Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings Article Swipe
Hiroaki Yamagiwa
,
Momose Oyama
,
Hidetoshi Shimodaira
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2406.10984
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2406.10984
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.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2406.10984
- https://arxiv.org/pdf/2406.10984
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4399794717
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4399794717Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2406.10984Digital Object Identifier
- Title
-
Revisiting Cosine Similarity via Normalized ICA-transformed EmbeddingsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-06-16Full publication date if available
- Authors
-
Hiroaki Yamagiwa, Momose Oyama, Hidetoshi ShimodairaList of authors in order
- Landing page
-
https://arxiv.org/abs/2406.10984Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2406.10984Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2406.10984Direct OA link when available
- Concepts
-
Cosine similarity, Similarity (geometry), Trigonometric functions, Mathematics, Computer science, Artificial intelligence, Pattern recognition (psychology), Geometry, Image (mathematics)Top concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4399794717 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2406.10984 |
| ids.doi | https://doi.org/10.48550/arxiv.2406.10984 |
| ids.openalex | https://openalex.org/W4399794717 |
| fwci | |
| type | preprint |
| title | Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11447 |
| topics[0].field.id | https://openalex.org/fields/17 |
| topics[0].field.display_name | Computer Science |
| topics[0].score | 0.9991000294685364 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1711 |
| topics[0].subfield.display_name | Signal Processing |
| topics[0].display_name | Blind Source Separation Techniques |
| topics[1].id | https://openalex.org/T10320 |
| topics[1].field.id | https://openalex.org/fields/17 |
| topics[1].field.display_name | Computer Science |
| topics[1].score | 0.9973000288009644 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1702 |
| topics[1].subfield.display_name | Artificial Intelligence |
| topics[1].display_name | Neural Networks and Applications |
| topics[2].id | https://openalex.org/T10860 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9810000061988831 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1711 |
| topics[2].subfield.display_name | Signal Processing |
| topics[2].display_name | Speech and Audio Processing |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C2780762811 |
| concepts[0].level | 3 |
| concepts[0].score | 0.7512717843055725 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1784941 |
| concepts[0].display_name | Cosine similarity |
| concepts[1].id | https://openalex.org/C103278499 |
| concepts[1].level | 3 |
| concepts[1].score | 0.6570471525192261 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q254465 |
| concepts[1].display_name | Similarity (geometry) |
| concepts[2].id | https://openalex.org/C178009071 |
| concepts[2].level | 2 |
| concepts[2].score | 0.5142690539360046 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q93344 |
| concepts[2].display_name | Trigonometric functions |
| concepts[3].id | https://openalex.org/C33923547 |
| concepts[3].level | 0 |
| concepts[3].score | 0.42957401275634766 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[3].display_name | Mathematics |
| concepts[4].id | https://openalex.org/C41008148 |
| concepts[4].level | 0 |
| concepts[4].score | 0.407919704914093 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[4].display_name | Computer science |
| concepts[5].id | https://openalex.org/C154945302 |
| concepts[5].level | 1 |
| concepts[5].score | 0.404678612947464 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[5].display_name | Artificial intelligence |
| concepts[6].id | https://openalex.org/C153180895 |
| concepts[6].level | 2 |
| concepts[6].score | 0.3811095654964447 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q7148389 |
| concepts[6].display_name | Pattern recognition (psychology) |
| concepts[7].id | https://openalex.org/C2524010 |
| concepts[7].level | 1 |
| concepts[7].score | 0.06091436743736267 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[7].display_name | Geometry |
| concepts[8].id | https://openalex.org/C115961682 |
| concepts[8].level | 2 |
| concepts[8].score | 0.0 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q860623 |
| concepts[8].display_name | Image (mathematics) |
| keywords[0].id | https://openalex.org/keywords/cosine-similarity |
| keywords[0].score | 0.7512717843055725 |
| keywords[0].display_name | Cosine similarity |
| keywords[1].id | https://openalex.org/keywords/similarity |
| keywords[1].score | 0.6570471525192261 |
| keywords[1].display_name | Similarity (geometry) |
| keywords[2].id | https://openalex.org/keywords/trigonometric-functions |
| keywords[2].score | 0.5142690539360046 |
| keywords[2].display_name | Trigonometric functions |
| keywords[3].id | https://openalex.org/keywords/mathematics |
| keywords[3].score | 0.42957401275634766 |
| keywords[3].display_name | Mathematics |
| keywords[4].id | https://openalex.org/keywords/computer-science |
| keywords[4].score | 0.407919704914093 |
| keywords[4].display_name | Computer science |
| keywords[5].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[5].score | 0.404678612947464 |
| keywords[5].display_name | Artificial intelligence |
| keywords[6].id | https://openalex.org/keywords/pattern-recognition |
| keywords[6].score | 0.3811095654964447 |
| keywords[6].display_name | Pattern recognition (psychology) |
| keywords[7].id | https://openalex.org/keywords/geometry |
| keywords[7].score | 0.06091436743736267 |
| keywords[7].display_name | Geometry |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2406.10984 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2406.10984 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2406.10984 |
| locations[1].id | doi:10.48550/arxiv.2406.10984 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2406.10984 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5062792778 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | Hiroaki Yamagiwa |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Yamagiwa, Hiroaki |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5076660351 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Momose Oyama |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Oyama, Momose |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5012479520 |
| authorships[2].author.orcid | https://orcid.org/0000-0002-3371-7724 |
| authorships[2].author.display_name | Hidetoshi Shimodaira |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Shimodaira, Hidetoshi |
| authorships[2].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2406.10984 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Revisiting Cosine Similarity via Normalized ICA-transformed Embeddings |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T11447 |
| primary_topic.field.id | https://openalex.org/fields/17 |
| primary_topic.field.display_name | Computer Science |
| primary_topic.score | 0.9991000294685364 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1711 |
| primary_topic.subfield.display_name | Signal Processing |
| primary_topic.display_name | Blind Source Separation Techniques |
| related_works | https://openalex.org/W2389818373, https://openalex.org/W126212742, https://openalex.org/W2220831889, https://openalex.org/W1948687848, https://openalex.org/W2033914206, https://openalex.org/W2953417386, https://openalex.org/W4312683641, https://openalex.org/W2042327336, https://openalex.org/W3027421045, https://openalex.org/W2576320324 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2406.10984 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2406.10984 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2406.10984 |
| primary_location.id | pmh:oai:arXiv.org:2406.10984 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2406.10984 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2406.10984 |
| publication_date | 2024-06-16 |
| publication_year | 2024 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 41, 120 |
| abstract_inverted_index.By | 104 |
| abstract_inverted_index.In | 22 |
| abstract_inverted_index.as | 47 |
| abstract_inverted_index.by | 34, 72 |
| abstract_inverted_index.is | 2, 94 |
| abstract_inverted_index.of | 31, 44, 50, 64, 75, 91, 116 |
| abstract_inverted_index.on | 15, 27 |
| abstract_inverted_index.to | 5 |
| abstract_inverted_index.we | 25, 118 |
| abstract_inverted_index.The | 55, 89 |
| abstract_inverted_index.and | 17, 39, 67, 100, 113 |
| abstract_inverted_index.are | 20 |
| abstract_inverted_index.for | 122 |
| abstract_inverted_index.sum | 49 |
| abstract_inverted_index.the | 7, 28, 48, 62, 68, 73, 76, 79, 83, 106, 114 |
| abstract_inverted_index.two | 10, 84 |
| abstract_inverted_index.axes | 30 |
| abstract_inverted_index.each | 65, 87, 111 |
| abstract_inverted_index.over | 53 |
| abstract_inverted_index.that | 109 |
| abstract_inverted_index.this | 23, 92 |
| abstract_inverted_index.used | 4 |
| abstract_inverted_index.along | 86 |
| abstract_inverted_index.angle | 16 |
| abstract_inverted_index.axes. | 54, 126 |
| abstract_inverted_index.axis, | 66 |
| abstract_inverted_index.axis. | 88 |
| abstract_inverted_index.based | 14 |
| abstract_inverted_index.focus | 26 |
| abstract_inverted_index.novel | 42 |
| abstract_inverted_index.while | 12 |
| abstract_inverted_index.(ICA), | 38 |
| abstract_inverted_index.Cosine | 0 |
| abstract_inverted_index.cosine | 45 |
| abstract_inverted_index.govern | 110 |
| abstract_inverted_index.method | 121 |
| abstract_inverted_index.shared | 80 |
| abstract_inverted_index.study, | 24 |
| abstract_inverted_index.widely | 3 |
| abstract_inverted_index.between | 9, 82 |
| abstract_inverted_index.common. | 21 |
| abstract_inverted_index.defined | 71 |
| abstract_inverted_index.exhibit | 59 |
| abstract_inverted_index.meaning | 81 |
| abstract_inverted_index.measure | 6 |
| abstract_inverted_index.product | 74, 115 |
| abstract_inverted_index.propose | 40, 119 |
| abstract_inverted_index.through | 96 |
| abstract_inverted_index.Analysis | 37 |
| abstract_inverted_index.approach | 93 |
| abstract_inverted_index.deriving | 105 |
| abstract_inverted_index.examples | 99 |
| abstract_inverted_index.semantic | 51, 69 |
| abstract_inverted_index.thorough | 101 |
| abstract_inverted_index.Component | 36 |
| abstract_inverted_index.component | 112 |
| abstract_inverted_index.enhancing | 61 |
| abstract_inverted_index.intuitive | 97 |
| abstract_inverted_index.numerical | 98, 102 |
| abstract_inverted_index.selecting | 123 |
| abstract_inverted_index.sparsity, | 60 |
| abstract_inverted_index.components | 77 |
| abstract_inverted_index.embeddings | 32, 58, 85 |
| abstract_inverted_index.normalized | 56 |
| abstract_inverted_index.represents | 78 |
| abstract_inverted_index.similarity | 1, 8, 46, 70 |
| abstract_inverted_index.Independent | 35 |
| abstract_inverted_index.coefficient | 19 |
| abstract_inverted_index.components, | 117 |
| abstract_inverted_index.correlation | 18 |
| abstract_inverted_index.embeddings, | 11 |
| abstract_inverted_index.probability | 107 |
| abstract_inverted_index.significant | 125 |
| abstract_inverted_index.transformed | 33 |
| abstract_inverted_index.demonstrated | 95 |
| abstract_inverted_index.experiments. | 103 |
| abstract_inverted_index.similarities | 52 |
| abstract_inverted_index.distributions | 108 |
| abstract_inverted_index.effectiveness | 90 |
| abstract_inverted_index.interpretable | 29 |
| abstract_inverted_index.statistically | 124 |
| abstract_inverted_index.interpretation | 43 |
| abstract_inverted_index.ICA-transformed | 57 |
| abstract_inverted_index.interpretations | 13 |
| abstract_inverted_index.interpretability | 63 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |