Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings

Hiroaki Yamagiwa, Momose Oyama, Hidetoshi Shimodaira


Abstract
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.
Anthology ID:
2025.coling-main.497
Volume:
Proceedings of the 31st International Conference on Computational Linguistics
Month:
January
Year:
2025
Address:
Abu Dhabi, UAE
Editors:
Owen Rambow, Leo Wanner, Marianna Apidianaki, Hend Al-Khalifa, Barbara Di Eugenio, Steven Schockaert
Venue:
COLING
SIG:
Publisher:
Association for Computational Linguistics
Note:
Pages:
7423–7452
Language:
URL:
https://aclanthology.org/2025.coling-main.497/
DOI:
Bibkey:
Cite (ACL):
Hiroaki Yamagiwa, Momose Oyama, and Hidetoshi Shimodaira. 2025. Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings. In Proceedings of the 31st International Conference on Computational Linguistics, pages 7423–7452, Abu Dhabi, UAE. Association for Computational Linguistics.
Cite (Informal):
Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings (Yamagiwa et al., COLING 2025)
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PDF:
https://aclanthology.org/2025.coling-main.497.pdf