Semantic Similarity Functions

Introduction

The go3 library provides several semantic similarity functions for comparing Gene Ontology (GO) terms. These measures rely on two main principles:

• Information Content (IC) derived from GO annotations.

• Graph-based topological relationships in the GO hierarchy.

In this section, we summarize the main similarity measures provided, along with their theoretical definitions and bibliographic references.

Similarity Measures

Resnik Similarity

The Resnik similarity [1] measures the similarity between two GO terms as the information content (IC) of their Most Informative Common Ancestor (MICA):

\[\mathrm{Sim}_{Resnik}(t_1, t_2) = IC(\mathrm{MICA}(t_1, t_2))\]

Lin Similarity

Lin’s similarity [2] normalizes Resnik’s similarity by the sum of the ICs of both terms:

\[\mathrm{Sim}_{Lin}(t_1, t_2) = \frac{2 \times IC(\mathrm{MICA}(t_1, t_2))}{IC(t_1) + IC(t_2)}\]

Jiang-Conrath Similarity

Jiang and Conrath define a distance between two GO terms based on IC [3]:

\[d_{JC} = IC(t_1) + IC(t_2) - 2 \times IC(\mathrm{MICA})\]

Similarity is then calculated as:

\[\mathrm{Sim}_{JC} = \frac{1}{d_{JC}}\]

SimRel Similarity

The SimRel measure [4] combines Lin’s similarity with an exponential relevance factor:

\[\mathrm{Sim}_{Rel} = \left( \frac{2 \times IC(\mathrm{MICA})}{IC(t_1) + IC(t_2)} \right) \times \left(1 - e^{-IC(\mathrm{MICA})}\right)\]

Information Coefficient

Li et al. [5] propose a normalization using the minimum IC of the two terms:

\[\mathrm{IC\_coef} = \frac{IC(\mathrm{MICA})}{\min(IC(t_1), IC(t_2))}\]

GraphIC Similarity

The GraphIC measure uses the maximum graph depth of the two terms to scale the similarity:

\[\mathrm{GraphIC} = \frac{IC(\mathrm{MICA})}{\max(\mathrm{depth}(t_1), \mathrm{depth}(t_2)) + 1}\]

Wang Similarity

The Wang similarity [6] considers the graph structure of GO by propagating weights from each term through its ancestors:

• Each ancestor node receives a weight based on the decay factor (usually \(w = 0.8\)).

• The similarity is computed as:

\[\text{Sim}_{Wang}(t_1, t_2) = \frac{\sum_{x \in A(t_1) \cap A(t_2)} (S_{t_1}(x) + S_{t_2}(x))}{SV(t_1) + SV(t_2)}\]

Where:

• :math:A(t) is the set of ancestors of term :math:t (including itself).

• :math:S_t(x) is the semantic contribution of ancestor :math:x to term :math:t.

• :math:SV(t) is the total semantic value of term :math:t.

The key idea is that ancestors that are closer to the term contribute more to its meaning than distant ancestors, capturing the hierarchical semantics of the ontology without relying on external annotation statistics.

Batch Computation

All these similarity measures are available in efficient batch versions in the go3 library, taking full advantage of Rust’s parallelism.

Bibliography

[1]

P. Resnik. Using information content to evaluate semantic similarity in a taxonomy. In Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI), 448–453. 1995.

[2]

D. Lin. An information-theoretic definition of similarity. In Proceedings of the 15th International Conference on Machine Learning (ICML), 296–304. 1998.

[3]

J. J. Jiang and D. W. Conrath. Semantic similarity based on corpus statistics and lexical taxonomy. In Proceedings of the International Conference on Research in Computational Linguistics (ROCLING), 19–33. 1997.

[4]

A. Schlicker, F. S. Domingues, J. Rahnenfuhrer, and T. Lengauer. A new measure for functional similarity of gene products based on gene ontology. BMC Bioinformatics, 7(1):302, 2006.

[5]

B. Li, J. Z. Wang, F. A. Feltus, J. Zhou, and F. Luo. Effectively integrating information content and structural relationship to improve the go-based similarity measure. Journal of Biomedical Informatics, 43(5):752–760, 2010.

[6]

J. Z. Wang, Z. Du, R. Payattakool, S. Y. Philip, and C. F. Chen. A new method to measure the semantic similarity of go terms. Bioinformatics, 23(10):1274–1281, 2007.