{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-gaussian-mixture-model-representation-of","title":"A Gaussian mixture model representation of endmember variability in hyperspectral unmixing","arxiv_id":"1710.00075","date":"2017-09-29","proceeding":null,"authors":["Yuan Zhou","Anand Rangarajan","Paul D. Gader"],"abstract":"Hyperspectral unmixing while considering endmember variability is usually\nperformed by the normal compositional model (NCM), where the endmembers for\neach pixel are assumed to be sampled from unimodal Gaussian distributions.\nHowever, in real applications, the distribution of a material is often not\nGaussian. In this paper, we use Gaussian mixture models (GMM) to represent the\nendmember variability. We show, given the GMM starting premise, that the\ndistribution of the mixed pixel (under the linear mixing model) is also a GMM\n(and this is shown from two perspectives). The first perspective originates\nfrom the random variable transformation and gives a conditional density\nfunction of the pixels given the abundances and GMM parameters. With proper\nsmoothness and sparsity prior constraints on the abundances, the conditional\ndensity function leads to a standard maximum a posteriori (MAP) problem which\ncan be solved using generalized expectation maximization. The second\nperspective originates from marginalizing over the endmembers in the GMM, which\nprovides us with a foundation to solve for the endmembers at each pixel. Hence,\nour model can not only estimate the abundances and distribution parameters, but\nalso the distinct endmember set for each pixel. We tested the proposed GMM on\nseveral synthetic and real datasets, and showed its potential by comparing it\nto current popular methods.","url_abs":"http://arxiv.org/abs/1710.00075v2","url_pdf":"http://arxiv.org/pdf/1710.00075v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-gaussian-mixture-model-representation-of","repo_url":"https://github.com/zhouyuanzxcv/Hyperspectral","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"hyperspectral-unmixing","task_name":"Hyperspectral Unmixing"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.00075","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}