{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T19:36:14Z","timestamp":1776886574647,"version":"3.51.2"},"reference-count":35,"publisher":"IEEE","license":[{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T00:00:00Z","timestamp":1588291200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1109\/icassp40776.2020.9054058","type":"proceedings-article","created":{"date-parts":[[2020,4,9]],"date-time":"2020-04-09T20:21:13Z","timestamp":1586463673000},"page":"3822-3826","source":"Crossref","is-referenced-by-count":8,"title":["Multivariate Tropical Regression and Piecewise-Linear Surface Fitting"],"prefix":"10.1109","author":[{"given":"Petros","family":"Maragos","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanouil","family":"Theodosis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2003.08.010"},{"key":"ref32","author":"cuninghame-green","year":"1979","journal-title":"Minimax Algebra"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-017-0207-8"},{"key":"ref30","article-title":"Tropical geometry and piecewise-linear approximation of curves and surfaces on weighted lattices","author":"maragos","year":"2019"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1684(97)00036-4"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1949-007-x"},{"key":"ref10","first-page":"1","article-title":"Log-Sum-Exp Neural Networks and Posynomial Models for Convex and LogLog-Convex Data","volume":"30","author":"calafiore","year":"2019","journal-title":"IEEE Trans Neural Networks and Learning Systems"},{"key":"ref11","article-title":"Introduction to Tropical Geometry","author":"maclagan","year":"2015","journal-title":"Amer Math Soc"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8268-2_8"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.06.009"},{"key":"ref14","author":"baccelli","year":"1992","journal-title":"Synchronization and Linearity An Algebra for Discrete Event Systems"},{"key":"ref15","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-84996-299-5","author":"butkovi?","year":"2010","journal-title":"Max-Linear Systems Theory and Algorithms"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1103925"},{"key":"ref17","author":"gondran","year":"2008","journal-title":"Graphs Dioids and Semirings New Models and Algorithms"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-007-0450-5"},{"key":"ref19","first-page":"50","article-title":"Tropical semirings","author":"perin","year":"1998","journal-title":"Idempotency"},{"key":"ref28","first-page":"5824","article-title":"Tropical geometry of deep neural networks","volume":"80","author":"zhang","year":"2018","journal-title":"Proc Int&#x2019;l Conf Machine Learning"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1109\/81.340865","article-title":"Explicit Piecewise-Linear Models","volume":"41","author":"lin","year":"1994","journal-title":"IEEE Trans Circuits Syst I Fund Theory and Appl"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2003.809427"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(99)00195-8"},{"key":"ref6","article-title":"Multivariate convex regression with adaptive partitioning","author":"hannah","year":"2011"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-20867-7_1"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2004.834521"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TCAD.2010.2053151"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s11081-016-9332-3"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/81.128016"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s11081-008-9045-3"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/31.1705"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/100788458"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1016\/B978-012119792-6\/50072-3"},{"key":"ref21","author":"heijmans","year":"1994","journal-title":"Morphological Image Operators"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1006\/csla.2001.0184"},{"key":"ref23","volume":"2","author":"serra","year":"1988","journal-title":"Image Analysis and Mathematical Morphology"},{"key":"ref26","first-page":"1319","article-title":"Maxout networks","volume":"28","author":"goodfellow","year":"2013","journal-title":"Proc Int&#x2019;l Conf Machine Learning"},{"key":"ref25","first-page":"3","article-title":"Morphological Perceptrons: Geometry and Training Algorithms","author":"charisopoulos","year":"2017","journal-title":"Proc Int&#x2019;l Symp Mathematical Morphology (ISMM)"}],"event":{"name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","location":"Barcelona, Spain","start":{"date-parts":[[2020,5,4]]},"end":{"date-parts":[[2020,5,8]]}},"container-title":["ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/9040208\/9052899\/09054058.pdf?arnumber=9054058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,28]],"date-time":"2022-06-28T00:24:28Z","timestamp":1656375868000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9054058\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5]]},"references-count":35,"URL":"https:\/\/doi.org\/10.1109\/icassp40776.2020.9054058","relation":{},"subject":[],"published":{"date-parts":[[2020,5]]}}}