{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:52:00Z","timestamp":1792792320528,"version":"4.5.0"},"reference-count":16,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T00:00:00Z","timestamp":1698278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"name":"Hong Kong RGC","award":["ECS 21313922"],"award-info":[{"award-number":["ECS 21313922"]}]},{"name":"Hong Kong RGC","award":["GRF 17301123"],"award-info":[{"award-number":["GRF 17301123"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>We develop a novel framework for the analysis of medical imaging data, including magnetic resonance imaging, functional magnetic resonance imaging, computed tomography and more. Medical imaging data differ from general images in two main aspects: (i) the sample size is often considerably smaller and (ii) the interpretation of the model is usually more crucial than predicting the outcome. As a result, standard methods such as convolutional neural networks cannot be directly applied to medical imaging analysis. Therefore, we propose the deep Kronecker network, which can adapt to the low sample size constraint and offer the desired model interpretation. Our approach is versatile, as it works for both matrix- and tensor-represented image data and can be applied to discrete and continuous outcomes. The deep Kronecker network is built upon a Kronecker product structure, which implicitly enforces a piecewise smooth property on coefficients. Moreover, our approach resembles a fully convolutional network as the Kronecker structure can be expressed in a convolutional form. Interestingly, our approach also has strong connections to the tensor regression framework proposed by Zhou et\u00a0al. (2013), which imposes a canonical low-rank structure on tensor coefficients. We conduct both classification and regression analyses using real magnetic resonance imaging data from the Alzheimer\u2019s Disease Neuroimaging Initiative to demonstrate the effectiveness of our approach.<\/jats:p>","DOI":"10.1093\/biomet\/asad049","type":"journal-article","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T00:27:44Z","timestamp":1693355264000},"page":"707-714","source":"Crossref","is-referenced-by-count":26,"title":["Deep Kronecker network"],"prefix":"10.1093","volume":"111","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2668-4805","authenticated-orcid":false,"given":"Long","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, The University of Hong Kong , Pokfulam Road , Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Data Science, City University of Hong Kong , 83 Tat Chee Ave , Kowloon Tong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,10,26]]},"reference":[{"key":"2024051307572472000_asad049-B1","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/S0140-6736(85)90965-1","article-title":"A new definition of Alzheimer\u2019s disease: a hippocampal dementia","volume":"325","author":"Ball","year":"1985","journal-title":"Lancet"},{"key":"2024051307572472000_asad049-B2","doi-asserted-by":"crossref","first-page":"e2097","DOI":"10.1002\/nla.2097","article-title":"A constructive arbitrary-degree Kronecker product decomposition of tensors","volume":"24","author":"Batselier","year":"2017","journal-title":"Numer. 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