Ranking Function

A ranking function is an function whose function range is an ordinal scale (can be ordered).

• AKA: Ordinal-Output Rank Function.
• Context:
  • range: an Ordinal Ranking.
  • It can range from being an Integer-Valued Ranking Function to being a Real-Valued Ranking Function.
  • It can range from being an Abstract Ranking Function to being a Ranking Function Structure.
  • It can be (often) used to place a Partial Order on a set of Objects.
  • It can be an input to a Ranking Task (solved by a ranking system).
  • It can range from being a Heuristic Ranking FUnction to being a Trained Ranking Function.
• Example(s):
  • [math]\displaystyle{ f_A }[/math](3.2) ⇒ Large, where Function Range([math]\displaystyle{ f_A }[/math]) = (Small < Medium < Large).
  • [math]\displaystyle{ f_B }[/math](9.2,Red,True,0,Null) ⇒ Small, where Function Range([math]\displaystyle{ f_B }[/math]) = (Small < Medium < Large).
  • an Information Retrieval Ranking Function.
  • a Constant Ranking Function.
  • a Term Frequency Ranking Function.
  • a TF-IDF Ranking Function.
  • a Graph Node Ranking Function (e.g. based on node centrality, node prestige, node diversity)
  • a Graph Edge Ranking Function.
  • a Okapi BM25 Ranking Function.
  • a Predictive Ranker, such as a probabilistic ranking function.
  • an Ordinal Random Variable.
  • …
• Counter-Example(s):
  • Class-Output Function/Classification Function, such as [math]\displaystyle{ f }[/math](9.2,Red,True,0,Null) ⇒ E.coli.
  • a Number-Output Function.
  • an Ordinal-Input Function.
• See: Ranking Algorithm, Partial Order, Ordinal Function, Ranking Model Learning Algorithm.

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References

2009

• (Liu, 2009) ⇒ Tie-Yan Liu. (2009). “Learning to Rank for Information Retrieval.” In: Foundations and Trends in Information Retrieval Journal, 3(3). doi:10.1561/1500000016
  • QUOTE: Learning to rank for Information Retrieval (IR) is a task to automatically construct a ranking model using training data, such that the model can sort new objects according to their degrees of relevance, preference, or importance.

2006

• (Agarwal, 2006) ⇒ Shivani Agarwal. (2006). “Ranking on Graph Data.” In: Proceedings of the 23rd International Conference on Machine Learning (ICML 2006) doi:10.1145/1143844.1143848

2004

• (Podelski & Rybalchenko, 2004) ⇒ Andreas Podelski, and Andrey Rybalchenko. (2004). “A complete method for the synthesis of linear ranking functions. In: Verification, Model Checking, and Abstract Interpretation.
  • QUOTE: … A heuristic-based approach for discovery of ranking functions is described in [DGG00]. It inspects the program source code for ranking function candidates. This method restricted to programs where the ranking function is exhibited already in the source code. ...

2003

• (Fagin et al., 2003b) ⇒ Ronald Fagin, Ravi Kumar, D. Sivakumar. (2003). “Comparing top k lists.” In: Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms.

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