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Intell. Syst. Technol."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>\n            The Collaborative Representation (CR) framework has provided various effective and efficient solutions to pattern analysis. By leveraging between discriminative coefficient coding (l\n            <jats:sub>2<\/jats:sub>\n            regularization) and the best reconstruction quality (collaboration), the CR framework can exploit discriminative patterns efficiently in high-dimensional space. Due to the limitations of its linear representation mechanism, the CR must sacrifice its superior efficiency for capturing the non-linear information with the kernel trick. Besides this, even if the coding is indispensable, there is no mechanism designed to keep the CR free from inevitable noise brought by real-world information systems. In addition, the CR only emphasizes exploiting discriminative patterns on coefficients rather than on the reconstruction. To tackle the problems of primitive CR with a unified framework, in this article we propose the Euler Collaborative Representation (E-CR) framework. Inferred from the Euler formula, in the proposed method, we map the samples to a complex space to capture discriminative and non-linear information without the high-dimensional hidden kernel space. Based on the proposed E-CR framework, we form two specific classifiers: the Euler Collaborative Representation based Classifier (E-CRC) and the Euler Probabilistic Collaborative Representation based Classifier (E-PROCRC). Furthermore, we specifically designed a robust algorithm for E-CR (termed as\n            <jats:italic>R-E-CR<\/jats:italic>\n            ) to deal with the inevitable noises in real-world systems. Robust iterative algorithms have been specially designed for solving E-CRC and E-PROCRC. We correspondingly present a series of theoretical proofs to ensure the completeness of the theory for the proposed robust algorithms. We evaluated E-CR and R-E-CR with various experiments to show its competitive performance and efficiency.\n          <\/jats:p>","DOI":"10.1145\/3625235","type":"journal-article","created":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T08:03:58Z","timestamp":1695715438000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Learning with Euler Collaborative Representation for Robust Pattern Analysis"],"prefix":"10.1145","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2423-2311","authenticated-orcid":false,"given":"Jianhang","family":"Zhou","sequence":"first","affiliation":[{"name":"University of Macau, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6391-6257","authenticated-orcid":false,"given":"Guancheng","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Macau, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4384-8787","authenticated-orcid":false,"given":"Shaoning","family":"Zeng","sequence":"additional","affiliation":[{"name":"University of Electronic Science and Technology of China, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2497-9519","authenticated-orcid":false,"given":"Bob","family":"Zhang","sequence":"additional","affiliation":[{"name":"Centre for Artificial Intelligence and Robotics, Institute of Collaborative Innovation, University of Macau, Taipa, Macau SAR, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,11,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/JIOT.2020.3030072"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.patcog.2016.12.017"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.322"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2017.2757923"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/tip.2017.2675341"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2019.2945367"},{"key":"e_1_3_2_8_2","first-page":"4387","volume-title":"Proceedings of the International Conference on Machine Learning","author":"Hsieh Kevin","year":"2020","unstructured":"Kevin Hsieh, Amar Phanishayee, Onur Mutlu, and Phillip Gibbons. 2020. 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