For example, in the MNIST database of handwritten digits, images can be classified into 10 distinct classes (i.e. digits) where all instances of any given class possess the same set of attributes (e.g. zeros are typically written as ellipses).

In contrast, a polythetic class encompasses members that might share a number of characteristics, but none of these attributes is essential for membership of that group or class. For example, one could group green zeros together with red ones in one polythetic class, and red zeros together with green ones in another one, as shown below.

Example polythetic classification

Are there any instances of biological datasets with similar properties? I am particularly thinking of genetics data (e.g. single nucleotide polymorphisms) where perhaps a certain mutation A counteracts the effect of mutation B? Any pointers are welcome.

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  • $\begingroup$ Hi @rvinas, this question seems far too general to be useful. There are, for example, plenty of examples of gene sets that have negatively correlated expression under different conditions, and heritable syndromes that have different physiological appearances depending on the parent they were inherited from. Could you please be more specific about what sort of data you're looking for. $\endgroup$
    – gringer
    May 7 at 6:29
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I may not be understanding exactly what you are talking about, but it seems to me that nearly any set of classes of interest must be polythetic. Most groups of comparable things differ in some characteristics but also have characteristics in common, and none of those characters is 100% identical with membership in the class.

Some examples off the top of my head:

  1. Biological species / taxonomic groups (classify according to phenotypic characters)
  2. Biological species / taxonomic groups (classify according to molecular sequence e.g. DNA)
  3. Cell types (classify according to cell epitopes)
  4. Cell types (classify according to transcriptional profile)
  5. Ecosystems (classify according to species profile)
  6. Disease state (classify according to any one of many molecular profiles)
  7. Members of population groups (classify according to genetic variation)

etc.

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