Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings
This work addresses interpretability issues in similarity measures for researchers in machine learning and natural language processing, but it is incremental as it builds on existing ICA methods.
The paper tackles the problem of interpreting cosine similarity in embeddings by proposing a novel interpretation as the sum of semantic similarities over axes derived from normalized ICA-transformed embeddings, which enhances sparsity and interpretability, with effectiveness demonstrated through numerical examples and experiments.
Cosine similarity is widely used to measure the similarity between two embeddings, while interpretations based on angle and correlation coefficient are common. In this study, we focus on the interpretable axes of embeddings transformed by Independent Component Analysis (ICA), and propose a novel interpretation of cosine similarity as the sum of semantic similarities over axes. The normalized ICA-transformed embeddings exhibit sparsity, enhancing the interpretability of each axis, and the semantic similarity defined by the product of the components represents the shared meaning between the two embeddings along each axis. The effectiveness of this approach is demonstrated through intuitive numerical examples and thorough numerical experiments. By deriving the probability distributions that govern each component and the product of components, we propose a method for selecting statistically significant axes.