{"url":"/method/embedded-gaussian-affinity","slug":"embedded-gaussian-affinity","name":"Embedded Gaussian Affinity","full_name":"Embedded Gaussian Affinity","full_name_withheld":false,"description_markdown":"**Embedded Gaussian Affinity** is a type of affinity or self-similarity function between two points $\\mathbf{x\\_{i}}$ and $\\mathbf{x\\_{j}}$ that uses a Gaussian function in an embedding space:\r\n\r\n$$ f\\left(\\mathbf{x\\_{i}}, \\mathbf{x\\_{j}}\\right) = e^{\\theta\\left(\\mathbf{x\\_{i}}\\right)^{T}\\phi\\left(\\mathbf{x\\_{j}}\\right)} $$\r\n\r\nHere $\\theta\\left(x\\_{i}\\right) = W\\_{θ}x\\_{i}$ and $\\phi\\left(x\\_{j}\\right) = W\\_{φ}x\\_{j}$ are two embeddings.\r\n\r\nNote that the self-attention module used in the original [Transformer](https://paperswithcode.com/method/transformer) model is a special case of non-local operations in the embedded Gaussian version. This can be seen from the fact that for a given $i$, $\\frac{1}{\\mathcal{C}\\left(\\mathbf{x}\\right)}\\sum\\_{\\forall{j}}f\\left(\\mathbf{x}\\_{i}, \\mathbf{x}\\_{j}\\right)g\\left(\\mathbf{x}\\_{j}\\right)$ becomes the [softmax](https://paperswithcode.com/method/softmax) computation along the dimension $j$. So we have $\\mathbf{y} = \\text{softmax}\\left(\\mathbf{x}^{T}W^{T}\\_{\\theta}W\\_{\\phi}\\mathbf{x}\\right)g\\left(\\mathbf{x}\\right)$, which is the self-attention form in the Transformer model. This shows how we can relate this recent self-attention model to the classic computer vision method of non-local means.","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#L99","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":8,"archive_num_papers":8,"papers_newest_first":[{"paper":null,"title":"Enhancing Tree Type Detection in Forest Fire Risk Assessment: Multi-Stage Approach and Color Encoding with Forest Fire Risk Evaluation Framework for UAV Imagery","date":"2024-07-27","arxiv_id":"2407.19184","n_code_links":0,"syntology":null},{"paper":"/paper/vision-based-food-nutrition-estimation-via","title":"Vision-based Food Nutrition Estimation via RGB-D Fusion Network","date":"2023-10-25","arxiv_id":null,"n_code_links":1,"syntology":null},{"paper":null,"title":"Fracture Detection in Wrist X-ray Images Using Deep Learning-Based Object Detection Models","date":"2021-11-14","arxiv_id":"2111.07355","n_code_links":0,"syntology":null},{"paper":null,"title":"Towards Balanced Learning for Instance Recognition","date":"2021-08-23","arxiv_id":"2108.10175","n_code_links":0,"syntology":null},{"paper":"/paper/foodlogodet-1500-a-dataset-for-large-scale","title":"FoodLogoDet-1500: A Dataset for Large-Scale Food Logo Detection via Multi-Scale Feature Decoupling Network","date":"2021-08-10","arxiv_id":"2108.04644","n_code_links":1,"syntology":null},{"paper":null,"title":"PBRnet: Pyramidal Bounding Box Refinement to Improve Object Localization Accuracy","date":"2020-03-10","arxiv_id":"2003.04541","n_code_links":0,"syntology":null},{"paper":"/paper/libra-r-cnn-towards-balanced-learning-for","title":"Libra R-CNN: Towards Balanced Learning for Object Detection","date":"2019-04-04","arxiv_id":"1904.02701","n_code_links":6,"syntology":null},{"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":8,"tasks":[{"task":"/task/object-detection","name":"Object Detection","papers":4},{"task":"/task/object-detection-1","name":"object-detection","papers":3},{"task":"/task/action-classification","name":"Action Classification","papers":1},{"task":"/task/action-recognition-in-videos","name":"Action Recognition","papers":1},{"task":"/task/ensemble-learning","name":"Ensemble Learning","papers":1},{"task":"/task/fire-detection","name":"Fire Detection","papers":1},{"task":"/task/food-recommendation","name":"Food recommendation","papers":1},{"task":"/task/fracture-detection","name":"Fracture detection","papers":1},{"task":"/task/instance-segmentation","name":"Instance Segmentation","papers":1},{"task":"/task/keypoint-detection","name":"Keypoint Detection","papers":1},{"task":"/task/management","name":"Management","papers":1},{"task":"/task/medical-object-detection","name":"Medical Object Detection","papers":1},{"task":"/task/nutrition","name":"Nutrition","papers":1},{"task":"/task/object-localization","name":"Object Localization","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/transfer-learning","name":"Transfer Learning","papers":1},{"task":"/task/video-classification","name":"Video Classification","papers":1}],"tasks_shown":19,"n_tasks":19,"usage_by_year":[{"year":"2017","papers":1},{"year":"2019","papers":1},{"year":"2020","papers":1},{"year":"2021","papers":3},{"year":"2023","papers":1},{"year":"2024","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/embedded-gaussian-affinity"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}