{"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/hybrid-orthogonal-projection-and-estimation","title":"Hybrid Orthogonal Projection and Estimation (HOPE): A New Framework to Probe and Learn Neural Networks","arxiv_id":"1502.00702","date":"2015-02-03","proceeding":null,"authors":["Shiliang Zhang","Hui Jiang"],"abstract":"In this paper, we propose a novel model for high-dimensional data, called the\nHybrid Orthogonal Projection and Estimation (HOPE) model, which combines a\nlinear orthogonal projection and a finite mixture model under a unified\ngenerative modeling framework. The HOPE model itself can be learned\nunsupervised from unlabelled data based on the maximum likelihood estimation as\nwell as discriminatively from labelled data. More interestingly, we have shown\nthe proposed HOPE models are closely related to neural networks (NNs) in a\nsense that each hidden layer can be reformulated as a HOPE model. As a result,\nthe HOPE framework can be used as a novel tool to probe why and how NNs work,\nmore importantly, to learn NNs in either supervised or unsupervised ways. In\nthis work, we have investigated the HOPE framework to learn NNs for several\nstandard tasks, including image recognition on MNIST and speech recognition on\nTIMIT. Experimental results have shown that the HOPE framework yields\nsignificant performance gains over the current state-of-the-art methods in\nvarious types of NN learning problems, including unsupervised feature learning,\nsupervised or semi-supervised learning.","url_abs":"http://arxiv.org/abs/1502.00702v2","url_pdf":"http://arxiv.org/pdf/1502.00702v2.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":[],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"speech-recognition","task_name":"Speech Recognition"},{"task_slug":"speech-recognition-1","task_name":"speech-recognition"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-classification-on-mnist","task":"Image Classification","dataset":"MNIST","model":"HOPE","rank_in_archive_order":27,"of":81,"metrics":{"Percentage error":"0.4"},"uses_additional_data":false}],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}