---
title: "GO-terms Semantic Similarity Measures"
author: "\\

	Guangchuang Yu (<guangchuangyu@gmail.com>)\\

        School of Public Health, The University of Hong Kong"
date: "`r Sys.Date()`"
bibliography: GOSemSim.bib
csl: nature.csl
output: 
  BiocStyle::html_document:
    toc: true
  BiocStyle::pdf_document:
    toc: true
vignette: >
  % \VignetteIndexEntry{An introduction to GOSemSim}
  % \VignetteEngine{knitr::rmarkdown}
  % \usepackage[utf8]{inputenc}
---

```{r style, echo=FALSE, results="asis", message=FALSE}
BiocStyle::markdown()
knitr::opts_chunk$set(tidy = FALSE,
                      warning = FALSE,
                      message = FALSE)
```

```{r echo=FALSE, results="hide", message=FALSE}
library(org.Hs.eg.db)
library(GO.db)
library(GOSemSim)
```

# Citation

If you use `r Biocpkg("GOSemSim")` in published research, please cite G. Yu (2010). In addition, please cite G. Yu (2012) when using `r Biocpkg("clusterProfiler")` for GO enrichment analysis and G. Yu (2015) when using `r Biocpkg("DOSE")` for Disease Ontology analysis.

```
G Yu, F Li, Y Qin, X Bo, Y Wu, S Wang. 
GOSemSim: an R package for measuring semantic similarity among GO terms and gene products.
Bioinformatics 2010, 26(7):976-978.
```

URL: [http://dx.doi.org/10.1093/bioinformatics/btq064](http://dx.doi.org/10.1093/bioinformatics/btq064)

```
G Yu, LG Wang, Y Han, QY He.
clusterProfiler: an R package for comparing biological themes among gene clusters.
OMICS: A Journal of Integrative Biology 2012, 16(5):284-287.
```

URL: [http://dx.doi.org/10.1089/omi.2011.0118](http://dx.doi.org/10.1089/omi.2011.0118)

```
G Yu, LG Wang, GR Yan, QY He.
DOSE: an R/Bioconductor package for Disease Ontology Semantic and Enrichment analysis.
Bioinformatics 2015, 31(4):608-609.
```

URL: [http://dx.doi.org/10.1093/bioinformatics/btu684](http://dx.doi.org/10.1093/bioinformatics/btu684)


# Introduction

Functional similarity of gene products can be estimated by controlled
biological vocabularies, such as Gene Ontology (GO). GO comprises of
three orthogonal ontologies, i.e. molecular function (MF), biological
process (BP), and cellular component (CC).


Four methods have been presented to determine the semantic similarity
of two GO terms based on the annotation statistics of their common
ancestor terms Resnik[@philip_semantic_1999], Jiang[@jiang_semantic_1997],
Lin[@lin_information-theoretic_1998] and Schlicker[@schlicker_new_2006]. Wang[@wang_new_2007] 
proposed a method to measure the similarity based on the graph structure of
GO. Each of these methods has its own advantages and
weaknesses. `r Biocpkg("GOSemSim")` package[@yu2010] is developed to compute
semantic similarity among GO terms, sets of GO terms, gene products,
and gene clusters, providing both five methods mentioned above. We have
developed another package, `r Biocpkg("DOSE")`[@yu_dose_2015], for measuring semantic
similarity among Disease Ontology (DO) terms and gene products at disease perspective.


To start with `r Biocpkg("GOSemSim")` package, type following code below:

```{r eval=FALSE, results='hide'}
library(GOSemSim)
help(GOSemSim)
```


# Semantic Similarity Measurement Based on GO

## Information content-based methods

Four methods proposed by Resnik[@philip_semantic_1999],
Jiang[@jiang_semantic_1997], Lin[@lin_information-theoretic_1998]
and Schlicker[@schlicker_new_2006] are information content (IC) based, which
depend on the frequencies of two GO terms involved and that of their
closest common ancestor term in a specific corpus of GO
annotations. The information content of a GO term is computed by the
negative log probability of the term occurring in GO corpus. A rarely used term contains a
greater amount of information.

The frequency of a term t is defined as:
$p(t) = \frac{n_{t'}}{N} | t' \in \left\{t, \; children\: of\: t \right\}$

where $n_{t'}$ is the number of term __*t'*__, and __*N*__ is the total number of terms in GO corpus.

Thus the information content is defined as:
$IC(t) = -\log(p(t))$

As GO allow multiple parents for each concept, two terms can share
parents by multiple paths. IC-based methods calculate similarity of two GO terms based on the information content of their closest common ancestor term, which was also called most informative information ancestor (MICA).

### Resnik method

The Resnik method is defined as:
$sim_{Resnik}(t_1,t_2) = IC(MICA)$

### Lin method

The Lin method is defined as:
$sim_{Lin}(t_1,t_2) = \frac{2IC(MICA)}{IC(t_1)+IC(t_2)}$

### Rel method

The Relevance method, which was proposed by Schlicker, combine Resnik's and Lin's method 
and is defined as:
$sim_{Rel}(t_1,t_2) = \frac{2IC(MICA)(1-p(MICA))}{IC(t_1)+IC(t_2)}$

### Jiang method

The Jiang and Conrath's method is defined as:
$sim_{Jiang}(t_1,t_2) = 1-\min(1, IC(t_1) + IC(t_2) - 2IC(MICA))$

At present, `r Biocpkg("GOSemSim")` supports about 20 species internally.
We used the following Bioconductor packages to calculate the information content.

+ `r Biocannopkg("org.At.tair.db")`    for __Arabidopsis__
+ `r Biocannopkg("org.Ag.eg.db")`      for __Anopheles__
+ `r Biocannopkg("org.Bt.eg.db")`      for __Bovine__
+ `r Biocannopkg("org.Cf.eg.db")`      for __Canine__
+ `r Biocannopkg("org.Gg.eg.db")`      for __Chicken__
+ `r Biocannopkg("org.Pt.eg.db")`      for __Chimp__
+ `r Biocannopkg("org.Sco.eg.db")`     for __Coelicolor__
+ `r Biocannopkg("org.EcK12.eg.db")`   for __E coli strain K12__
+ `r Biocannopkg("org.EcSakai.eg.db")` for __E coli strain Sakai__
+ `r Biocannopkg("org.Dm.eg.db")`      for __Fly__
+ `r Biocannopkg("org.Hs.eg.db")`      for __Human__
+ `r Biocannopkg("org.Pf.plasmo.db")`  for __Malaria__
+ `r Biocannopkg("org.Mm.eg.db")`      for __Mouse__
+ `r Biocannopkg("org.Ss.eg.db")`      for __Pig__
+ `r Biocannopkg("org.Rn.eg.db")`      for __Rat__
+ `r Biocannopkg("org.Mmu.eg.db")`     for __Rhesus__
+ `r Biocannopkg("org.Ce.eg.db")`      for __Celegans__
+ `r Biocannopkg("org.Xl.eg.db")`      for __Xenopus__
+ `r Biocannopkg("org.Sc.sgd.db")`     for __Yeast__
+ `r Biocannopkg("org.Dr.eg.db")`      for __Zebrafish__


The information content will update regularly.

## Graph-based method
Graph-based methods using the topology of GO graph structure to
compute semantic similarity. Formally, a GO term A can be represented
as $DAG_{A}=(A,T_{A},E_{A})$ where $T_{A}$ is the set of GO terms in
$DAG_{A}$, including term A and all of its ancestor terms in the GO
graph, and $E_{A}$ is the set of edges connecting the GO terms in
$DAG_{A}$.

### Wang method
To encode the semantic of a GO term in a measurable format to enable a quantitative comparison, Wang[@wang_new_2007] firstly defined the semantic value of term A as the aggregate contribution of all terms in $DAG_{A}$ to the semantics of term A, terms closer to term A in $DAG_{A}$ contribute more to its semantics. Thus, defined the contribution of a GO term __*t*__ to the semantic of GO term A as the S-value of GO term __*t*__ related to term A. For any of term __*t*__ in $DAG_{A}$, its S-value related to term A, $S_{A}(\textit{t})$ is defined as:
$\left\{\begin{array}{l} S_{A}(A)=1 \\ S_{A}(\textit{t})=\max\{w_{e} \times S_{A}(\textit{t}') | \textit{t}' \in children \: of(\textit{t}) \} \; if \: \textit{t} \ne A \end{array} \right.$

where $w_{e}$ is the semantic contribution factor for edge $e \in E_{A}$ linking term __*t*__ with its child term __*t'*__. 
Term A contributes to its own is defined as one. After obtaining the S-values for all terms in $DAG_{A}$, 
the semantic value of DO term A, SV(A), is calculated as:

$SV(A)=\displaystyle\sum_{t \in T_{A}} S_{A}(t)$

Thus given two GO terms A and B, the semantic similarity between these two terms is defined as:

$sim_{Wang}(A, B) = \frac{\displaystyle\sum_{t \in T_{A} \cap T_{B}}{S_{A}(t) + S_{B}(t)}}{SV(A) + SV(B)}$

where $S_{A}(\textit{t})$ is the S-value of GO term __*t*__ related to term A 
and $S_{B}(\textit{t})$ is the S-value of GO term __*t*__ related to term B.

This method proposed by Wang[@wang_new_2007] determines the semantic
similarity of two GO terms based on both the locations of these terms
in the GO graph and their relations with their ancestor terms.

## goSim and mgoSim function
In `r Biocpkg("GOSemSim")`, we implemented all these IC-based and graph-based methods. __*goSim*__ function calculates semantic similarity between two GO terms, while __*mgoSim*__ function calculates semantic similarity between two sets of GO terms.

```{r}
goSim("GO:0004022", "GO:0005515", ont="MF", measure="Wang")
go1 = c("GO:0004022","GO:0004024","GO:0004174")
go2 = c("GO:0009055","GO:0005515")
mgoSim(go1, go2, ont="MF", measure="Wang", combine=NULL)
mgoSim(go1, go2, ont="MF", measure="Wang", combine="BMA")
```

# Gene Semantic Similarity Measurement

On the basis of semantic similarity between GO terms, `r Biocpkg("GOSemSim")` can
also compute semantic similarity among sets of GO terms, gene products, and gene clusters.

Suppose we have gene $g_1$ annotated by GO terms sets $GO_{1}=\{go_{11},go_{12} \cdots go_{1m}\}$
and $g_2$ annotated by $GO_{2}=\{go_{21},go_{22} \cdots go_{2n}\}$, `r Biocpkg("GOSemSim")` implemented four methods which called __*max*__, __*avg*__, __*rcmax*__, and __*BMA*__ to combine
semantic similarity scores of multiple GO terms. The similarities
among gene products and gene clusters which annotated by multiple GO
terms were also calculated by the same combine methods mentioned
above.


## Combine methods
### max

The __*max*__ method calculates the maximum semantic similarity score over all pairs of GO terms between these two GO term sets.
$sim_{max}(g\_1, g\_2) = \displaystyle\max_{1 \le i \le m, 1 \le j \le n} sim(go_{1i}, go_{2j})$

### avg
The __*avg*__ calculates the average semantic similarity score over all pairs of GO terms.
$sim_{avg}(g_1, g_2) = \frac{\displaystyle\sum_{i=1}^m\sum_{j=1}^nsim(go_{1i}, go_{2j})}{m \times n}$

### rcmax
Similarities among two sets of GO terms form a matrix, the __*rcmax*__ method uses the maximum of RowScore and ColumnScore as the similarity, where RowScore (or ColumnScore) is the average of maximum similarity on each row (or column).
$sim_{rcmax}(g_1, g_2) = \max(\frac{\displaystyle\sum_{i=1}^m \max_{1 \le j \le n} sim(go_{1i}, go_{2j})}{m},\frac{\displaystyle\sum_{j=1}^n \max_{1 \le i \le m} sim(go_{1i},go_{2j})}{n})$

### BMA
The __*BMA*__ method, used the best-match average strategy, calculates the average of all maximum similarities on each row and column, and is defined as:
$sim_{BMA}(g_1, g_2) = \frac{\displaystyle\sum_{1=i}^m \max_{1 \le j \le n}sim(go_{1i}, go_{2j}) + \displaystyle\sum_{1=j}^n \max_{1 \le i \le m}sim(go_{1i}, go_{2j})} {m+n}$

## geneSim and mgeneSim
In `r Biocpkg("GOSemSim")`, we implemented __*geneSim*__ to calculate semantic similarity between two gene products, and __*mgeneSim*__ to calculate semantic similarity among multiple gene products.

```{r}
geneSim("241", "251", ont="MF", organism="human", measure="Wang", combine="BMA")
mgeneSim(genes=c("835", "5261","241", "994"), 
	 ont="MF", organism="human", measure="Wang",verbose=FALSE)
```

## clusterSim and mclusterSim
We also implemented __*clusterSim*__ for calculating semantic similarity between two gene clusters
and __*mclusterSim*__ for calculating semantic similarities among multiple gene clusters.

```{r}
gs1 <- c("835", "5261","241", "994", "514", "533")
gs2 <- c("578","582", "400", "409", "411")
clusterSim(gs1, gs2, ont="MF", organism="human", measure="Wang", combine="BMA")

x <- org.Hs.egGO
hsEG <- mappedkeys(x)
set.seed <- 123
clusters <- list(a=sample(hsEG, 20), b=sample(hsEG, 20), c=sample(hsEG, 20))
mclusterSim(clusters, ont="MF", organism="human", measure="Wang", combine="BMA")
```

# Case Study

We proposed a method for measuring functional similarity of microRNAs[@yu_new_2011]. 
This method was based on semantic similarity of microRNAs' target genes, 
and was calculated by `r Biocpkg("GOSemSim")`. 
We further analyzed viral microRNAs using this method and compared significant KEGG pathways regulated by different viruses' microRNAs[@yu2011] using `r Biocpkg("clusterProfiler")`[@yu2012].


# GO enrichment analysis

GO enrichment analysis can be supported by our package `r Biocpkg("clusterProfiler")`[@yu2012], which supports hypergeometric test and Gene Set Enrichment Analysis (GSEA). Enrichment results across different gene clusters can be compared using __*compareCluster*__ function.

# Disease Ontology Semantic and Enrichment analysis

Disease Ontology (DO) annotates human genes in the context of disease. DO is important annotation in translating molecular findings from high-throughput data to clinical relevance. 
`r Biocpkg("DOSE")`[@yu_dose_2015] supports semantic similarity computation among DO terms and genes. 
Enrichment analysis including hypergeometric model and GSEA are also implemented to support discovering disease associations of high-throughput biological data.


# External documents

More documents can be found in <http://www.bioconductor.org/packages/clusterProfiler>, <http://www.bioconductor.org/packages/DOSE> and <http://guangchuangyu.github.io/tags/gosemsim>.

# Bugs/Feature Requests

If you have any, [let me know](https://github.com/GuangchuangYu/GOSemSim/issues). 

# Session Information

Here is the output of `sessionInfo()` on the system on which this document was compiled:

```{r echo=FALSE}
sessionInfo()
```

# References

