@inproceedings{yamagiwa-etal-2025-revisiting,
title = "Revisiting Cosine Similarity via Normalized {ICA}-transformed Embeddings",
author = "Yamagiwa, Hiroaki and
Oyama, Momose and
Shimodaira, Hidetoshi",
editor = "Rambow, Owen and
Wanner, Leo and
Apidianaki, Marianna and
Al-Khalifa, Hend and
Eugenio, Barbara Di and
Schockaert, Steven",
booktitle = "Proceedings of the 31st International Conference on Computational Linguistics",
month = jan,
year = "2025",
address = "Abu Dhabi, UAE",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2025.coling-main.497/",
pages = "7423--7452",
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."
}
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<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.</abstract>
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%0 Conference Proceedings
%T Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings
%A Yamagiwa, Hiroaki
%A Oyama, Momose
%A Shimodaira, Hidetoshi
%Y Rambow, Owen
%Y Wanner, Leo
%Y Apidianaki, Marianna
%Y Al-Khalifa, Hend
%Y Eugenio, Barbara Di
%Y Schockaert, Steven
%S Proceedings of the 31st International Conference on Computational Linguistics
%D 2025
%8 January
%I Association for Computational Linguistics
%C Abu Dhabi, UAE
%F yamagiwa-etal-2025-revisiting
%X 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.
%U https://aclanthology.org/2025.coling-main.497/
%P 7423-7452
Markdown (Informal)
[Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings](https://aclanthology.org/2025.coling-main.497/) (Yamagiwa et al., COLING 2025)
ACL