Non-projective Dependency Parsing using Spanning Tree Algorithms

2.1 Edge Based Factorization

1. How does edge-based factorization score a dependency tree?
   As the sum of its edge scores, each a dot product of a weight vector and a feature vector of the edge: \(s(x, y) = \sum_{(i,j) \in y} s(i, j) = \sum_{(i,j) \in y} \mathbf{w} \cdot \mathbf{f}(i, j)\). Parsing is finding the highest-scoring tree.
   • McDonald et al., 2005, Non-projective Dependency Parsing using Spanning Tree Algorithms (Proceedings of Human Language Technology Conference and Conference on Empirical Methods in Natural Language Processing (HLT/EMNLP 2005)), §2.1, pp. 524–525