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Table 1 The process of solving the optimal path by Viterbi algorithm

From: Named entity recognition for Chinese judgment documents based on BiLSTM and CRF

Initialization:  
  δ1(j)=w · F1(y0=start,y1=j,x), j=1,2,...,m
Recurrence for I = 2,3,..., n:  
  \({\delta _{i}}(l) = \underset {1 \le j \le m}{\max } \left \{{\delta _{i - 1}}(j) + w\; \cdot \;{F_{i}}\left ({y_{i - 1}} = j,{y_{i}} = l,x\right)\right \},\;\;\;l = 1,2,...,m\)
  \({\varphi _{i}}(l) \!= \arg \underset {1 \le j \le m}{\max } \left \{\! {\delta _{i - 1}}(j) + w\; \cdot \;{F_{i}}\left ({y_{i - 1}}= j,{y_{i}} = l,x\right)\right \},\;\;\;l = 1,2,...,m\)
Termination when i = n:  
  \(\underset {y}{\max } \left (w\; \cdot \;F(y,x)\right) = \underset {i \le j \le m}{\max } {\delta _{n}}(j)\)
  \(y_{n}^{*} = \arg \underset {i \le j \le m}{\max } {\delta _{n}}(j)\)
Return path:  
  \(y_{1}^{*} = {\varphi _{i + 1}}\left (y_{i + 1}^{*}\right),\;\;\;i = n - 1,n - 2,...,1\)