Define a mapping $m$ as the pointwise distance between the target frame embedding and the source frame embedding.

Conceptual mapping: Embedding of the target verb + mapping m\
Then select the most similar word to the resulting vector.

Benefits: 
1. only rely on embeddings of input words and frames
2. require no labeled metaphor data (but still require FrameNet-tagged corpora)

Drawbacks: without contextual information

University of Michigan - Ann Arbor

Replace the focus verb with its FrameNet frame label (either provided in the Gold data, or tagged via the parser), and train embedding models(word2vec skip-gram Glove, and Fast-Text) on the resulting data. \
This yields joint embedding spaces that contain both common words and FrameNet frame embeddings.

Evaluation metrics: 
1. This lexical metric (lex) evaluates whether the frame embedding is similar to words within its frame and dissimilar to those without.\
$lex(f) = \sum_{w\in f}\frac{cos(E_w, E_f)}{|f|} - \sum_{w\notin f}^{k}\frac{cos(E_w, E_f)}{|k|}$
2. The structural similarity metric str is evaluating whether the frame embeddings are more similar around their neighbors as FrameNet also contains linking relations between frames (eg. used-by, uses), yielding a hierarchy of connected frames.\
$str(f) = \sum_{n\in N}\frac{cos(E_n, E_f)}{|N|} - \sum_{n\notin N}^{k}\frac{cos(E_n, E_f)}{|k|}$

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