Classification Function

A classification function is a discrete value output-function whose function range is a categorical set (with categories).

• AKA: Category-Outputing Model, Classification Scheme.
• Context:
  • domain: a Sample Space Member.
  • range: a Class Member.
  • range: a Categorical Set (or one of more class labels).
  • It can range from being an Abstract Classification Function to being a Classification Structure.
  • It can range from being a Binary Classification Function to being a Multi-Valued Classification Function.
  • It can range from being a Deterministic Classifier to being a Probabilistic Classifier.
  • It can range from being a Simple Classification Function to being a Complex Classification Function (such as an ensemble classifier).
  • It can range from being a Heuristic Classifier to being a Predictive Classifier.
  • It can range from being a Human-Readable Classification Function to being a Machine-Readable Classification Function.
  • It can range from being a Deduced Classification Function to being an Induced Classification Function, (that was induced by classification function learning).
  • It can range, based on the Input Structure, from being a Tuple Classifier (such as a vector classifier) to being a Sequence Classifier (such as a text item classifier) to being a Structure Object Classifier (such as a graph classifier).
  • a Sequence Tagger, such as a POS Tagging Function.
  • It can range, based on the Function Structure, from being a Decision Tree-based Classifier, to being an SVM-based Classifier, to being a Rule-based Classifier, to ...
  • It can be an input to a Classification Task.
  • It can be used by a Classification System (e.g. a Mechanized Classifier or a Human Classifier).
• Example(s):
  • a Vector Classifier, such as [math]\displaystyle{ f(1.1, 2.3, 3.9) \Rightarrow \text{True} }[/math].
  • a Tuple Classifier, such as [math]\displaystyle{ f(1.1,Yellow,3.9) \Rightarrow \text{red} }[/math].
  • a Class Prediction Tree.
  • a Complex Input Classification Function, such as a Sequence Classifier (such as a Text Classification Function).
  • a Complex Output Classification Function, such as a Sequence Tagger (such as a POS Tagging Function).
  • a Categorical Feature Function.
  • …
• Counter-Example(s):
  • an Ordinal-Valued Function, such as [math]\displaystyle{ f(1.5) \Rightarrow Large }[/math].
  • a Real-Valued Function, such as [math]\displaystyle{ f(1.5) \Rightarrow 5.1 }[/math] or [math]\displaystyle{ f(1.1,Yellow,3.9) \Rightarrow 0.37 }[/math].
  • an Integer-Valued Function, such as [math]\displaystyle{ f(1.5) \Rightarrow 1 }[/math],
  • a Vector-Valued Function, such as [math]\displaystyle{ f(1.5) \Rightarrow (3.1,2.3) }[/math].
• See: Concept Hierarchy, Decision Function, Categorical Random Variable.

---

---

References

2008

• (Dextre Clarke et al., 2008) ⇒ Stella Dextre Clarke, Alan Gilchrist, Ron Davies and Leonard Will. (2008). “Glossary of Terms Relating to Thesauri and Other Forms of Structured Vocabulary for Information Retrieval." Willpower Information
  • classification scheme
    • schedule of concepts, arranged by classification

2007

• http://gondolin.rutgers.edu/MIC/text/how/catalog_glossary.htm
  • A scheme, usually consisting of numbers or alphanumericor other notation that categorizes or subdivides a subject area or collection of materials. Most classification schemes were originally intended to organize physical items on the shelf. The result was a unique shelving location (call number) for each item that facilitated browsing of material by subject or author.

2005

• (Woodley, 2005b) ⇒ Mary S. Woodley, Gail Clement, and Pete Winn. (2005). “DCMI Glossary." Dublin Core Metadata Initiative.
  • QUOTE: classification A logical scheme for arrangement of knowledge, usually by subject. Classification schema are alpha and/or numeric; for example, Library of Congress Classification, Dewey Classification, Universal Decimal Classification.

1995

• (Kohavi, 1995) ⇒ Ron Kohavi. (1995). “A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection.” In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence (IJCAI 1995).
  • QUOTE: A classifier is a function that maps an unlabelled instance to a label using internal data structures.

---