# Record Linkage of Chinese Patent Inventors and Authors of Scientific Articles
## 2 Record Linkage Algorithm
### Generation of Features for Comparison
#### 2.1.1 The Similarity of Scientist Names, Features 1-5  
Our algorithm in preliminary step completes, cleanss and normalize the English names. Chinese names were used as they are, because assessment of their quality and pre-processing requires domain knowledge.  
We use and evaluate three fuzzy similarity functions specialized for multi-word comparison: Monge-Elkan, SoftTFIDF, and extended Jaccard. All three functions process the name of an author and one or more names of patent inventors. Then, we use the maximal values over all author-inventor combinations as features #3, #4, and #5 in the feature vector depicted in Table 1. For each of them, Jaro-Winkler was used as the supporting similarity function. The Jaro-Winkler similarity function is depicted in Equation (1), for two strings \(s_{1}\) and \(s_{2}\) counts the number of matching characters \(m\), that are the same and are not further from each other than half the length of the longer string. The number of transpositions \(t\), which is half the number of matching, but different sequence order characters. \(l\) is the length of the matching prefix, \(p\) is the prefix scale parameter.  
\[sim_{jaro-winkler}(s_{1},s_{2})=sim_{jaro}(s_{1},s_{2})+lp(1-sim_{jaro}(s_{1},s_ {2})), \tag{1}\]  
where  
\[sim_{jaro}(s_{1},s_{2})=1/3(m/|s_{1}|+m/|s_{2}|+(m-t)/m)).\]  
The Monge-Elkan similarity function [30] extracts tokens (single words) from the two input strings and then uses a support similarity function, \(sim^{{}^{\prime}}\), to find the most similar pairs of tokens in the sets (or bags) of tokens, as depicted in Equation (2), where \(A\) and \(B\) are sets of tokens extracted from \(s_{1}\) and \(s_{2}\), respectively.  
\[sim_{monge\_elkan}(s_{1},s_{2})=1/|A|\sum_{i=1}^{|A|}\sum_{j=1}^{|B|}sim^{{}^ {\prime}}(A_{i},B_{j}) \tag{2}\]  
The SoftTFIDF similarity function [31] additionally computes TF-IDF weights for the tokenized strings. This function is depicted in Equation (3), where \(close(\theta,A,B)\) denote the set of all tokens \(a_{i}\in A\) such that there is some token \(b_{j}\in B\) such that \(sim^{{}^{\prime}}(a_{i},b_{j})>=\theta\), for \(0<\theta<1\). For \(a_{i}\in close(\theta,A,B)\) let \(S(a_{i},B)=max_{b_{j}\in B}sim^{{}^{\prime}}(a_{i},b_{j})\). \(V(i,X)\) is the TF-IDF weight of the token \(i\) in the token-set \(X\).  
\[sim_{softTFidf}(s_{1},s_{2})=\sum_{u\in close(\theta,A,B)}V(u,A)\cdot V(u,B) \cdot S(u,B) \tag{3}\]  
An extended Jaccard measure [32] generalizes the basic Jaccard index, which in turn calculates the similarity of the two sets, by lifting the restriction that two tokens have to be identical to be included in the set of overlapping tokens. Extension is made by utilization of a token similarity function \(sim^{{}^{\prime}}\). The intersection of \(A\) and \(B\), that allows partial similarity of the tokens, \(T\), is defined by Equation (4), where \(\theta\) is the similarity threshold, such that \(0<\theta<1\).  
\[T=\{(a_{i},b_{j})|a_{i}\in A\wedge b_{j}\in B:sim^{{}^{\prime}}(a_{i},b_{j}) \geq\theta\} \tag{4}\]  
The extended Jaccard score is depicted in Equation (5), where \(U_{A}\) and \(U_{B}\) denote sets of tokens from \(A\) and \(B\), respectively, that are not in \(T\).  
\[sim_{ext\_jaccard}(s_{1},s_{2})=|T|/(|A\cup B|)=|T|/(|T|+|U_{A}|+|U_{B}|) \tag{5}\]