{"url":"/method/concatenation-affinity","slug":"concatenation-affinity","name":"Concatenation Affinity","full_name":"Concatenation Affinity","full_name_withheld":false,"description_markdown":"**Concatenation Affinity** is a type of affinity or self-similarity function between two points $\\mathbb{x\\_{i}}$ and $\\mathbb{x\\_{j}}$ that uses a concatenation function:\r\n\r\n$$ f\\left(\\mathbb{x\\_{i}}, \\mathbb{x\\_{j}}\\right) = \\text{ReLU}\\left(\\mathbb{w}^{T}\\_{f}\\left[\\theta\\left(\\mathbb{x}\\_{i}\\right), \\phi\\left(\\mathbb{x}\\_{j}\\right)\\right]\\right)$$\r\n\r\nHere $\\left[·, ·\\right]$ denotes concatenation and $\\mathbb{w}\\_{f}$ is a weight vector that projects the concatenated vector to a scalar.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Non-local Neural Networks","paper":"/paper/non-local-neural-networks","first_author":"Xiaolong Wang","n_authors":4,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/non-local-neural-networks"},"source":{"url":"http://arxiv.org/abs/1711.07971v3","title":"Non-local Neural Networks","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/tea1528/Non-Local-NN-Pytorch/blob/986937674eb3b85d3d3fbaaa8f384c0a26624121/models/non_local.py#L105","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Affinity Functions","url":"/methods/category/affinity-functions","pwc_aliases":[]}],"n_papers_tagged":1,"archive_num_papers":1,"papers_newest_first":[{"paper":"/paper/non-local-neural-networks","title":"Non-local Neural Networks","date":"2017-11-21","arxiv_id":"1711.07971","n_code_links":32,"syntology":{"ran":3,"of":4,"unverified":1,"pointer_only":4}}],"papers_shown":1,"tasks":[{"task":"/task/action-classification","name":"Action Classification","papers":1},{"task":"/task/action-recognition-in-videos","name":"Action Recognition","papers":1},{"task":"/task/instance-segmentation","name":"Instance Segmentation","papers":1},{"task":"/task/keypoint-detection","name":"Keypoint Detection","papers":1},{"task":"/task/object-detection","name":"Object Detection","papers":1},{"task":"/task/pose-estimation","name":"Pose Estimation","papers":1},{"task":null,"name":"Position","papers":1},{"task":"/task/text-to-sql","name":"Text-To-SQL","papers":1},{"task":"/task/video-classification","name":"Video Classification","papers":1}],"tasks_shown":9,"n_tasks":9,"usage_by_year":[{"year":"2017","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/concatenation-affinity"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}