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Consider a group of objects denoted $O = \{o_0, o_1, \cdots\}$ where each object is associated with a feature vector $F = \{f_0, f_1, \cdots\, f_{N-1}\}$. For this case, assume the features are categorical e.g., $f_i \in \{0,1,\cdots, M-1\}$.

The objective to assign a class $c \in C$ to the set of objects given the objects defined by the associated features.

In general, a particular group of objects may not map to a unique class. For example, a certain class may share objects from another class, and if the objects in one class (e.g., say class $A$) are a subset of objects in another class (e.g., say class $B$), then we can't know for certain if a given set of objects $O$ should be assigned $A$ or $B$ as both are valid classes.

What is the the terminology for this issue? Is there a procedure for determining if such a class is ambiguous for some problems given the features?

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1 Answer 1

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If a single object can potentially be associated with multiple classes, and the goal is, given an object, predict all classes associated with that object, then this is known as multi-label classification.

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  • $\begingroup$ Yes, but those classes are dependent on the input features. Say generally class A contains a,b,c and class B contains a,b,d, then given the objects a,b, the output will be A or B, but we can't distinguish between what class the objects originated because A and B contain similar objects $\endgroup$
    – Ralff
    Dec 1, 2022 at 19:24
  • $\begingroup$ I am wondering if there is a measure or name for this type of scenario. For example, given the features and training data, how reliable is the network based on the similar between classes and features. I am looking for terminology, so I can search this in more detail $\endgroup$
    – Ralff
    Dec 1, 2022 at 19:25

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