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However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP\/PARAFAC decomposition (CPD), the ideal value for the number of components is known as the canonical rank and greatly affects the quality of the decomposition results. Existing methods use heuristics or Bayesian methods to estimate this value by repeatedly calculating the CPD, making them extremely computationally expensive. In this work, we propose\n                    <jats:sc>FRAPPE<\/jats:sc>\n                    , the first method to estimate the canonical rank of a tensor without having to compute the CPD. This method is the result of two key ideas. First, it is much cheaper to generate synthetic data with known rank compared to computing the CPD. Second, we can greatly improve the generalization ability and speed of our model by generating synthetic data that matches a given input tensor in terms of size and sparsity. We can then train a specialized single-use regression model on a synthetic set of tensors engineered to match a given input tensor and use that to estimate the canonical rank of the tensor\u2014all without computing the expensive CPD.\n                    <jats:sc>FRAPPE<\/jats:sc>\n                    is over\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$24\\times $$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>24<\/mml:mn>\n                            <mml:mo>\u00d7<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    faster than the best-performing baseline, and exhibits a\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$10\\%$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mn>10<\/mml:mn>\n                            <mml:mo>%<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    improvement in MAPE on a synthetic dataset. It also performs as well as or better than the baselines on real-world datasets.\n                  <\/jats:p>","DOI":"10.1007\/s10618-024-01071-6","type":"journal-article","created":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T00:01:43Z","timestamp":1727308903000},"page":"4217-4232","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["FRAPPE: fast rank approximation with explainable features for tensors"],"prefix":"10.1007","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5813-2266","authenticated-orcid":false,"given":"William","family":"Shiao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3411-8483","authenticated-orcid":false,"given":"Evangelos E.","family":"Papalexakis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,9,26]]},"reference":[{"key":"1071_CR1","volume-title":"Matlab tensor toolbox version 2.2","author":"B Bader","year":"2007","unstructured":"Bader B, Kolda T (2007) Matlab tensor toolbox version 2.2. 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As with all machine learning methods, our method is not infallible and may produce incorrect results. In certain mission-critical systems, that can potentially lead to severe consequences if care is not taken to validate model results. Another ethical concern is the possibility of adversarial attacks on the model. In our work, we do not consider the case of adversarially crafted input tensors designed to trick the model into performing poorly or predicting an extremely high rank, which could potentially result in maliciously altered results.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Statement"}}]}}