{"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/on-data-driven-saak-transform","title":"On Data-Driven Saak Transform","arxiv_id":"1710.04176","date":"2017-10-11","proceeding":null,"authors":["C. -C. Jay Kuo","Yueru Chen"],"abstract":"Being motivated by the multilayer RECOS (REctified-COrrelations on a Sphere)\ntransform, we develop a data-driven Saak (Subspace approximation with augmented\nkernels) transform in this work. The Saak transform consists of three steps: 1)\nbuilding the optimal linear subspace approximation with orthonormal bases using\nthe second-order statistics of input vectors, 2) augmenting each transform\nkernel with its negative, 3) applying the rectified linear unit (ReLU) to the\ntransform output. The Karhunen-Lo\\'eve transform (KLT) is used in the first\nstep. The integration of Steps 2 and 3 is powerful since they resolve the sign\nconfusion problem, remove the rectification loss and allow a straightforward\nimplementation of the inverse Saak transform at the same time. Multiple Saak\ntransforms are cascaded to transform images of a larger size. All Saak\ntransform kernels are derived from the second-order statistics of input random\nvectors in a one-pass feedforward manner. Neither data labels nor\nbackpropagation is used in kernel determination. Multi-stage Saak transforms\noffer a family of joint spatial-spectral representations between two extremes;\nnamely, the full spatial-domain representation and the full spectral-domain\nrepresentation. We select Saak coefficients of higher discriminant power to\nform a feature vector for pattern recognition, and use the MNIST dataset\nclassification problem as an illustrative example.","url_abs":"http://arxiv.org/abs/1710.04176v2","url_pdf":"http://arxiv.org/pdf/1710.04176v2.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":"on-data-driven-saak-transform","repo_url":"https://github.com/davidsonic/Saak-Transform","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null},{"paper_slug":"on-data-driven-saak-transform","repo_url":"https://github.com/rickerish-nah/Digital-Image-Processing-Cpp-","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}