{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T06:49:16Z","timestamp":1764053356969,"version":"3.41.0"},"reference-count":43,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2014,6,1]],"date-time":"2014-06-01T00:00:00Z","timestamp":1401580800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["#116394"],"award-info":[{"award-number":["#116394"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Knowl. Discov. Data"],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p>\n            Tensors (multidimensional arrays) are widely used for representing high-order dimensional data, in applications ranging from social networks, sensor data, and Internet traffic. Multiway data analysis techniques, in particular tensor decompositions, allow extraction of hidden correlations among multiway data and thus are key components of many data analysis frameworks. Intuitively, these algorithms can be thought of as\n            <jats:italic>multiway clustering<\/jats:italic>\n            schemes, which consider multiple facets of the data in identifying clusters, their weights, and contributions of each data element. Unfortunately, algorithms for fitting multiway models are, in general, iterative and very time consuming. In this article, we observe that, in many applications, there is a priori background knowledge (or metadata) about one or more domain dimensions. This metadata is often in the form of a hierarchy that clusters the elements of a given data facet (or mode). We investigate whether such single-mode data hierarchies can be used to boost the efficiency of tensor decomposition process, without significant impact on the final decomposition quality. We consider each domain hierarchy as a guide to help provide higher- or lower-resolution views of the data in the tensor on demand and we rely on these metadata-induced multiresolution tensor representations to develop a multiresolution approach to tensor decomposition. In this article, we focus on an alternating least squares (ALS)--based implementation of the two most important decomposition models such as the PARAllel FACtors (PARAFAC, which decomposes a tensor into a diagonal tensor and a set of factor matrices) and the Tucker (which produces as result a core tensor and a set of dimension-subspaces matrices). Experiment results show that, when the available metadata is used as a rough guide, the proposed multiresolution method helps fit both PARAFAC and Tucker models with consistent (under different parameters settings) savings in execution time and memory consumption, while preserving the quality of the decomposition.\n          <\/jats:p>","DOI":"10.1145\/2532169","type":"journal-article","created":{"date-parts":[[2014,6,17]],"date-time":"2014-06-17T12:38:13Z","timestamp":1403008693000},"page":"1-38","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":12,"title":["Multiresolution Tensor Decompositions with Mode Hierarchies"],"prefix":"10.1145","volume":"8","author":[{"given":"Claudio","family":"Schifanella","sequence":"first","affiliation":[{"name":"University of Torino"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. Sel\u00e7uk","family":"Candan","sequence":"additional","affiliation":[{"name":"Arizona State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Luisa","family":"Sapino","sequence":"additional","affiliation":[{"name":"University of Torino"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2014,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1002\/cem.1335"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2008.112"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/060676489"},{"key":"e_1_2_1_4_1","unstructured":"B. W. Bader T. G. Kolda J. Sung etal 2012. Matlab tensor toolbox version 2.5. Available at http:\/\/www.sandia.gov\/tgkolda\/TensorToolbox\/index-2.5.html.  B. W. Bader T. G. Kolda J. Sung et al. 2012. Matlab tensor toolbox version 2.5. 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A.","year":"1972","unstructured":"R. A. Harshman . 1972 . PARAFAC2: Mathematical and technical notes . UCLA Working Papers in Phonetics 22 , 30 -- 44 . R. A. Harshman. 1972. PARAFAC2: Mathematical and technical notes. UCLA Working Papers in Phonetics 22, 30--44.","journal-title":"UCLA Working Papers in Phonetics"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/cem.808"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/090764827"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TKDE.2004.77"},{"volume-title":"Proceedings of the 15th Scandinavian Conference on Image Analysis (SCIA\u201907)","author":"Kaarna A.","key":"e_1_2_1_22_1","unstructured":"A. Kaarna , A. Andriyashin , S. Nakauchi , and J. Parkkinen . 2007. Multiresolution approach in computing ntf . In Proceedings of the 15th Scandinavian Conference on Image Analysis (SCIA\u201907) .Springer-Verlag, Berlin, 334--343. A. Kaarna, A. Andriyashin, S. Nakauchi, and J. Parkkinen. 2007. Multiresolution approach in computing ntf. In Proceedings of the 15th Scandinavian Conference on Image Analysis (SCIA\u201907).Springer-Verlag, Berlin, 334--343."},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02293984"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595287997"},{"volume-title":"Proceedings of the SIAM Data Mining Conference Workshop on Link Analysis, Counterterrorism and Security.","author":"Kolda T.","key":"e_1_2_1_25_1","unstructured":"T. Kolda and B. Bader . 2006. The TOPHITS model for higher-order web link analysis . In Proceedings of the SIAM Data Mining Conference Workshop on Link Analysis, Counterterrorism and Security. T. Kolda and B. Bader. 2006. The TOPHITS model for higher-order web link analysis. 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