Improving Correlation with Human Judgments by Integrating Semantic Similarity with Second--Order Vectors

Abstract: Vector space methods that measure semantic similarity and relatedness often rely on distributional information such as co--occurrence frequencies or statistical measures of association to weight the importance of particular co--occurrences. In this paper, we extend these methods by incorporating a measure of semantic similarity based on a human curated taxonomy into a second--order vector representation. This results in a measure of semantic relatedness that combines both the contextual information available in a corpus--based vector space representation with the semantic knowledge found in a biomedical ontology. Our results show that incorporating semantic similarity into a second order co--occurrence matrices improves correlation with human judgments for both similarity and relatedness, and that our method compares favorably to various different word embedding methods that have recently been evaluated on the same reference standards we have used.

Measures of semantic similarity and relatedness quantify the degree to which two concepts are similar (e.g., INLINEFORM0 – INLINEFORM1 ) or related (e.g., INLINEFORM2 – INLINEFORM3 ). Semantic similarity can be viewed as a special case of semantic relatedness – to be similar is one of many ways that a pair of concepts may be related. The automated discovery of groups of semantically similar or related terms is critical to improving the retrieval BIBREF0 and clustering BIBREF1 of biomedical and clinical documents, and the development of biomedical terminologies and ontologies BIBREF2 .
There is a long history in using distributional methods to discover semantic similarity and relatedness (e.g., BIBREF3 , BIBREF4 , BIBREF5 , BIBREF6 ). These methods are all based on the distributional hypothesis, which holds that two terms that are distributionally similar (i.e., used in the same context) will also be semantically similar BIBREF7 , BIBREF8 . Recently word embedding techniques such as word2vec BIBREF9 have become very popular. Despite the prominent role that neural networks play in many of these approaches, at their core they remain distributional techniques that typically start with a word by word co–occurrence matrix, much like many of the more traditional approaches.
However, despite these successes distributional methods do not perform well when data is very sparse (which is common). One possible solution is to use second–order co–occurrence vectors BIBREF10 , BIBREF11 . In this approach the similarity between two words is not strictly based on their co–occurrence frequencies, but rather on the frequencies of the other words which occur with both of them (i.e., second order co–occurrences). This approach has been shown to be successful in quantifying semantic relatedness BIBREF12 , BIBREF13 . However, while more robust in the face of sparsity, second–order methods can result in significant amounts of noise, where contextual information that is overly general is included and does not contribute to quantifying the semantic relatedness between the two concepts.
Our goal then is to discover methods that automatically reduce the amount of noise in a second–order co–occurrence vector. We achieve this by incorporating pairwise semantic similarity scores derived from a taxonomy into our second–order vectors, and then using these scores to select only the most semantically similar co–occurrences (thereby reducing noise).
We evaluate our method on two datasets that have been annotated in multiple ways. One has been annotated for both similarity and relatedness, and the other has been annotated for relatedness by two different types of experts (medical doctors and medical coders). Our results show that integrating second order co–occurrences with measures of semantic similarity increases correlation with our human reference standards. We also compare our result to a number of other studies which have applied various word embedding methods to the same reference standards we have used. We find that our method often performs at a comparable or higher level than these approaches. These results suggest that our methods of integrating semantic similarity and relatedness values have the potential to improve performance of purely distributional methods.
This section describes the similarity and relatedness measures we integrate in our second–order co–occurrence vectors. We use two taxonomies in this study, SNOMED–CT and MeSH. SNOMED–CT (Systematized Nomenclature of Medicine Clinical Terms) is a comprehensive clinical terminology created for the electronic representation of clinical health information. MeSH (Medical Subject Headings) is a taxonomy of biomedical terms developed for indexing biomedical journal articles.
We obtain SNOMED–CT and MeSH via the Unified Medical Language System (UMLS) Metathesaurus (version 2016AA). The Metathesaurus contains approximately 2 million biomedical and clinical concepts from over 150 different terminologies that have been semi–automatically integrated into a single source. Concepts in the Metathesaurus are connected largely by two types of hierarchical relations: INLINEFORM0 / INLINEFORM1 (PAR/CHD) and INLINEFORM2 / INLINEFORM3 (RB/RN).
Measures of semantic similarity can be classified into three broad categories : path–based, feature–based and information content (IC). Path–based similarity measures use the structure of a taxonomy to measure similarity – concepts positioned close to each other are more similar than those further apart. Feature–based methods rely on set theoretic measures of overlap between features (union and intersection). The information content measures quantify the amount of information that a concept provides – more specific concepts have a higher amount of information content.
RadaMBB89 introduce the Conceptual Distance measure. This measure is simply the length of the shortest path between two concepts ( INLINEFORM0 and INLINEFORM1 ) in the MeSH hierarchy. Paths are based on broader than (RB) and narrower than (RN) relations. CaviedesC04 extends this measure to use parent (PAR) and child (CHD) relations. Our INLINEFORM2 measure is simply the reciprocal of this shortest path value (Equation EQREF3 ), so that larger values (approaching 1) indicate a high degree of similarity. DISPLAYFORM0 
While the simplicity of INLINEFORM0 is appealing, it can be misleading when concepts are at different levels of specificity. Two very general concepts may have the same path length as two very specific concepts. WuP94 introduce a correction to INLINEFORM1 that incorporates the depth of the concepts, and the depth of their Least Common Subsumer (LCS). This is the most specific ancestor two concepts share. In this measure, similarity is twice the depth of the two concept's LCS divided by the product of the depths of the individual concepts (Equation EQREF4 ). Note that if there are multiple LCSs for a pair of concepts, the deepest of them is used in this measure. DISPLAYFORM0 
ZhongZLY02 take a very similar approach and again scale the depth of the LCS by the sum of the depths of the two concepts (Equation EQREF5 ), where INLINEFORM0 . The value of INLINEFORM1 was set to 2 based on their recommendations. DISPLAYFORM0 
PekarS02 offer another variation on INLINEFORM0 , where the shortest path of the two concepts to the LCS is used, in addition to the shortest bath between the LCS and the root of the taxonomy (Equation EQREF6 ). DISPLAYFORM0 
Feature–based methods represent each concept as a set of features and then measure the overlap or sharing of features to measure similarity. In particular, each concept is represented as the set of their ancestors, and similarity is a ratio of the intersection and union of these features.
MaedcheS01 quantify the similarity between two concepts as the ratio of the intersection over their union as shown in Equation EQREF8 . DISPLAYFORM0 
BatetSV11 extend this by excluding any shared features (in the numerator) as shown in Equation EQREF9 . DISPLAYFORM0 
Information content is formally defined as the negative log of the probability of a concept. The effect of this is to assign rare (low probability) concepts a high measure of information content, since the underlying assumption is that more specific concepts are less frequently used than more common ones.
Resnik95 modified this notion of information content in order to use it as a similarity measure. He defines the similarity of two concepts to be the information content of their LCS (Equation EQREF11 ). DISPLAYFORM0 
JiangC97, Lin98, and PirroE10 extend INLINEFORM0 by incorporating the information content of the individual concepts in various different ways. Lin98 defines the similarity between two concepts as the ratio of information content of the LCS with the sum of the individual concept's information content (Equation EQREF12 ). Note that INLINEFORM1 has the same form as INLINEFORM2 and INLINEFORM3 , and is in effect using information content as a measure of specificity (rather than depth). If there is more than one possible LCS, the LCS with the greatest IC is chosen. DISPLAYFORM0 
JiangC97 define the distance between two concepts to be the sum of the information content of the two concepts minus twice the information content of the concepts' LCS. We modify this from a distance to a similarity measure by taking the reciprocal of the distance (Equation EQREF13 ). Note that the denominator of INLINEFORM0 is very similar to the numerator of INLINEFORM1 . DISPLAYFORM0 
PirroE10 define the similarity between two concepts as the information content of the two concept's LCS divided by the sum of their individual information content values minus the information content of their LCS (Equation EQREF14 ). Note that INLINEFORM0 can be viewed as a set–theoretic version of INLINEFORM1 . DISPLAYFORM0 
The information content of a concept may be derived from a corpus (corpus–based) or directly from a taxonomy (intrinsic–based). In this work we focus on corpus–based techniques.
For corpus–based information content, we estimate the probability of a concept INLINEFORM0 by taking the sum of the probability of the concept INLINEFORM1 and the probability its descendants INLINEFORM2 (Equation EQREF16 ). DISPLAYFORM0 
The initial probabilities of a concept ( INLINEFORM0 ) and its descendants ( INLINEFORM1 ) are obtained by dividing the number of times each concept and descendant occurs in the corpus, and dividing that by the total numbers of concepts ( INLINEFORM2 ).
Ideally the corpus from which we are estimating the probabilities of concepts will be sense–tagged. However, sense–tagging is a challenging problem in its own right, and it is not always possible to carry out reliably on larger amounts of text. In fact in this paper we did not use any sense–tagging of the corpus we derived information content from.
Instead, we estimated the probability of a concept by using the UMLSonMedline dataset. This was created by the National Library of Medicine and consists of concepts from the 2009AB UMLS and the counts of the number of times they occurred in a snapshot of Medline taken on 12 January, 2009. These counts were obtained by using the Essie Search Engine BIBREF14 which queried Medline with normalized strings from the 2009AB MRCONSO table in the UMLS. The frequency of a CUI was obtained by aggregating the frequency counts of the terms associated with the CUI to provide a rough estimate of its frequency. The information content measures then use this information to calculate the probability of a concept.
Another alternative is the use of Intrinsic Information Content. It assess the informativeness of concept based on its placement within a taxonomy by considering the number of incoming (ancestors) relative to outgoing (descendant) links BIBREF15 (Equation EQREF17 ). DISPLAYFORM0 
where INLINEFORM0 are the number of descendants of concept INLINEFORM1 that are leaf nodes, INLINEFORM2 are the number of concept INLINEFORM3 's ancestors and INLINEFORM4 are the total number of leaf nodes in the taxonomy.
Lesk86 observed that concepts that are related should share more words in their respective definitions than concepts that are less connected. He was able to perform word sense disambiguation by identifying the senses of words in a sentence with the largest number of overlaps between their definitions. An overlap is the longest sequence of one or more consecutive words that occur in both definitions. BanerjeeP03 extended this idea to WordNet, but observed that WordNet glosses are often very short, and did not contain enough information to distinguish between multiple concepts. Therefore, they created a super–gloss for each concept by adding the glosses of related concepts to the gloss of the concept itself (and then finding overlaps).
PatwardhanP06 adapted this measure to second–order co–occurrence vectors. In this approach, a vector is created for each word in a concept's definition that shows which words co–occur with it in a corpus. These word vectors are averaged to create a single co-occurrence vector for the concept. The similarity between the concepts is calculated by taking the cosine between the concepts second–order vectors. LiuMPMP12 modified and extended this measure to be used to quantify the relatedness between biomedical and clinical terms in the UMLS. The work in this paper can be seen as a further extension of PatwardhanP06 and LiuMPMP12.
In this section, we describe our second–order similarity vector measure. This incorporates both contextual information using the term pair's definition and their pairwise semantic similarity scores derived from a taxonomy. There are two stages to our approach. First, a co–occurrence matrix must be constructed. Second, this matrix is used to construct a second–order co–occurrence vector for each concept in a pair of concepts to be measured for relatedness.
We build an INLINEFORM0 similarity matrix using an external corpus where the rows and columns represent words within the corpus and the element contains the similarity score between the row word and column word using the similarity measures discussed above. If a word maps to more than one possible sense, we use the sense that returns the highest similarity score.
For this paper our external corpus was the NLM 2015 Medline baseline. Medline is a bibliographic database containing over 23 million citations to journal articles in the biomedical domain and is maintained by National Library of Medicine. The 2015 Medline Baseline encompasses approximately 5,600 journals starting from 1948 and contains 23,343,329 citations, of which 2,579,239 contain abstracts. In this work, we use Medline titles and abstracts from 1975 to present day. Prior to 1975, only 2% of the citations contained an abstract. We then calculate the similarity for each bigram in this dataset and include those that have a similarity score greater than a specified threshold on these experiments.
We obtain definitions for each of the two terms we wish to measure. Due to the sparsity and inconsistencies of the definitions in the UMLS, we not only use the definition of the term (CUI) but also include the definition of its related concepts. This follows the method proposed by PatwardhanP06 for general English and WordNet, and which was adapted for the UMLS and the medical domain by LiuMPMP12. In particular we add the definitions of any concepts connected via a parent (PAR), child (CHD), RB (broader than), RN (narrower than) or TERM (terms associated with CUI) relation. All of the definitions for a term are combined into a single super–gloss. At the end of this process we should have two super–glosses, one for each term to be measured for relatedness.
Next, we process each super–gloss as follows:
We extract a first–order co–occurrence vector for each term in the super–gloss from the co–occurrence matrix created previously.
We take the average of the first order co–occurrence vectors associated with the terms in a super–gloss and use that to represent the meaning of the term. This is a second–order co–occurrence vector.
After a second–order co–occurrence vector has been constructed for each term, then we calculate the cosine between these two vectors to measure the relatedness of the terms.
We use two reference standards to evaluate the semantic similarity and relatedness measures . UMNSRS was annotated for both similarity and relatedness by medical residents. MiniMayoSRS was annotated for relatedness by medical doctors (MD) and medical coders (coder). In this section, we describe these data sets and describe a few of their differences.
MiniMayoSRS: The MayoSRS, developed by PakhomovPMMRC10, consists of 101 clinical term pairs whose relatedness was determined by nine medical coders and three physicians from the Mayo Clinic. The relatedness of each term pair was assessed based on a four point scale: (4.0) practically synonymous, (3.0) related, (2.0) marginally related and (1.0) unrelated. MiniMayoSRS is a subset of the MayoSRS and consists of 30 term pairs on which a higher inter–annotator agreement was achieved. The average correlation between physicians is 0.68. The average correlation between medical coders is 0.78. We evaluate our method on the mean of the physician scores, and the mean of the coders scores in this subset in the same manner as reported by PedersenPPC07.
UMNSRS: The University of Minnesota Semantic Relatedness Set (UMNSRS) was developed by PakhomovMALPM10, and consists of 725 clinical term pairs whose semantic similarity and relatedness was determined independently by four medical residents from the University of Minnesota Medical School. The similarity and relatedness of each term pair was annotated based on a continuous scale by having the resident touch a bar on a touch sensitive computer screen to indicate the degree of similarity or relatedness. The Intraclass Correlation Coefficient (ICC) for the reference standard tagged for similarity was 0.47, and 0.50 for relatedness. Therefore, as suggested by Pakhomov and colleagues,we use a subset of the ratings consisting of 401 pairs for the similarity set and 430 pairs for the relatedness set which each have an ICC of 0.73.
We conducted our experiments using the freely available open source software package UMLS::Similarity BIBREF16 version 1.47. This package takes as input two terms (or UMLS concepts) and returns their similarity or relatedness using the measures discussed in Section SECREF2 .
Correlation between the similarity measures and human judgments were estimated using Spearman's Rank Correlation ( INLINEFORM0 ). Spearman's measures the statistical dependence between two variables to assess how well the relationship between the rankings of the variables can be described using a monotonic function. We used Fisher's r-to-z transformation BIBREF17 to calculate the significance between the correlation results.
Table TABREF26 shows the Spearman's Rank Correlation between the human scores from the four reference standards and the scores from the various measures of similarity introduced in Section SECREF2 . Each class of measure is followed by the scores obtained when integrating our second order vector approach with these measures of semantic similarity.
The results for UMNSRS tagged for similarity ( INLINEFORM0 ) and MiniMayoSRS tagged by coders show that all of the second-order similarity vector measures ( INLINEFORM1 ) except for INLINEFORM2 - INLINEFORM3 obtain a higher correlation than the original measures. We found that INLINEFORM4 - INLINEFORM5 and INLINEFORM6 - INLINEFORM7 obtain the highest correlations of all these results with human judgments.
For the UMNSRS dataset tagged for relatedness and MiniMayoSRS tagged by physicians (MD), the original INLINEFORM0 measure obtains a higher correlation than our measure ( INLINEFORM1 ) although the difference is not statistically significant ( INLINEFORM2 ).
In order to analyze and better understand these results, we filtered the bigram pairs used to create the initial similarity matrix based on the strength of their similarity using the INLINEFORM0 and the INLINEFORM1 measures. Note that the INLINEFORM2 measure holds to a 0 to 1 scale, while INLINEFORM3 ranges from 0 to an unspecified upper bound that is dependent on the size of the corpus from which information content is estimated. As such we use a different range of threshold values for each measure. We discuss the results of this filtering below.
Table TABREF29 shows the results of applying the threshold parameter on each of the reference standards using the INLINEFORM0 measure. For example, a threshold of 0 indicates that all of the bigrams were included in the similarity matrix; and a threshold of 1 indicates that only the bigram pairs with a similarity score greater than one were included.
These results show that using a threshold cutoff of 2 obtains the highest correlation for the UMNSRS dataset, and that a threshold cutoff of 4 obtains the highest correlation for the MiniMayoSRS dataset. All of the results show an increase in correlation with human judgments when incorporating a threshold cutoff over all of the original measures. The increase in the correlation for the UMNSRS tagged for similarity is statistically significant ( INLINEFORM0 ), however this is not the case for the UMNSRS tagged for relatedness nor for the MiniMayoSRS data.
Similarly, Table TABREF30 shows the results of applying the threshold parameter (T) on each of the reference standards using the INLINEFORM0 measure. Although, unlike INLINEFORM1 whose scores are greater than or equal to 0 without an upper limit, the INLINEFORM2 measure returns scores between 0 and 1 (inclusive). Therefore, here a threshold of 0 indicates that all of the bigrams were included in the similarity matrix; and a threshold of INLINEFORM3 indicates that only the bigram pairs with a similarity score greater than INLINEFORM4 were included. The results show an increase in accuracy for all of the datasets except for the MiniMayoSRS tagged for physicians. The increase in the results for the UMNSRS tagged for similarity and the MayoSRS is statistically significant ( INLINEFORM5 ). This is not the case for the UMNSRS tagged for relatedness nor the MiniMayoSRS.
Overall, these results indicate that including only those bigrams that have a sufficiently high similarity score increases the correlation results with human judgments, but what quantifies as sufficiently high varies depending on the dataset and measure.
Recently, word embeddings BIBREF9 have become a popular method for measuring semantic relatedness in the biomedical domain. This is a neural network based approach that learns a representation of a word by word co–occurrence matrix. The basic idea is that the neural network learns a series of weights (the hidden layer within the neural network) that either maximizes the probability of a word given its context, referred to as the continuous bag of words (CBOW) approach, or that maximizes the probability of the context given a word, referred to as the Skip–gram approach. These approaches have been used in numerous recent papers.
muneeb2015evalutating trained both the Skip–gram and CBOW models over the PubMed Central Open Access (PMC) corpus of approximately 1.25 million articles. They evaluated the models on a subset of the UMNSRS data, removing word pairs that did not occur in their training corpus more than ten times. chiu2016how evaluated both the the Skip–gram and CBOW models over the PMC corpus and PubMed. They also evaluated the models on a subset of the UMNSRS ignoring those words that did not appear in their training corpus. Pakhomov2016corpus trained CBOW model over three different types of corpora: clinical (clinical notes from the Fairview Health System), biomedical (PMC corpus), and general English (Wikipedia). They evaluated their method using a subset of the UMNSRS restricting to single word term pairs and removing those not found within their training corpus. sajad2015domain trained the Skip–gram model over CUIs identified by MetaMap on the OHSUMED corpus, a collection of 348,566 biomedical research articles. They evaluated the method on the complete UMNSRS, MiniMayoSRS and the MayoSRS datasets; any subset information about the dataset was not explicitly stated therefore we believe a direct comparison may be possible.
In addition, a previous work very closely related to ours is a retrofitting vector method proposed by YuCBJW16 that incorporates ontological information into a vector representation by including semantically related words. In their measure, they first map a biomedical term to MeSH terms, and second build a word vector based on the documents assigned to the respective MeSH term. They then retrofit the vector by including semantically related words found in the Unified Medical Language System. They evaluate their method on the MiniMayoSRS dataset.
Table TABREF31 shows a comparison to the top correlation scores reported by each of these works on the respective datasets (or subsets) they evaluated their methods on. N refers to the number of term pairs in the dataset the authors report they evaluated their method. The table also includes our top scoring results: the integrated vector-res and vector-faith. The results show that integrating semantic similarity measures into second–order co–occurrence vectors obtains a higher or on–par correlation with human judgments as the previous works reported results with the exception of the UMNSRS rel dataset. The results reported by Pakhomov2016corpus and chiu2016how obtain a higher correlation although the results can not be directly compared because both works used different subsets of the term pairs from the UMNSRS dataset.
We have presented a method for quantifying the similarity and relatedness between two terms that integrates pair–wise similarity scores into second–order vectors. The goal of this approach is two–fold. First, we restrict the context used by the vector measure to words that exist in the biomedical domain, and second, we apply larger weights to those word pairs that are more similar to each other. Our hypothesis was that this combination would reduce the amount of noise in the vectors and therefore increase their correlation with human judgments. We evaluated our method on datasets that have been manually annotated for relatedness and similarity and found evidence to support this hypothesis. In particular we discovered that guiding the creation of a second–order context vector by selecting term pairs from biomedical text based on their semantic similarity led to improved levels of correlation with human judgment.
We also explored using a threshold cutoff to include only those term pairs that obtained a sufficiently large level of similarity. We found that eliminating less similar pairs improved the overall results (to a point). In the future, we plan to explore metrics to automatically determine the threshold cutoff appropriate for a given dataset and measure. We also plan to explore additional features that can be integrated with a second–order vector measure that will reduce the noise but still provide sufficient information to quantify relatedness. We are particularly interested in approaches that learn word, phrase, and sentence embeddings from structured corpora such as literature BIBREF23 and dictionary entries BIBREF24 . Such embeddings could be integrated into a second–order vector or be used on their own.
Finally, we compared our proposed method to other distributional approaches, focusing on those that used word embeddings. Our results showed that integrating semantic similarity measures into second–order co–occurrence vectors obtains the same or higher correlation with human judgments as do various different word embedding approaches. However, a direct comparison was not possible due to variations in the subsets of the UMNSRS evaluation dataset used. In the future, we would not only like to conduct a direct comparison but also explore integrating semantic similarity into various kinds of word embeddings by training on pair–wise values of semantic similarity as well as co–occurrence statistics.

Figure and table captions:
Table 1: Spearman’s Correlation Results
Table 2: Threshold Correlation with vector-res
Table 3: Threshold Correlation with vector-faith
Table 4: Comparison with Previous Work

Questions about this paper:
What is a second order co-ocurrence matrix?
How many humans participated?

Answers:
The matrix containing co-occurrences of the words which occur with the both words of every given pair of words.
16