Topological Semantic Similarity Measure

Context:
- It can be produced/calculated by a Topological Semantic Similarity System.
- It can range from being an Edge-based Semantic Similarity Measure to being a Node-based Semantic Similarity Measure.
- It can range between being a Pairwise Semantic Similarity Measure to being a Groupwise Semantic Similarity Measure.
Example(s):
- an Edge-based Semantic Similarity Measure such as:
- a Node-based Semantic Similarity Measure such as:
  - Resnik's Semantic Similarity Measure (Resnik, 1995),
  - Lin's Semantic Similarity Measure (Lin, 1998),
- a Hybrid Semantic Similarity Measure such as:
- ...
- …
Counter-Example(s):
See: Semantic Word Similarity Measure, Gene Semantic Similarity Measure, Knowledge-based Semantic Similarity, Corpus-based Similarity, Taxonomy-based Semantic Similarity Measure, Ontology-based Semantic Similarity Measure, Deep Semantic Similarity Neural Network, Path Distance Similarity Measure.

References

(Benabderrahmane et al., 2010 ) ⇒ Sidahmed Benabderrahmane, Malika Smail-Tabbone, Olivier Poch, Amedeo Napoli, and Marie-Dominique Devignes (2010). "IntelliGO: a New Vector-based Semantic Similarity Measure Including Annotation Origin. BMC bioinformatics, 11(1), 1-16.
- QUOTE: Concerning the comparison between individual ontology terms, the two types of approaches reviewed by Pesquita et al. (2009) are similar to those proposed by Blanchard et al. (2008), namely the edge-based measures which rely on counting edges in the graph, and node-based measures which exploit information contained in the considered term, its descendants and its parents.
  In most edge-based measures, the Shortest Path-Length (SPL) is used as a distance measure between two terms in a graph.

(Pesquita et al., 2009 ) ⇒ Catia Pesquita, Daniel Faria, Andre O. Falcao, Phillip Lord, and Francisco M. Couto (2009). "Semantic Similarity in Biomedical Ontologies". In: PLoS Computational Biology 5(7): e1000443.
- QUOTE: Since the first application of semantic similarity in biology, by Lord et al. (2003) , several semantic similarity measures have been developed for use with GO, as shown in Table 1.

**Table 1:** Summary of term measures, their approaches, and their techniques.
Measure	Approach	Techniques
Resnik	Node-based	MICA
Lin (Lin, 1998)	Node-based	MICA
Jiang and Conrath (Jiang & Conrath, 1997)	Node-based	MICA
GraSM (Couto et al., 2005)	Node-based	DCA
Schlicker et al. (2006)	Node-based	MICA
Wu et al. (2005)	Edge-based	Shared path
Wu et al. (2006)	Edge-based	Shared path; distance
Bodenreider et al. (2008)	Node-based	Shared annotations
Othman et al. (2008)	Hybrid	IC/depth/number of children; distance
Wang et al. (2007)	Hybrid	Shared ancestors
Riensche et al. (2007)	Node-based	IC/MICA; shared annotations
Yu et al. (2005)	Edge-based	Shared path
Cheng et al. (2004)	Edge-based	Shared path
Pozo et al. (2008)	Edge-based	Shared path

$T(a, b)=\dfrac{\delta(\operatorname{root}, c)}{\delta(a, c)+\delta(b, c)+\delta(root, c)}$

(2)

where $c = lcs(a,b)$. $T$ is such that $0\leq T \leq 1$, with 1 standing for the maximum taxonomic similarity.

$T$ is directly proportional to the number of edges from the least common super-concept to the root, which agrees with the intuition that a given number of edges between two concrete concepts signifies greater similarity than the same number of edges between two abstract concepts.

(Resnik, 1995) ⇒ Philip Resnik. (1995). “Using Information Content to Evaluate Semantic Similarity in a Taxonomy.” In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 1995).