{"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/quantum-clustering-and-gaussian-mixtures","title":"Quantum Clustering and Gaussian Mixtures","arxiv_id":"1612.09199","date":"2016-12-29","proceeding":null,"authors":["Mahajabin Rahman","Davi Geiger"],"abstract":"The mixture of Gaussian distributions, a soft version of k-means , is\nconsidered a state-of-the-art clustering algorithm. It is widely used in\ncomputer vision for selecting classes, e.g., color, texture, and shapes. In\nthis algorithm, each class is described by a Gaussian distribution, defined by\nits mean and covariance. The data is described by a weighted sum of these\nGaussian distributions. We propose a new method, inspired by quantum\ninterference in physics. Instead of modeling each class distribution directly,\nwe model a class wave function such that its magnitude square is the class\nGaussian distribution. We then mix the class wave functions to create the\nmixture wave function. The final mixture distribution is then the magnitude\nsquare of the mixture wave function. As a result, we observe the quantum class\ninterference phenomena, not present in the Gaussian mixture model. We show that\nthe quantum method outperforms the Gaussian mixture method in every aspect of\nthe estimations. It provides more accurate estimations of all distribution\nparameters, with much less fluctuations, and it is also more robust to data\ndeformations from the Gaussian assumptions. We illustrate our method for color\nsegmentation as an example application.","url_abs":"http://arxiv.org/abs/1612.09199v1","url_pdf":"http://arxiv.org/pdf/1612.09199v1.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":"quantum-clustering-and-gaussian-mixtures","repo_url":"https://github.com/mrpintime/Quantum_Gaussian_Mixtures_Clustering","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}