## Appendix A  
```
1:Input:\(authors=\{u_{1},\,u_{2},\,u_{3},\ldots,u_{n}\}\),\(\mathit{papers}=\{p_{1},\,p_{2},\ldots,p_{m}\}\), \(year(p)\)\(=publication\ year\ of\ p,\ citation(p)\)\(=\) citation count of \(p\)
2:Output: Number of paper, citation, years range
3:Begin
4:\(p_{j}=0\)
5:for\(\forall\ author\ \in authors\)do
6:if\(paper_{i}\) was written by\(author_{j}\)then
7:\(p_{j}=p_{j}+1\)
8:\(PNum(author)\gets p_{j}\)
10:endif
11:endfor
12:for\(\forall\ author\ \in authors\)do
13:\(Cite(author)\leftarrow\sum_{i=1}^{m}\ citation(p_{i})\),\(author(p_{i})\ == author\)
14:endfor
15:for\(\forall\ author\ \in authors\)do
16:\(years\ \leftarrow\{year(p)\ \forall\ p\in papers,\ author(p)\ == author\}\)
17:\(F_{p}\gets x\in years,\ 0<x<y,\ \ \forall\ y\in years,\ \ x\
eq y\)
18:\(L_{p}\gets x\in years,\ 0<x>y,\ \ \forall\ y\in years,\ \ x\
eq y\)
19:\(Years(author)\leftarrow\ L_{p}-F_{p}\)
20:endfor
21:End
```  
**Algorithm A1** Authors' Publication Statistics  
```
1:Input:\(authors\)=\(\{u_{1},\,u_{2},\,u_{3},\ldots,u_{n}\}\),\(\mathit{keywords}\),\(\mathit{PNum}\),\(\mathit{Cite}\),\(\mathit{Years}\)
2:Output:\(\mathit{Authors}\) Similarity Matrix
3:Begin
4:\(\mathit{Compute}\) similarity of keywords
5:\(\mathit{Word}_{sim}\leftarrow\ \mathit{cosine}(keywords_{author_{1}},\, keywords_{author_{2}})\)
6:\(\mathit{Compute}\) author \(\mathit{PCYum}\) features
7:\(f_{author_{1}}\leftarrow[\mathit{PNum}(author_{1}),\,\,Cite(author_{1}),\,\, [PERSON](author_{1})]\)
8:\(f_{author_{2}}\leftarrow[\mathit{PNum}(author_{2}),\,\,Cite(author_{2}),\,\, [PERSON](author_{2})]\)
9:\(\mathit{PCY}_{sim}\leftarrow\ \mathit{cosine}\big{(}f_{author_{1}},\,\,f_{author_{2}}\big{)}\)
10: Calculate similarity of topics
11: Get authors\(\mathit{topics}\ \leftarrow\ \{t_{p1},\,t_{p2},\,\ldots,\,t_{pm}\ \}\)
12:\(T_{author_{1}}\leftarrow mean\big{(}t_{p}\ \forall\ p\in papers,\ author(p)\ == author_{1}\big{)}\)
13:\(T_{author_{2}}\leftarrow mean\big{(}t_{p}\ \forall\ p\in papers,\ author(p)\ == author_{2}\big{)}\)
14:\(\mathit{Topic}_{sim}\leftarrow\ \mathit{cosine}\big{(}T_{author_{1}},\,\,T_{author_{2}}\big{)}\)
15: Compute authors similarities
16:\(\alpha\leftarrow\mathit{set}\ \mathit{weight}\)
17:\(Author_{sim}\leftarrow\ \alpha\ast\ (\mathit{Topic}_{sim})+(1-\alpha)\ \ast\ (\mathit{Word}_{sim}+\mathit{PCY}_{sim})\)
18: return\(Author_{sim}\)
19:End
```  
**Algorithm A2** Authors' Similarities  
```
1:Input:\(authors\)=\(\{u_{1},\,u_{2},\,u_{3},\ldots,u_{n}\}\),\(\mathit{keywords}\),\(\mathit{PNum}\),\(\mathit{Cite}\),\(\mathit{Years}\)
2:Output:\(\mathit{Authors}\) Similarity Matrix
3:Begin
4:\(\mathit{Compute}\) similarity of keywords
5:\(\mathit{Word}_{sim}\leftarrow\ \mathit{cosine}(keywords_{author_{1}},\, keywords_{author_{2}})\)
6: Compute author \(\mathit{PCYum}\) features
7:\(f_{author_{1}}\leftarrow[\mathit{PNum}(author_{1}),\,\,Cite(author_{1}),\,\, [PERSON](author_{1})]\)
8:\(f_{author_{2}}\leftarrow[\mathit{PNum}(author_{2}),\,\,Cite(author_{2}),\, [PERSON](author_{2})]\)
9:\(\mathit{PCY}_{sim}\leftarrow\ \mathit{cosine}\big{(}f_{author_{1}},\,f_{author_{2}}\big{)}\)
10: Calculate similarity of topics
11: Get authors\(\mathit{topics}\ \leftarrow\ \{t_{p1},\,t_{p2},\,\ldots,\,t_{pm}\ \}\)
12:\(T_{author_{1}}\leftarrow mean\big{(}t_{p}\ \forall\ p\in papers,\ author(p)\ == author_{1}\big{)}\)
13:\(T_{author_{2}}\leftarrow mean\big{(}t_{p}\ \forall\ p\in papers,\ author(p)\ == author_{2}\big{)}\)
14:\(\mathit{Topic}_{sim}\leftarrow\ \mathit{cosine}\big{(}T_{author_{1}},\,\,T_{author_{2}}\big{)}\)
15: Compute authors similarities
16:\(\alpha\leftarrow\mathit{set}\ \mathit{weight}\)
17:\(Author_{sim}\leftarrow\ \alpha\ast\ (\mathit{Topic}_{sim})+(1-\alpha)\ \ast\ (\mathit{Word}_{sim}+\mathit{PCY}_{sim})\)
18:return\(Author_{sim}\)
19:End
```  
**Algorithm A3** Authors' Similarities
```
1:Input:\(authors=\{u_{1},\,u_{2},\,u_{3},\ldots,u_{n}\},\,\,\,\,T_{i}=\{t_{0},\,t_{1},\ldots,t_{k}\}\),
2:\(TWeight_{i}=\{tw_{0},\,tw_{1},\ldots,tw_{m}\}\), Cite
3:Output:Expert Authors
4:Begin
5:for\(\forall\,author_{i}\in authors\)do
6:for\(\forall\,p\,\in\,papers\)do
7:for\(\forall\,t_{i}\,\in\,T_{i}\)do
8:\(P_{weight}\gets t_{i}\,\forall\,\,p\,\in\,papers,\,\,author(p)\,==\,author_{i}\)
9:endfor
10:endfor
11:Get the paper main topic
12:for\(\forall\,p\,\in\,papers\)do
13:if\(t_{i}=max\big{(}P_{weight}\big{)}\) then
14:\(t_{i}\leftarrow\) 1
15:else
16:\(t_{i}\leftarrow\) 0
17:endif
18:endfor
19:endfor
20:for\(\forall\,author_{i}\in authors\)do
21:\(PNum_{t_{i}}\leftarrow\sum_{i=1}^{k}\,papers(t_{i})\)
22:\(Cite_{t_{i}}\leftarrow\sum_{i=1}^{k}\,citation(t_{i})\)
23:endfor
24:Get the weighted average for each author
25:\(\alpha\,\leftarrow\,set\,weight\)
26:for\(\forall\,author_{i}\,\in\,authors\)do
27:\(A\!g_{Weight_{i}}\leftarrow\,\alpha\,\ast\,TWeight_{i}+(1-\alpha)\,\ast\,(PNum_{t_{i}}+Cite_{t_{i}})\)
28:endfor
29:for\(\forall\,t_{i}\,\in\,\,T_{i}\)do
30:\(Experts_{t_{i}}=max\big{(}A\!g_{Weight_{i}}\big{)}\)
31:endfor
32:return\(Experts_{t_{i}}\)
33:End
```  
**Algorithm A3** Extracting Authors' Expertise