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1 Introduction
In Natural Language Processing (NLP), semantic similarity plays an important role and one of the fundamental tasks for many NLP applications and its related areas. Semantic Textual Similarity (STS) can be defined by a metric over a set of documents with the idea is to finding the semantic similarity between them. Similarity between the documents is based on the direct and indirect relationships among them 13, 49. These relationships can be measured and recognized by the presence of semantic relations among them. Identification of STS in short texts was proposed in 2006 in the works reported in 30, 35. After that, focus was shifted on large documents or individual words.
After that, since 2012 the task of semantic similarity is not only limited to find out the similarity between two texts, but also to generate a similarity score from 0 to 5 by different SemEval tasks1 1, 2, 3. In this task, a scale of 0 means unrelated and 5 means complete semantically equivalence.
Since its inception, the problem has seen a large number of solutions in a relatively small amount of time. The central idea behind the most solution is that, the identification and alignment of semantically similar or related words across the two sentences and the aggregation of these similarities to generate an overall similarity 23, 35, 65.
One of the major goals of STS task, is to create a unified framework by combining several independent semantic components in order to find their impact over several NLP tasks. Developing such framework is an important research problem, having many important applications in NLP such as information retrieval (IR) and in digital education like text summarization 4, 61, question answering 37, relevance feedback and text classification 47, word sense disambiguation 30, and extractive summarization 50.
Semantic similarity also contributes for many semantic web applications like community extraction, ontology generation and entity disambiguation. It is also useful for Twitter search 50, where it is required the ability to accurately measure semantic relatedness between concepts or entities. In IR one of the main problems is to retrieve a set of documents and retrieving images by captions 11, which is semantically related to a given user query in a web search engine.
In the database field also, text similarity can be used for schema matching to solve the semantic heterogeneity for data sharing system, data integration system, message passing system, and peer-to-peer data management system 19. It is also useful for relational join operations in database where join attributes are textually similar to each other. It has a verity of application domain including integration and querying of data from heterogeneous resources, cleaning of data, and mining of data 12, 51.
In NLP it is noticed that, STS is related to both textual entailment (TE) and paraphrasing, but differs in a number of ways. In NLP, TE can draw three directional relationships between two text fragments while the task considered two text fragments as text (t) and hypothesis (h) respectively. On the other hand, paraphrasing identification is the task of recognizing text fragments with approximately the same meaning within a specific context. So, TE and paraphrasing gives a yes/no decision and STS identifies the degree of equivalence of text and rated them on the basis of their semantic relationships.
Measuring semantic similarity between texts can be categorized into the following ways: (i) topological (ii) statistical similarity (iii) semantic based (iv) vector space model (v) word alignment based and (vi) machine learning. Among these methods, topological studies plays an important role to understand intended meaning of an ambiguous word, which is very difficult to process computationally. For many NLP related task it is important to understand the semantic relation between the word/ concepts. To decompose such systems we need to work with word level relation and those can be considered as hierarchical, associative and equivalence.
The rest of this paper is organised as follows: in Section 2, we reported the related work on topological methods. In Section 3, we examined the details implementation of three similarity methods. Topological methods are reported in Section 3.1 and statistical similarity measures are reported in Section 3.2. In Section 3.3, we reported string based similarity measures in two categories such as character based and term based similarity (Section 3.3.1 and 3.3.2). We also proposed a new method for detection of textual similarity between sentences based on language model and WordNet taxonomy in Section 4 and we reported a short experiment on the proposed method in Section 5. In Section 6, we listed out available software's and tools those are used for measuring the similarity. Applications of STS are reported in Section 7, and finally conclusion of the work is drawn in Section 8.
2 Related Work on Topological Methods
In many cases determining the intended meaning of an ambiguous word is difficult for human and it is quite difficult to process automatically also. This ambiguity can be eliminated by considering the following relationships among the words or concepts: (i) hierarchical (e.g. IS-A or hypernym-hyponym, part-whole etc.), (ii) associative (e.g. cause-effect) and, (iii) equivalence 25. Among these, IS-A relation is widely used and studied, which maps to the human cognitive view of classification (i.e. taxonomy). The IS-A relation among the concepts has been suggested and employed as a special case of semantic similarity of distance 42. Semantic similarity can be estimated by defining a topological similarity by using ontologies to define the distance between term and concepts.
Taxonomy is often represented as a hierarchical structure and also considered as a network structure. To measuring the similarity information of this network can be useful. There are several ways to determine the conceptual similarity between two words in a hierarchical semantic network. There are essentially two types of approaches, which calculate topological similarity between ontological concepts. Those are (i) node based (information-content approach) and (ii) edge-based (distance based).
Issues related to lexical association was reported in 45, where a generalization technique of lexical association was proposed. To solve these issues (i.e. reliable word/ word correspondence) author facilitate different statistical facts by considering word classes rather than individual words. In this task, a set of possible word classes were constructed from WordNet 36 and an investigation was conducted to identify the relationship between word/ classes using mutual information. For word-based information retrieval, information from WordNet was passed over a SMART environment where a content description was added (only part-of-speech information) with the input text.
Ambiguity of word form during document indexing was investigated using a semantic based network where semantic distance between network nodes was considered 62. In this work, word sense during document indexing was studied using the WordNet semantic network. Distance between multiple senses of input word was disambiguated by finding the combination of senses from a set of contiguous terms.
In another work, Philip Resnik proposed a method for identification of semantic similarity in a taxonomy based on the notion of information content 45. Similarity between two words/ concepts was evaluated by considering the common information between them and a set of fifty thousand (50,000) nodes form WordNet taxonomy of noun class was considered for this task. To calculate the frequencies of concepts Brown Corpus of American English (having 1000,000 words) was considered 27.
Jiang and Conrath introduces a new approach for measuring semantic similarity between words using lexical taxonomy structure with corpus statistical information. So the semantic distance between nodes in the semantic space was constructed by the taxonomy, which provides a better result with the computational evidence those are derived from a distributional analysis of corpus data. This proposed method, is a combined approach in which edge counting scheme was inherited and further enhanced by node based approach 25.
To find the similarity between phrases and sentences a random walk over a graph was proposed in 43. In this work, local semantic information and semantic resources of WordNet was combined together. Semantic signature generated by random walk was compared to another such distribution to get the similarity score. It is identified that, graph work similarity between texts can be used as feature for recognizing textual entailment task.
Methods reported in this section are based on topological similarity between ontological concepts and apart from these, methods related to ontological instances namely: (i) pair-wise; and (ii) group-wise are also found in literature. It was founded that methods based on ontological instances are mainly used to represent medical knowledge's and no such work was noticed, which was used for semantic textual similarity between classes or phrases or sentences. So all these tasks are not reported here, because the proposed work is planned for textual similarity only. In the next section a detailed illustration is reported for methods used to identify the semantic similarities between words/ classes based on taxonomical concepts.
3 Semantic Similarity Methodologies
3.1 Topological/ Knowledge-based Methods
In the field of Information Retrieval (IR), document retrieval based on semantic similarity of words has been largely investigated and all these methods consider the semantic and ontological relationships that exist between the words (e.g. polysemy, synonym etc.). So based on this knowledge semantic similarity between objects in ontology can broadly be categorised into three groups like: (1) node-based; (2) edged-based; and (3) hybrid where it combines node and edge-based.
1. Node Based/ Information Content Approach: Node based or Information Content (IC) approaches 44, 45, are used to determine the semantic similarity between concepts. In this method, each of the concept or node poses IS-A taxonomy are kept in one set called C and all of these nodes carry unique concepts. Intuitively, one key to the similarity of two concepts is that to which they share information in common. In taxonomy direct relation between two concepts can be found by an edge counting method. In this method, if the minimal path between two nodes is long, that means it is necessary to go high in the hierarchy to find a least upper bound. An example of IS-A relationship between the concepts is shown in Fig. 1, where two concepts NICKEL and DIME both subsumes COIN. In this example NICKEL and CREDIT CARD shares a common super class MEDIUM OF EXCHANGE 64.
In order to avoid unreliability edge-distances between nodes, it is possible to associate probability with taxonomy. The value of IC of a class is obtained by estimating the probability in a large corpus with a function p : C → [0,1] if c ∈ C, p(c), being the probability of encountering an instance c. Considering the notation of information theory 52, IC of a class can be calculated as follows:
Quantifying information content in this way: if the probability increases, its information content decreases. It means that if there is a unique top in the tree, then its probability is 1, so the information content is 0 and the similarity of two concepts can be calculated as follows:
where sim(c1, c2) is the set of concepts that subsume both c1 and c2. From Fig. 1, it is identified that, similarity of NICKEL and DIME can be calculated by considering all the upper bounds. Among those upper bounds node having highest information content value is considered as similarity score between these two nodes.
To implement the information content model reported in 61, WordNet fifty thousand nodes were considered, where taxonomy of concepts represented by nouns and compound nominals 36. Before implementing IC, two concepts need to define as sets of words(c) and classes(w). Words(c) is the set of words subsumed by the class and classes(w) is defined as the classes in which the word is contained. The class can be seen as a sub-tree in the whole hierarchy and classes(w) is the set of possible senses that the word has:
A simple class/ concept frequency formula is also defined in 45 and 46, where the number of word sense is the key factor:
and
Finally, the class probability can be computed using Maximum Likelihood Estimation (MLE):
where N is the total number of nouns observed (excluding those not subsumed by any WordNet class, of course).
An example of multiple inheritance concepts like NICKLE and GOLD those have more super classes as shown in Fig. 2. In this case one word have more sense, so the similarity can be determined by the best similarity value among all the class pairs, which belongs to their various senses 25:
where sen(w) denotes the set of possible senses for word w.
In another task 43, extends the node based method to vector space model for semantic measure using random walk algorithm. In this approach, instead of comparing between two text segments directly, it compares distribution of each text and a random walk is generated over a graph, which is derived from WordNet and corpus statistics.
WordNet is itself a graph over clusters, which contains one sense of one or more similar words. Each node in the graph represents a synset. Word having different meaning: multiple synsets (or cluster) is generated based on different meaning. For example the word bank belongs to the two different synsets, one for financial bank and other for river bank. By constructing each edge created from a WordNet relationship is guaranteed to have a corresponding edge in the opposite direction. Nodes are connected with edges (represents the relation) corresponding too many relationships from WordNet is as follows: hypernym/hyponym, in-stance/instanceof, all holonym/meronym links, antonym, entails/entailed by, adjective satellite, causes/caused by, participle, pertains to, derives/derived from, attribute/has attribute, and topical (but not regional or usage) domain links. Following types of nodes from WordNet was considered for graph construction:
Synset: Each WordNet synset has a corresponding node. For example, one node corresponds to the synset referred to by "dog#n#3," the third sense of dog as noun, whose meaning is "an informal term for a man."
TokenPOS: One node is allocated to every word coupled with a Part Of Speech (PoS), such as "dog#n" meaning dog as a noun. These nodes link to all the synsets they participate in, so that "dog#n" links the synset nodes for canine, hound, hot dog etc.
Token: Nodes do not have any part-of-speech information in synsets, all the TokenPOS nodes were linked with all such nodes.
Random walk methods have following advantages over traditional node based method:
It enables the similarity measure to have a principled means by combining multiple types of edges from WordNet.
By traversing all the links, random walk aggregates the local similarity statistics across the entire graph 22.
A random walk of an undirected weighted graph was defined with transition probability between the links of the elements of database, which is designed with WordNet. So, a random walker can jump from element to element and each element of Markov-chain is represented as state into the taxonomy. Finally, the similarities between text passages was computed using Markov-chain Model 16.
In Markov-chain model, a weighted graph G with weight wij between node i and j was considered, where the database elements and links represents node and edges of the graph. The weight wij must have following convention: the relation between i and j is more, the larger the value of wij and the walk should be minimum and the value of wij > 0 and wij: = wji.
Sequence of node visited by a random walker are called a random walk and described by a Markov-chain. A random variable s(t) contains the current state of the Markov-chain at time t: if the random walker is in state i at time t, then s(t) = i. The random walk is defined with the following single - step transition probabilities of jumping from any state or node i = s(t) to an adjacent node j as follows:
where
We need to compare the stationary distribution of two Markov-chains of two text passages to calculate the semantic relations between them. The transition probability
where P(ni |nj) is the probability of transition-ing from nj to ni.
2. Edge-based/ Distance Approach: The edge based approach is the direct way of computing semantic similarity in taxonomy. It counts the number of edges between two nodes those corresponds to the concepts being compared. Minimum the path between two nodes they are more similar 25.
It was pointed out that, in a hierarchical taxonomy distance between nodes must satisfy the matrix properties like: zero property, semantic property, positive property. Because of distance between two adjacency nodes should not necessarily equal, so it is necessary an edge connecting two nodes must be weighted. To determine the weight following structural characteristics should be considered 42:
Network Density: higher densities in WordNet need to consider for example plant-flora section in WordNet for measuring the network density. Distance between the nodes is closer to the local density which is reported in 46.
Node Depth: in terms of the depth it can be said that, distance shrinks as one descends down a hierarchy.
Type of link: it represents the relation between two nodes. In many edge-based model only IS-A link is considered 21, 42. Other relations can also consider such as Meronym-Holonym, which have different effect for calculating the weight.
Link strength of specific child link: this could be measured using WordNet relationships between child node and its parent node.
Weight measurement also done manually for the edges and those works are reported in 18, 21, 42, 66. To measure weight automatically, certain observations were considered over the Hierarchical Concept Graph (HCG). For measuring the weight of a link, density, depth of the HCG and link strength between child and parent nodes is considered 46. The density of a HCG for a specific link type is estimated by counting the number of links of that type. The strength between the links was estimated as a function of nodes IC value and its sibling and parents node. Finally, results of these two operations were normalized by dividing the depth of the link.
A minimum and maximum range was taken before measuring the weight between two nodes 62. Because of an edge represents two inverse relations, the final weight of an edge was fixed by averaging the two weight values. The depth-relative scaling process was adopted in which the average value is divided by the depth of the edge within the overall tree. The weight of an edge between two adjacent nodes n1 and n2 was calculated in the following way:
given
where →r is a relation of type r, and →r´ is its reverse, d is the depth of the deeper one of the two and nr(X) is the number of relations of type r leaving node X.
The value of 0 was assigned for all synonym type relations. Holonymy, hyponymy, hypernymy, and meronymy are the types of relation, where weights ranging from 1 to 2 and for antonym type relation weights was assigned as 2.5.
Edge counting method has been considered to determine the edge based similarity 45. To convert the distance measure to the similarity measure, by subtracting the path length from the maximum possible path length as follows:
where dmax represents the maximum depth in the taxonomy, and then c1 and c2 ranges over senses of word w1 and w2 respectively.
3. Hybrid Approach: Node and edge based methods discussed in previous sections have many differences in between them. The edge-based methods, looks true without any concise reasoning and on the other hand, node-based approach looks more accurate than distance-based. The distance measure was relayed on the subjective knowledge of the network while the WordNet was used not for measuring the similarity, but for the construction of the network layers.
On the other side information content was not sensitive to the link types 45, but it is dependent on the structure of the taxonomy. Although these two methods are different from each other, a combined method was derived from edge-based while it considers the information content as a decision factor 25. In this method, a link strength factor was first considered by taking the conditional probability of the child concept ci of its parent concepts p:
The link strength (LS) was defined by considering the negative logarithm of the conditional probability (see Eq.(14)), by following the argument of information theory (see Eq.(1)) as follows:
From Eq.(14) it is clearly understood that, the difference of information content values between child and parent has been considered as LS.
By considering other structural characteristics mentioned edge-based approach also considered here to calculate the weight wt of a child node as follows:
where d(p), and E(P) denotes the depth and the local density of the node p respectively and
3.2 Statistical/ Corpus-Based Similarity
Statistical similarity learned from data (i.e corpus), which is a collection of written or spoken text. In this method, a statistical model was build first and then similarity is estimated. Several models have been proposed during the past few years and we found following categorization:
1. Latent Semantic Analysis (LSA): In this method, the contextual information of words have been extracted and represented from a large corpus of text 28. In the first step, text is represented as a matrix in which rows and column represents the unique words and text segments. Each entry represents the frequency count of the word, which appears in the text 29. Cell frequencies are weighted by a function, which expresses two meanings: (1) importance of a word in a text and (2) the degree to the word type sharing information in the domain of discourse. Two ways it can be implemented: (1) as a similarity matrix between the words and text segments for the contextual usage taken as practical expedient; and (2) as a computational process model to represent the underlying substantial portions of the acquisition and utilization of knowledge. To reduce the number of rows the Singular Value Decomposition (SVD), is used while preserving the similarity structure among the columns. To measure the similarity the cosine angle between the word vectors is considered, which is formed by any two rows.
2.Generalized Latent Semantic Analysis (GLSA): Performance of LSA degrades when word vectors are generated from text corpus, which is heterogeneous in nature 5. GLSA framework is used to find the terms and document vectors, based on semantically motivated pair-wise term similarities, instead of bag-of-words document vectors, which is used in LSA 48. It is a framework in which different measures of semantic associations of terms are combined with different methods of dimensionality reduction 33. Implementation of GLSA is as follows:
Consider that, D, V and C as a set of documents, vocabulary and large web corpus.
Constructed a weighted term-document matrix M based on D.
For the words in V, obtain a pair-wise similarity matrix S, based on the corpus C.
By preserving the similarities obtain a low dimensional vector space representation as
Finally compute the document vectors by combining term vectors as
where columns of
3.Explicit Semantic Analysis (ESA): In this method, the meaning of any text is represented as a weighted vector of Wikipedia-based concepts. With the help of machine learning techniques, representation of vectors have been done over a high-dimensional space. This method is useful for fine-grained semantic representations of unrestricted natural language text 17. To represent the text as a weighted mixture of natural concepts, the Wikipedia articles are used, because it is a collection of largest encyclopedia, which is defined by humans and can be easily explained. Semantic interpretation vectors were build to maps the natural language fragments to a weighted sequence of Wikipedia concepts based on the their order of the input. Semantic similarity is computed by comparing the vectors, using the cosine metric 68. This semantic analysis is explicit in nature, because meaning of concepts is done on human cognition, rather latent concepts used in LSA.
4.Pointwise Mutual Information - Information Retrieval (PMI - IR): It is a unsupervised learning algorithm, to recognizing the synonym of a problem word from a set of alternative words. This algorithm uses any search engine to issuing a search query and analyze the query result to find the synonym word. The unsupervised learning algorithm uses the Pointwise Mutual Information (PMI), to analyze the statistics of data, which is collected by the search engine, i.e., Information Retrieval (IR). The performance of the method depends on two things: (1) power of the search engine query language and (2) indexing of the search engine (i.e., collection of documents).
5.Normalized Google Distance (NGD): This method is feature free and uses the web and search engine to provide the contents and automatically generates the semantic relations between the words and phrases [10]. The drawback of this method is, it completely depends the accuracy of search engine and it was also noted that, google count can be inaccurate when search queries included the OR operator 6. To find the similarity between two strings s1 and s2 it has the following steps:
where K(s1, s2 ) is the Kolmogorov complexity of a compressor, which produces the shortest binary length of the pair s1, s2.
(b) The next step is to find a distance D by considering all admissible distances, whose length is equal to a prefix program of given s1, s2, has the equal binary length of the distance D(s1, s2) and then
where cD is a constant and it can be said that E(s1, s2 ) minorizes D(s1, s2 ) up to an additive constant.
(c) Third step is to find the normalized information distance (NID), for every pair of string and generate a similarity score in between 0 and 1, on the basis of the feature in which they are similar. The NID is defined as
(d) Next we need to measure Normalized Compressed Distance (NCD), because NID is limited, where K(s1) is the number of shortest code and s1 can be decompressed. So the NCD is
(e) Now, to find the google similarity distance between s1 and s2, the Google code of length G(x) is considered. It represents the shortest expected prefix code of the associated Google event s1. Next Google distributor g is used as a compressor for the Google semantics associated with the search terms and the associated NCD, called the Normalized Google Distance (NGD), which is expressed as
where f(s1) and f(s1, s2) denotes the number of pages returned by Google search engine containing s1 and both s1, s2.
6. Hyperspace Analogue to Language (HAL): In this method, a set of words considered as window is analyzed, by passed over a corpus. A key assumption is made that co-occurring words of a window have a strength inversely proportional to the words which are separating them 31. It produces a n x n matrix, where row and column contains the co-occurrence information of the words appearing before and following it and n is the size of the window. The resultant is a co-occurrence matrix and a vector can be formed of size 2n high dimensional space. It was found that during the experiment the co-occurrence value is 100 to 200 most variant vector elements, as reported in 31. After the matrix construction, similarity can be measured between the word vectors. It was preferred that to measuring similarity two distance metrics: Euclidean if (r = 2) and city-block if (r = 1) metrics of Minkowski family of distance metrics is considered as follows:
This is due to thefact that the vectors were normalized to a constant length by retaining small number of principal components and these metrics are sensitive to magnitude of the vector.
3.3 String-Based Similarity Measure
3.3.1 Character-Based Similarity Measure
1. Longest Common Substring (LCS): This algorithm is used to find the longest substring of a string. It compares the two strings and find the similarity based on the longest common chain of characters. It can be measured as follows:
where m and n are the length of two string and LCSuff is a function, which finds the of longest common suffixes of possible prefixes of S1 and S2.
2. Damerau-Levenshtein: It is a distance or string metric between two strings, which gives a number that required to transform one string into another. This transformation is done by insertion, deletion or substitution of a single character or a transposition of two adjacent characters 8.
3. Jaro: It is distance for similarity measure of two strings and the Jaro distance score is normalized to 0 means no similarity and 1 means an exact match. The Jaro distance dj of two string is
where m is the number of matching characters and t is half the number of transpositions. The two characters of s1 and s2 are matched only when they are same and not far from
4. Jaro-Winkler: It is a semantic similarity measure of two strings. It is atype of edit distance and variant of Jaro distance metric and higher the Jaro-Winkler distance of two strings is more similar. This method is more useful for short strings such as person name. The Jaro-Winkler distance dw of two string s1 and s2 is:
where p is the prefix scale gives ratings to the string that match from the beginning for a prefix length l and dj is the Jaro distance 67.
5. Needleman-Wunsch: It is a type of dynamic algorithm used in Bioinformatics to align the protein sequences. It is also refereed as optimal matching algorithm and global alignment technique 38.
6. Smith-Waterman: It is a variation of Needleman-Wunsch algorithm and performs the local sequence alignment to measure the similarity between two strings or nucleotide or protein sequences. To measure the similarity it compares within the segments of the string and optimize the similarity. In general it is not used in large scale problem, because of its cubic computational complexity 59.
7. n-gram: It is a probabilistic language model used for predicting the next term in a sequence of (n - 1) terms or characters. n-gram model is used in various fields such as computational biology (for instance, biological sequence analysis), data compression, computational linguistic (for instance, statistical natural language processing) and computational theory. The main advantage of this model is simplicity and scalability 9.
8. syntactic n-gram: It is a modification of the n-gram language model, when the n-gram elements are taken not in the order as they appear in a text, but in the order that they appear in the corresponding syntactic tree 54,53,55 This approach allows introduciton of linguistic (syntactic) information into otherwise purely statisistical n-gram model. They can be applied in all tasks when traditional n-grams can be used 41 ,58. Obviously, in this case previous parsing is needed.
3.3.2 Term-Based Similarity Measure
1. Block Distance: It is also called city block distance or Snake distance or Manhattan distance or Manhattan length or L1 distance or Taxicab distance 26. It used to find the distance between two points. The taxicab distance, d1, of two vectors p and q is
2. Cosine Similarity: It is a similarity measure of two non zero vectors of an inner product space, which finds cosine of the angle between them. Cosine of 0° is 1 and less than 1 for any other angle. The cosine similarity of two vectors have same orientation is 1 and vectors are in 90° have similarity 0. It is also used in data mining to finds the cohesion between them 63. The cosine of two non zero vectors can be measured by Euclidean dot product.
The cosine similarity cos(θ) of two vectors A and B is
where Ai and Bi is the component of A and B.
3. Soft Cosine Similarity: It is a novel variant of the cosine similarity, when we take into account similarity of features in Vector Space Model 56.
where sij is the value from the matrix of similarity between features i and j. Note that if this is diagonal matrix, i.e., the features are similar only to themselves, then soft cosine is equivalent to traditional cosine measure.
The similarity of features can be calculated for example, using WordNet similarity measures in case of words, or Levenshtein distance in case of strings or n-grams, or tree edit distance 57 in case of syntactic n-grams (n-grams constructed by following paths in syntactic trees 41, 58, 54 ) .
4. Sorensen-Dice index: It is also known as Sorensen index or Dice's coefficient and used to measure the similarity of two samples 14, 60. It was adopted to find the presence or absence of data of two sets
where |X| and |y| is the number of elements in two sets and QS is the quotient of similarity and ranges between 0 and 1. When it is used to measure the similarity of strings S1 and S2 then coefficient can be calculated as bigrams as follows:
where nt is the bigram count of the strings and nS1 , nS2 is the number of bigrams in string S1 and S2.
5. Euclidean Distance: It is a distance between two points in Euclidean space. The Euclidean distance between two points s and t is
6. Jaccard Index: It is also known as Jaccard similarity coefficient, is a statistics used to find the similarity and diversity between two finite sets 24. It is defined as follows
The Jaccard distance is used to find the dissimilarity between two finite sets and is obtained by subtracting the Jaccard Index form 1 and refereed as dJ .
7. Simple Matching Coefficient (SMC): It is a statistics used to find the similarity and diversity between two objects. It accepts the objects as a collection of n binary attributes and SMC of A and B is
where a00 represents total attributes as 0 in A and B; and a10 represents total attribute as 1's and 0's in A and B; and a01 represents total attributes as 0's and 1's in A and B; and a11 represents total attribute as 1's in A and B.
8. Overlap Coefficient: It is also called Szymkiewicz-Simpson coefficient, is also a similarity measure related to Jaccard index. The overlap between two sets is defined as
The overlap coefficient is equal to one when set A is a subset of set B.
4 Proposed Method
In this paper, a language model based semantic network has been proposed to find the semantic similarity between two English sentences. Among these two sentences one is considered as source, S, and other as target text, T. We assume that both, S and T, are syntactically and semantically correct. The proposed system can be brought down into the following stages:
1. In any language processing it is important to remove all the stop words before start any semantic similarity task. Initially all the stop words, have stored in a Java array and after that all the words of S and T is considered one after another for identification. Although stop words are most commonly used words but there is no universal list available for all language processing task2. These identified stop words are ignored during similarity stage.
2. In first step, Penn Treebank tag set 32 is used to label the words for part-of-speech (POS) information, which is most commonly used syntactic information. Further these identified tags and words are input to the system to generate the parse tree.
3. To generate the parse tree top down parsing is followed by considering its advantages over the bottom up parsing. For parsing all English grammatical role is considered. After that identified phrase structures is used to generate the top-down parse tree.
4. In this stage, a multi-stage (equal to level of the tree) undirected weighted graph is designed by considering the parse tree along with other statistical information found in the previous stages. Following characterises is considered for graph construction:
(a)Part-of-Speech: All the stop words based on its POS information is not considered, when two words are found same in two parse tree at same level.
(b)Node Depth: Starting from the root node S all possible paths are considered till the search ends with a word/concept at higher lever (i.e. leaf node) of the tree. The depth of any word is consider in the similarity measuring stage when a word is found in both the parse tree at same level and shares same POS tag.
(c)String Matching: If any word is found in the parse tree of S and T, which possess nnp as POS tag then a weight value to the link is assigned if both the node are same.
5. After the completion of graph construction stage weight is measured between the nodes of two graphs. Assigning of weight is performed under the following condition:
(a) if POS tag is found different of two nodes of same level then WordNet taxonomy relationship is considered. To calculate the information content i.e. weight w i of the link the negative logarithm of the conditional probability (see Eq.(14)) as well as argument of information theory is considered.
(b) if POS tag is different but strings are matched then two different weight values are calculated.
and
where c 1 and c 2 represents two concepts of two parse tree at same level. N represents as total number of words along with POS tag from a large text corpus and c i represents total of class c. Finally, the maximum of
(c) if no condition matched and phrase is identified as noun class and words are proper noun then no weight is measured for the link between the current node and proper noun node.
(d) Finally, similarity is calculated as the minimum distance path while considering maximum weight of the link. After that, an average is calculated by summing of all weights of links starting form start node S till the leaf node.
5 Experimental Results for the Proposed Method
In order to evaluate the text similarity measure, pair of 50 sentences is taken from SemEval 2015 training dataset3. For this task, two different runs are conducted. For the first run, we consider WordNet taxonomy relationships and 0.46 similarity score is reported in this run. For this task WordNet version 2.0 is considered. In second run, we improved the similarity score using information content. For this task highest score is 0.78. In this method, we calculate the IC value by the combining of WordNet taxonomy and unigram language model, which outperforms the other methods reported in 22, 25 and 44.
6 Software for Semantic Similarity
Semantic Measures Library (SML) and Toolkit/: It is a Java library and distributed under the open − source CeCILL license and designed for semantic measures. It can also used for computation and analysis purpose of semantic similarities between the term/ concepts defined in terminologies and ontologies 20. It also supports comparison of entities (e.g. genes) annotated by concepts. Various ontological formats and specifications such as OBO, RDF and OWL also supported by this library. It also supports multi-threaded application for parallel computation. Based on SML an open-source toolkit also designed, which supports non-developers to use the functionalities through command prompt.
WordNet-Similarity: It is a WordNet based Perl module implements over the information found in the lexical database WordNet and able to find the semantic similarities and related measure. It supports list of measures like Rensik, Jiang-Conarth, Wu-Palmer, Banerjee-Pedersen, Patwardhan-Pedersen, Hirst-St.Onge, Leacock-Chodorow, and Lin. It has pre-computed pairwise similarity module for nouns and verbs 39.
UMLS-Similarity: Unified Medical Language System (UMLS), is a open source Perl module to find the semantic similarity and relatedness measure based on ontologies and terminologies found in medical domain. It gives a numerical value between a pair of medical concepts, which indicates the similarity between them 34.
SEMILAR - A SEMantic SimiLARityToolkit: It is a single platform for user, researchers and developers to access the fully implemented Java based similarity methods. Its provides a GUI-based as well as a library to access the similarity methods. To access the similarity Methods offered in this tool starts from lexical to word-to-word similarity metrics to more sophisticated methods rely on unsupervised methods such as Latent Semantic Analysis and Latent Dirichlet Allocation to kernel-based methods. It also offers another tool called the SEMantic simILarity Annotation Tool (SEMILAT) for manual assessment and annotation by experts 49.
DISCO Builder and API: It is a Java based open source library to measure the similarity between words and phrases. It also allows to convert the Word2Vec or Glove vector files into DISCO word space index, which can be queried by DISCO API. DISCO4 Builder is licensed under the Creative Commons Attribution-NonCommercial license and API is license under Apache.
REST API: It computes surface level semantic similarity between two texts using Cosine, Jaccard and Dice based similarity5.
TakeLab STS System: It is a semantic text similarity system submitted as a evaluation exercise for task 6 in SemEval-20126.
7 Applications of Semantic Textual Similarity
Biomedical Informatics: To developed the biomedical ontologies namely the Gene Ontology we used the semantic similarity 40. Similarity methods are mainly used to compare the genes and they can also used in other bio-entities 15.
Geo-Informatics: Similarity measure also used to find the similarities between geographical feature type ontologies. Several tools are available to do this task such as (i) The OSM Semantic Network used to compute the semantic similarity of tags in OpenStreetMap 7. (ii) Similarity Calculator is used to find the similarity between two geographical concepts in the Geo-Net-PT ontology and (iii) SIM-DL similarity server computes the similarity between geographical feature type ontologies.
Natural Language Processing: It is field of Computer Science and linguistics. There are several fields where STS can play an important role directly or indirectly such as sentiment analysis, natural language understanding and machine translation.
8 Conclusion
In this survey, we explain four different measures for STS. We divide the String similarity measures into two categories as character based and term based. These two measures works on string sequences and character compositions, and measures the similarities and dissimilarities by calculating the distance between two strings or sets or vectors. We reported in total fourteen string similarity measures categorised into two groups. We also discussed three categories of topological methods such as node-based, edge-based and hybrid, the latter being a combination of node and edge-based. These topological studies are mainly used for finding the similarities and diversities between the terms and ontological concepts.
We also found that, node based approaches fully depends on the information content value between two nodes and distance based approaches depends on the depth of semantic network. On the other side, hybrid method works with weight value between child and parent nodes to find the similarity of two classes. In the statistical approach, we reported six different methods such as LSA, GLSA, ESA, PMI - IR, NGD, HAL. These statistical measures generates a vector space model from corpus and reduces the dimensionality of the vectors and finds the similarities and dissimilarities. Each cell of the matrix represents a frequency or weight value of a particular word in a paragraph or text passages.
