## September 7, 2016

# Measures of Semantic Similarity

Semantic similarity can be easily understood as “how much a word A is related to the word B?" Determining semantic similarities often comes up in applications of Natural Language Processing. In this blog, I will elaborate on some well-known algorithms with their key characteristics.

## Path Length

Path Length is a score denoting a count of edges between two words in the shortest path. The shorter the path between two words/senses in a thesaurus hierarchy graph, the more similar they are. A thesaurus hierarchy graph is a tree drawn from a broader category of words to narrower category of words. For example, dime and Nickel can be two nodes of coins, and men and women can be two nodes of humans. It is a simple node counting scheme to get to a score:

Sim_{path} (c1, c2) = number of edges in shortest path

### Key Characteristics

- It is very simple
- It is a path-based measure
- The score provided is discrete and not normalized
- This requires tagged data and is hugely dependent on the graph quality
- It assumes a uniform cost; there is no weight on the graph edges

## Leakcock-Chodorow

This is a score denoting count of edges between two words/senses with log smoothing. This is more or less the same as path length with log smoothing, and has the same characteristics except it is continuous in nature due to the log smoothing.

Sim_{LC} = -Log (Path Similarity)

### Key Characteristics

- Simple
- Continuous
- Required tagged data and dependent on the graph quality
- Assumes a uniform cost; there is no specific weight on the graph edges

## Wu & Palmer

This is a score that takes into account the position of concepts c1 and c2 in the taxonomy relative to the position of the Least Common Subsumer (c1, c2). It assumes that the similarity between two concepts is the function of path length and depth, in path-based measures.

The Least Common Subsumer of two node,s v and w, in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define each node to be a descendant of itself (so if v has a direct connection from w, w is the lowest common ancestor).

Sim_{wup} (c1, c2) = (2* Dep(LCS(c1, c2))) / (Len(c1, c2) + 2*dep(LCS(c1, c2)))

LCS(c1, c2) = Lowest node in hierarchy that is a hypernym of c1, c2.

### Key Characteristics

- Continuous and normalized
- The score can never be zero
- Heavily dependent on the quality of the graph
- No distinction between similarity/relatedness

## Resnik Similarity

This is a score denoting how similar two word senses are, based on the Information Content (IC) of the Least Common Subsumer.

Information content is the frequency counts of concepts as found in a corpus of text. The frequency associated with a concept is incremented in WordNet each time that the concept is observed, as are the counts of the ancestor concepts in the WordNet hierarchy (for nouns and verbs). Information Content can only be computed for nouns and verbs in WordNet, since these are the only parts of speech where concepts are organized in hierarchies.

Sim_{Resnik} (c1, c2) = IC(LCS(c1, c2))

LCS(c1, c2) = Lowest node in hierarchy that is a hypernym of c1, c2.

IC(c) = -logP(c)

### Key Characteristics

- Value will always be greater than or equal to zero
- Refines path-based approach using normalizations based on hierarchy depth
- Relies on structure of thesaurus
- Dependent on information content; the result is dependent on the corpus used to generate the information content and the specifics of how the information content was created
- IC-based similarity results are better than path-based

## Lin Similarity

This is a score using both the amount of information needed to state the commonality between the two concepts and the information needed to fully describe these terms.

Sim_{Lin} = 2 * IC(LCS(c1, c2)) / (IC(c1) + IC(c2))

### Key Characteristics

- Refines path-based approach using normalizations based on hierarchy depth
- Relies on structure of thesaurus
- Dependent on information content; the result is dependent on the corpus used to generate the information content and the specifics of how the information content was created
- IC-based similarity results are better than path-based

## Jiang-Conrath Distance

This is a score using both the amount of information needed to state the commonality between the two concepts and the information needed to fully describe these terms. It is similar to Lin Similarity.

Sim_{JCN} = 1/distJC(c1, c2)

distJC(c1, c2) = 2 * log P(LCS(c1, c2)) - (log P(c1) + log P(c2))

### Key Characteristics

- Refines path-based approach using normalizations based on hierarchy depth
- Relies on structure of thesaurus
- Dependent on information content; the result is dependent on the corpus used to generate the information content and the specifics of how the information content was created
- IC-based similarity results are better than path-based
- Care must be taken to handle distJC = 0 scenario

## References

- http://www.d.umn.edu/~tpederse/Pubs/pedersen-naacl-2010.pdf
- http://www.cartagena99.com/recursos/alumnos/ejercicios/Article%201.pdf
- http://www.nltk.org/howto/wordnet.html
- http://atlas.ahc.umn.edu/umls_similarity/similarity_measures.html
- http://www.d.umn.edu/~tpederse/Pubs/pedersen-naacl-2010.pdf
- https://en.wikipedia.org/wiki/Semantic_similarity
- https://en.wikipedia.org/wiki/Lowest_common_ancestor

I hoe you enjoyed reading this. If you have any questions or queries, please leave a comment below. I highly appreciate your feedback!