Training Policies
There are multiple ways to define the set of positive and negative examples for training the binary classifiers. In HiClass we implemented 6 policies described at 1, which were based on previous work from 2 and 3. In the table below the notation used to define the sets of positive and negative examples is presented, as described by 1.
Symbol |
Meaning |
\(Tr\) |
The set of all training examples |
\(Tr^+(c_i)\) |
The set of positive training examples of \(c_i\) |
\(Tr^-(c_i)\) |
The set of negative training examples of \(c_i\) |
\(\uparrow (c_i)\) |
The parent category of \(c_i\) |
\(\downarrow (c_i)\) |
The set of children categories of \(c_i\) |
\(\Uparrow (c_i)\) |
The set of ancestor categories of \(c_i\) |
\(\Downarrow (c_i)\) |
The set of descendant categories of \(c_i\) |
\(\leftrightarrow (c_i)\) |
The set of sibling categories of \(c_i\) |
\(*(c_i)\) |
Denotes examples whose most specific known class is \(c_i\) |
Based on this notation, we can define the different policies and their sets of positive and negative examples as follows:
Policy |
Positive examples |
Negative examples |
Exclusive |
\(Tr^+(c_i) = *(c_i)\) |
\(Tr^-(c_i) = Tr \setminus *(c_i)\) |
Less exclusive |
\(Tr^+(c_i) = *(c_i)\) |
\(Tr^-(c_i) = Tr \setminus *(c_i) \cup \Downarrow (c_i)\) |
Less inclusive |
\(Tr^+(c_i) = *(c_i) \cup \Downarrow (c_i)\) |
\(Tr^-(c_i) = Tr \setminus *(c_i) \cup \Downarrow (c_i)\) |
Inclusive |
\(Tr^+(c_i) = *(c_i) \cup \Downarrow (c_i)\) |
\(Tr^-(c_i) = Tr \setminus *(c_i) \cup \Downarrow (c_i) \cup \Uparrow (c_i)\) |
Siblings |
\(Tr^+(c_i) = *(c_i) \cup \Downarrow (c_i)\) |
\(Tr^-(c_i) = \leftrightarrow (c_i) \cup \Downarrow (\leftrightarrow (c_i))\) |
Exclusive siblings |
\(Tr^+(c_i) = *(c_i)\) |
\(Tr^-(c_i) = \leftrightarrow (c_i)\) |
Using as example the class “Wolf” from the hierarchy represented in the image below, we have the following sets of positive and negative examples for each policy:
Policy |
\(Tr^+(c_{Wolf})\) |
\(Tr^-(c_{Wolf})\) |
Exclusive |
Wolf |
Reptile, Snake, Lizard, Mammal, Cat, Dog |
Less exclusive |
Wolf |
Reptile, Snake, Lizard, Mammal, Cat |
Less inclusive |
Wolf, Dog |
Reptile, Snake, Lizard, Mammal, Cat |
Inclusive |
Wolf, Dog |
Reptile, Snake, Lizard, Cat |
Siblings |
Wolf, Dog |
Cat |
Exclusive siblings |
Wolf |
Cat |
See also
In terms of code, we explain how to select those different policies here: Binary Training Policies.
- 1(1,2)
Silla, C. N., & Freitas, A. A. (2011). A survey of hierarchical classification across different application domains. Data Mining and Knowledge Discovery, 22(1), 31-72.
- 2
Eisner, R., Poulin, B., Szafron, D., Lu, P., & Greiner, R. (2005, November). Improving protein function prediction using the hierarchical structure of the gene ontology. In 2005 IEEE symposium on computational intelligence in bioinformatics and computational biology (pp. 1-10). IEEE.
- 3
Fagni, T., & Sebastiani, F. (2007, October). On the selection of negative examples for hierarchical text categorization. In Proceedings of the 3rd language technology conference (pp. 24-28).