Revealing and avoiding bias in semantic similarity scores for protein pairs
© Wang et al; licensee BioMed Central Ltd. 2010
Received: 9 February 2010
Accepted: 28 May 2010
Published: 28 May 2010
Semantic similarity scores for protein pairs are widely applied in functional genomic researches for finding functional clusters of proteins, predicting protein functions and protein-protein interactions, and for identifying putative disease genes. However, because some proteins, such as those related to diseases, tend to be studied more intensively, annotations are likely to be biased, which may affect applications based on semantic similarity measures. Thus, it is necessary to evaluate the effects of the bias on semantic similarity scores between proteins and then find a method to avoid them.
First, we evaluated 14 commonly used semantic similarity scores for protein pairs and demonstrated that they significantly correlated with the numbers of annotation terms for the proteins (also known as the protein annotation length). These results suggested that current applications of the semantic similarity scores between proteins might be unreliable. Then, to reduce this annotation bias effect, we proposed normalizing the semantic similarity scores between proteins using the power transformation of the scores. We provide evidence that this improves performance in some applications.
Current semantic similarity measures for protein pairs are highly dependent on protein annotation lengths, which are subject to biological research bias. This affects applications that are based on these semantic similarity scores, especially in clustering studies that rely on score magnitudes. The normalized scores proposed in this paper can reduce the effects of this bias to some extent.
Many scores for measuring semantic similarity (also termed functional similarity) between proteins have been proposed, based on the Gene Ontology (GO) terms  used to annotate the proteins. Some semantic similarity scores for a protein pair [2, 3] are calculated by combining the similarity scores for the term pairs [4–7] describing the two proteins. Other scores between proteins that do not use pairwise similarity scores between terms have also been proposed [8, 7, 9–12]. Similarity scores for protein pairs have been widely applied in functional genomic research . These scores are commonly used to analyze the correlation between functional similarity and similarities on other aspects, such as amino acid sequence similarity [2, 8, 14–16], or expression similarity [17–19]. Another type of applications is finding functional clusters of proteins [7, 20–22], or functional modules in physical or genetic protein-protein interaction networks [23–28]. Similarity scores are also used to predict protein functions [29–35], protein-protein interactions [36–41] and putative disease genes [42–45].
GO protein annotations are known to be incomplete , and suffer from a large research bias, because certain proteins, such as those related to diseases, tend to be studied more intensively [43, 47, 48]. Such an annotation bias may affect protein semantic similarity scores. In this paper, we evaluated 14 common semantic similarity scores for protein pairs, and demonstrated that the scores significantly correlated with the numbers of annotation terms for the proteins (i.e., the annotation length). Thus, we proposed normalizing the scores based on their power transformation to reduce annotation bias effects, and we provide evidence that this improves performance in some applications.
Gene Ontology (GO)
The GO annotation data for human was downloaded from the UniProt database http://www.ebi.ac.uk/GOA/index.html, including versions in November (Nov) 2001, Nov 2002, Nov 2003, Nov 2004, Nov 2005, Nov 2006, Nov 2007 and August 2008. The GO vocabulary data were downloaded from the GO website http://www.geneontology.org in August 2008. Here, we considered only IS-A links in GO [5, 6], and we mainly present the results based on the "Biological Process" (BP) sub-ontology. We also observed that all the semantic similarity scores for pairs of term groups are dependent on the annotation lengths when using "Molecular Function" and "Cellular Component" (data not shown).
Online Mendelian Inheritance in Man (OMIM) database and disease classification
The data for 1996 genes associated with 2192 diseases were downloaded from the OMIM database ftp://ftp.ncbi.nih.gov/repository/OMIM in August 2008, of which 1752 genes were annotated to GO BP terms. According to Goh et al. , the 2192 diseases were classified into 20 primary disorder classes based on the affected physiological systems. Diseases with multiple clinical features were assigned to the "multiple" class, and disease assigned to "Unclassified" class were not analyzed.
Similarity scores for term pairs
Similarity scores for protein pairs based on pairwise similarity scores between term groups
In some methods, the similarity scores for term pairs describing two proteins are combined to calculate the semantic similarity scores of the two proteins. Here, two combination methods were evaluated: the arithmetic average (AVG) of the pairwise semantic similarity scores between two groups of GO terms describing the two proteins  and the best-match average (BMA) approach .
where , .
Summary of 14 semantic similarity scores for protein pairs.
Similarity scores for term pairs
Information content of the most informative common ancestor of two terms
Normalized Resnik similarity score by assessing how close two terms are to their most informative common ancestor
Weighted Lin similarity score by using the probability of annotations of the most informative common ancestor
Based on the difference between two terms and their most informative common ancestor in information content
Similarity scores for protein pairs based on pairwise similarity scores between term groups
The average of the similarity scores for all pairs of terms between two groups of protein annotations
Same with those for the corresponding similarity scores for term pairs
The score of the best-matching pairs between two groups of protein annotations
Similarity scores for protein pairs based on groupwise similarity scores between term groups
The number of terms shared by the annotations for two proteins
Dividing TO by the minimum of the annotation lengths of two proteins
Dividing TO by the average of annotation lengths of two proteins
A chance-corrected measure of co-occurrence between two groups of protein annotations
Jaccard index weighted by the information content of each GO term
Cosine similarity weighted by the information content of each GO term
Similarity scores for protein pairs based on groupwise similarity scores between term groups
- (1)The TO (Term Overlap) score  simply counts the number of overlapped terms for two proteins P 1 and P 2 as follows:
where n is the number of all the GO BP terms and is the information content of term k if it is annotated with protein P 1 (P 2 ) while is 0 if the term k is not an annotation of the protein P 1 (P 2 ).
In total, we evaluated 14 semantic similarity scores for protein pairs (see Table 1). We note that some other semantic similarity scores for protein pairs [13, 51] were not evaluated in this paper. For example, the score proposed by Wang et al. , which weights the IS-A and PART-OF links of GO, was not analyzed, because we considered only IS-A links in this study.
Using randomly selected pairs of term groups, we evaluated the increase in protein semantic similarity score that resulted from only the increased annotation length, regardless of other biological factors. First, we randomly selected 10,000 pairs of term groups with the same sizes (corresponding to the annotation lengths of proteins) ranging from 1 to 10, since only 1.5% of proteins had more than 10 annotations in GO BP ontology. Then, using each of the 14 semantic similarity scores described above, we calculated the semantic similarity scores for random term group pairs, and analyzed whether these scores increased as the group size increased using the Spearman rank correlation coefficient .
Normalization based on power transformation
As demonstrated in the Results section, a similarity score for two groups of terms is dependent on the lengths of the term groups. To reduce the effect of the lengths on the scores, we took two steps to make the scores for pairs of term groups with given length combinations follow the standard normal distribution.
where M SS is the median of the random SS(TG1, TG2) distribution which was estimated by the similarity scores for 10,000 pairs of random term groups (with lengths L 1 and L 2 ). T q and T1-qare the lower and upper q th quantiles of this distribution ( ). By the one-sample Kolmogorov-Smirnov test for distribution goodness-of-fit , at the significance level of 0.1, we tested whether the power-transformed scores for pairs of term groups with given length combinations fit normal distributions.
In the above normalization formula, M TSS and STD TSS are the median and standard deviation of the power-transformed scores respectively. Here, we used the median rather than the mean in the normalization formula because it might be more appropriate for measuring the location parameter of a distribution when the distribution might be skewed [56–58]. As shown in the Results section, most of the normalized scores for pairs of term groups with given length combinations follow normal distributions. In this situation, the means and the medians are equal.
Sequence similarity scores for protein pairs
Amino acid sequence data for human proteins was downloaded from UniProt ftp://ftp.uniprot.org in August 2008. The sequence similarity between two proteins was measured by the ln(bit score), and calculated by the NCBI "blastall" program . Sequence similarity scores were obtained for a total of 499,878 protein pairs with GO BP annotations.
Clustering algorithm and enrichment analysis
where Max SS and Min SS are the maximum and minimum values of the original similarity scores for all protein pairs from a protein set (e.g., a set of proteins encoded by a set of disease genes). Max NSS and Min NSS are the maximum and minimum values of the normalized similarity scores for all these protein pairs.
Then, we calculated the distance between two proteins as D(P 1 , P 2 ) = 1-MM(P 1 , P 2 ) based on the original score. Similarly, based on the normalized score, the distance was calculated as ND(P 1 , P 2 ) = 1-NM(P 1 , P 2 ). Both D(P 1 , P 2 ) and ND(P 1 , P 2 ) take values ranging from 0 to 1 and satisfy three main properties of distance metrics : (i) symmetry, D(P 1 , P 2 ) = D(P 2 , P 1 ) (ND(P 1 , P 2 ) = ND(P 2 , P 1 )); (ii) non-negative, D(P 1 , P 2 ) ≥ 0 (ND(P 1 , P 2 ) ≥ 0); (iii) triangle inequality, D(P 1 , P 3 ) ≤ D(P 1 , P 2 )+D(P 2 , P 3 ) (ND(P 1 , P 3 ) ≤ ND(P 1 , P 2 )+ND(P 2 , P 3 )). Using D(P 1 , P 2 ) and ND(P 1 , P 2 ) respectively, we clustered disease genes by the complete linkage clustering algorithm .
To evaluate the clustering results, using the hypergeometric distribution model [63, 64], we calculated the probability p of detecting at least the observed number of genes related to a disease category proposed by Goh et al.  in a cluster of disease genes by random chance. The p values were corrected by the false discovery rate (FDR) by the Benjamini-Hochberg (BH) procedure . With FDR of 1%, we found the disease categories enriched in a cluster of disease genes found by the clustering algorithm.
The dependence of the semantic similarity scores on annotation lengths
Applications of the normalized scores
The performance of different data transformation methods*.
λ = 1
Inverse (λ = -1)
Cube-root (λ = 1/3)
Square-root (λ = 1/2)
Square (λ = 2)
In this paper, we found that most semantic similarity scores for protein pairs increased as protein annotation lengths increased. Because protein annotations are likely to be subject to biological research bias, most applications based on current semantic similarity scores for protein pairs will be biased. Without the annotation bias, one could argue that over-annotated proteins might be more likely to be similar than under-annotated proteins, when considering only shared functions, and disregarding differences. However, currently, most semantic similarity scores for protein pairs evaluate the overall functional similarity between proteins. Depending on the available knowledge about domains, and the final aim of the application, different criteria could be used to define similarity between proteins. We note that protein annotations in GO for most model organisms (e.g., Saccharomyces cerevisiae) are also incomplete and suffer from the research bias because important genes such as the homologues of human disease genes tend to be studied more intensively [79, 80]. By analyzing the Saccharomyces cerevisiae data, we also found that the similarity scores between two groups of terms increased significantly with the annotation lengths (data not shown). Thus, our conclusion on the bias of semantic similarity scores for proteins would be applicable to other organisms.
A protein is usually annotated to a group of GO terms. Often, the semantic similarity scores between two proteins are calculated using some combination methods [2, 3] based on the semantic similarity scores for pairs of terms annotated with the two proteins. Many semantic similarity scores for term pairs such as the Resnik , Lin , Relevance (RS)  and Jiang  are based on the information content (related to the annotation specificity) of the terms. Based on these similarity scores for term pairs, the similarity scores for two proteins might not always increase, if the proteins have many annotations with low-specificity. However, as shown here, all the AVG and BMA scores for protein pairs based on the Resnik, Lin, RS and Jiang scores for term pairs still significantly correlated with the protein annotation lengths.
To reduce the effects of protein annotation bias, we normalized the scores based on the power transformation by estimating power . The normalization method based on the power transformation can transform most scores based on nine of the similarity measures to fit normal distributions but it performs poorly for the other five similarity measures. Thus, future works are needed to further improve the data transformation and normalization method.
The feasibility of the normalized scores was analyzed for two types of applications and the results showed that the normalized scores were useful in these applications. Analysis of the correlation between functional similarities and similarities on other aspects [2, 8, 14–19] might be less affected by the annotation bias, because the ranks of semantic similarity scores for protein pairs and their corresponding normalized scores were highly correlated. Our results also showed that clustering analysis [7, 20–22] using the magnitude of the semantic similarity scores might be more seriously affected by biased protein annotations, and the results could be improved by using the normalized scores.
A third type of applications that uses protein semantic similarity scores is predicting protein functions [29–35], protein-protein interactions [36–41] and disease genes [42–45]. However, because many other factors, such as the selection of algorithms and the definition of positive and negative sets  can affect the prediction results, we did not evaluate the effect of the annotation bias on these uses. Nevertheless, because this type of applications also uses the similarity score magnitudes, we recommend also using normalized scores in prediction studies, to reduce the effects of the annotation bias.
To avoid the influence of annotation bias, other approaches may be attempted. For example, the statistical p-value of a semantic similarity score for a protein pair could be evaluated by comparing this score with the scores of random protein pairs with the same annotation lengths. If the semantic similarity score of the two proteins was significantly larger than the score expected by random chance, at a given significance level (p-value), we could determine that the two proteins are functionally similar . Functional modules could be found by linking functionally related proteins. To analyze the functional relationships of proteins more comprehensively, the semantic similarity scores should be combined with other functional data, such as protein-protein interaction, co-expression and co-conservation of proteins [83–85].
Current protein semantic similarity scores are highly dependent on protein annotation lengths, which are subject to biological research bias. This bias may affect many current applications based on these scores. The proposed normalization method might solve this problem to some extend.
This work was supported by the National Natural Science Foundation of China (grant nos. 30571034, 30970668, 30670539).
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