{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T22:02:11Z","timestamp":1764194531866,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T00:00:00Z","timestamp":1614384000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T00:00:00Z","timestamp":1614384000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973022","61973024","61703027"],"award-info":[{"award-number":["61973022","61973024","61703027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China Scholarship Council State-Sponsored Scholarship Program","award":["201806880024","201806885004"],"award-info":[{"award-number":["201806880024","201806885004"]}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["JD1708"],"award-info":[{"award-number":["JD1708"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Research Fund of State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University","award":["18I01"],"award-info":[{"award-number":["18I01"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s00500-021-05641-4","type":"journal-article","created":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T12:02:56Z","timestamp":1614427376000},"page":"6489-6504","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Integrating virtual sample generation with input-training neural network for solving small sample size problems: application to purified terephthalic acid solvent system"],"prefix":"10.1007","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9659-0751","authenticated-orcid":false,"given":"Zhong-Sheng","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun-Xiong","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan-Lin","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing-Lin","family":"Su","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiqing C.","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoltan K.","family":"Nagy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,2,27]]},"reference":[{"key":"5641_CR1","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1109\/JBHI.2016.2515993","volume":"21","author":"B Bayar","year":"2017","unstructured":"Bayar B, Bouaynaya N, Shterenberg R (2017) SMURC: high-dimension small-sample multivariate regression with covariance estimation. IEEE J Biomed Health Inform 21:573\u2013581","journal-title":"IEEE J Biomed Health Inform"},{"key":"5641_CR2","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.neunet.2017.07.001","volume":"94","author":"S Blaes","year":"2017","unstructured":"Blaes S, Burwick T (2017) Few-shot learning in deep networks through global prototyping. Neural Netw 94:159\u2013172","journal-title":"Neural Netw"},{"key":"5641_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2907070","volume":"49","author":"P Branco","year":"2016","unstructured":"Branco P, Torgo L, Ribeiro RP (2016) A survey of predictive modeling on imbalanced domains. ACM Comput Surv 49:1\u201350","journal-title":"ACM Comput Surv"},{"key":"5641_CR4","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.cam.2017.05.045","volume":"329","author":"J Chen","year":"2018","unstructured":"Chen J (2018) The quadrilateral Mindlin plate elements using the spline interpolation bases. J Comput Appl Math 329:68\u201383","journal-title":"J Comput Appl Math"},{"key":"5641_CR5","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1016\/j.engappai.2016.12.024","volume":"59","author":"ZS Chen","year":"2017","unstructured":"Chen ZS, Zhu B, He YL, Yu LA (2017) A PSO based virtual sample generation method for small sample sets: Applications to regression datasets. Eng Appl Artif Intell 59:236\u2013243","journal-title":"Eng Appl Artif Intell"},{"key":"5641_CR6","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.cherd.2016.10.047","volume":"116","author":"LS Dias","year":"2016","unstructured":"Dias LS, Ierapetritou MG (2016) Integration of scheduling and control under uncertainties: review and challenges. Chem Eng Res Des 116:98\u2013113","journal-title":"Chem Eng Res Des"},{"key":"5641_CR7","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.inffus.2018.10.005","volume":"50","author":"A Diez-Olivan","year":"2019","unstructured":"Diez-Olivan A, Del Ser J, Galar D, Sierra B (2019) Data fusion and machine learning for industrial prognosis: trends and perspectives towards Industry 4.0. Inf Fus 50:92\u2013111","journal-title":"Inf Fus"},{"key":"5641_CR8","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1016\/j.neucom.2014.07.057","volume":"149","author":"S Espezua","year":"2015","unstructured":"Espezua S, Villanueva E, Maciel CD, Carvalho A (2015) A projection pursuit framework for supervised dimension reduction of high dimensional small sample datasets. Neurocomputing 149:767\u2013776","journal-title":"Neurocomputing"},{"key":"5641_CR9","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/j.apenergy.2017.04.007","volume":"197","author":"HF Gong","year":"2017","unstructured":"Gong HF, Chen ZS, Zhu QX, He YL (2017) A Monte Carlo and PSO based virtual sample generation method for enhancing the energy prediction and energy optimization on small data problem: an empirical study of petrochemical industries. Appl Energy 197:405\u2013415","journal-title":"Appl Energy"},{"key":"5641_CR10","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1016\/j.energy.2018.01.059","volume":"147","author":"YL He","year":"2018","unstructured":"He YL, Wang PJ, Zhang MQ, Zhu QX, Xu Y (2018) A novel and effective nonlinear interpolation virtual sample generation method for enhancing energy prediction and analysis on small data problem: a case study of Ethylene industry. Energy 147:418\u2013427","journal-title":"Energy"},{"key":"5641_CR11","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.jvcir.2017.11.010","volume":"50","author":"SH Hong","year":"2018","unstructured":"Hong SH, Wang L, Truong TK (2018) Low-complexity direct computation algorithm for cubic-spline interpolation scheme. J Vis Commun Image Represent 50:159\u2013166","journal-title":"J Vis Commun Image Represent"},{"key":"5641_CR12","doi-asserted-by":"publisher","first-page":"1328","DOI":"10.1109\/TPAMI.2012.129","volume":"35","author":"S Huang","year":"2013","unstructured":"Huang S et al (2013) A sparse structure learning algorithm for Gaussian Bayesian Network identification from high-dimensional data. IEEE Trans Pattern Anal Mach Intell 35:1328\u20131342","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"5641_CR13","doi-asserted-by":"publisher","unstructured":"Lee Y, Kang J, Kang B, Ryu KR (2006) Bayesian sampling of virtual examples to improve classification accuracy. In: SICE-ICASE International Joint Conference, IEEE, Busan, South Korea, pp 1009\u20131014. http:\/\/doi.org\/https:\/\/doi.org\/10.1109\/SICE.2006.315740","DOI":"10.1109\/SICE.2006.315740"},{"key":"5641_CR14","doi-asserted-by":"publisher","first-page":"1575","DOI":"10.1016\/j.eswa.2011.08.071","volume":"39","author":"DC Li","year":"2012","unstructured":"Li DC, Chen CC, Chang CJ, Lin WK (2012) A tree-based-trend-diffusion prediction procedure for small sample sets in the early stages of manufacturing systems. Expert Syst Appl 39:1575\u20131581","journal-title":"Expert Syst Appl"},{"key":"5641_CR15","doi-asserted-by":"publisher","first-page":"966","DOI":"10.1016\/j.cor.2005.05.019","volume":"34","author":"DC Li","year":"2007","unstructured":"Li DC, Wu CS, Tsai TI, Lina YS (2007) Using mega-trend-diffusion and artificial samples in small data set learning for early flexible manufacturing system scheduling knowledge. Comput Oper Res 34:966\u2013982","journal-title":"Comput Oper Res"},{"key":"5641_CR16","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.dss.2014.06.004","volume":"66","author":"DC Li","year":"2014","unstructured":"Li DC, Lin LS (2014) Generating information for small data sets with a multi-modal distribution. Decis Support Syst 66:71\u201381","journal-title":"Decis Support Syst"},{"key":"5641_CR17","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.dss.2013.12.007","volume":"59","author":"DC Li","year":"2014","unstructured":"Li DC, Lin LS, Peng LJ (2014) Improving learning accuracy by using synthetic samples for small datasets with non-linear attribute dependency. Decis Support Syst 59:286\u2013295","journal-title":"Decis Support Syst"},{"key":"5641_CR18","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.dss.2017.10.013","volume":"105","author":"DC Li","year":"2018","unstructured":"Li DC, Lin WK, Chen CC, Chen HY, Lin LS (2018) Rebuilding sample distributions for small dataset learning. Decis Support Syst 105:66\u201376","journal-title":"Decis Support Syst"},{"key":"5641_CR19","doi-asserted-by":"publisher","first-page":"156","DOI":"10.1016\/j.eng.2018.11.018","volume":"5","author":"Y Liu","year":"2019","unstructured":"Liu Y, Zhou Y, Liu X, Dong F, Wang C, Wang Z (2019) Wasserstein GAN-based small-sample augmentation for new-generation artificial intelligence: a case study of cancer-staging data in biology. Engineering 5:156\u2013163","journal-title":"Engineering"},{"key":"5641_CR20","doi-asserted-by":"publisher","first-page":"3066","DOI":"10.1109\/TIA.2016.2618756","volume":"53","author":"I Martin-Diaz","year":"2017","unstructured":"Martin-Diaz I, Morinigo-Sotelo D, Duque-Perez O, Romero-Troncoso RD (2017) Early fault detection in induction motors using adaboost with imbalanced small data and optimized sampling. IEEE Trans Ind Appl 53:3066\u20133075","journal-title":"IEEE Trans Ind Appl"},{"key":"5641_CR21","doi-asserted-by":"publisher","first-page":"2196","DOI":"10.1109\/5.726787","volume":"86","author":"P Niyogi","year":"1998","unstructured":"Niyogi P, Girosi F, Poggio T (1998) Incorporating prior information in machine learning by creating virtual examples. Proc IEEE 86:2196\u20132209","journal-title":"Proc IEEE"},{"key":"5641_CR22","doi-asserted-by":"publisher","unstructured":"Ohashi T, Watanabe H, Tokuno J, Katagiri S, Ohsaki M, Matsuda S, Kashioka H (2012) Increasing virtual samples through loss smoothness determination in large geometric margin minimum classification error training. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), IEEE, Kyoto, Japan, pp 2081\u20132084. http:\/\/doi.org\/https:\/\/doi.org\/10.1109\/ICASSP.2012.6288320","DOI":"10.1109\/ICASSP.2012.6288320"},{"key":"5641_CR23","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/j.compchemeng.2019.04.003","volume":"126","author":"SJ Qin","year":"2019","unstructured":"Qin SJ, Chiang LH (2019) Advances and opportunities in machine learning for process data analytics. Comput Chem Eng 126:465\u2013473","journal-title":"Comput Chem Eng"},{"key":"5641_CR24","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/j.procir.2016.10.107","volume":"56","author":"C Reuter","year":"2016","unstructured":"Reuter C, Brambring F, Weirich J, Kleines A (2016) Improving data consistency in production control by adaptation of data mining algorithms. Procedia CIRP 56:545\u2013550","journal-title":"Procedia CIRP"},{"key":"5641_CR25","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.solener.2017.05.024","volume":"151","author":"MC Rodriguez-Amigo","year":"2017","unstructured":"Rodriguez-Amigo MC, Diez-Mediavilla M, Gonzalez-Pena D, Perez-Burgos A, Alonso-Tristan C (2017) Mathematical interpolation methods for spatial estimation of global horizontal irradiation in Castilla-Leon, Spain: A case study. Sol Energy 151:14\u201321","journal-title":"Sol Energy"},{"key":"5641_CR26","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1016\/j.ins.2014.08.051","volume":"291","author":"JA Saez","year":"2015","unstructured":"Saez JA, Luengo J, Stefanowski J, Herrera F (2015) SMOTE-IPF: Addressing the noisy and borderline examples problem in imbalanced classification by a re-sampling method with filtering. Inf Sci 291:184\u2013203","journal-title":"Inf Sci"},{"key":"5641_CR27","doi-asserted-by":"publisher","first-page":"1471","DOI":"10.1002\/aic.690410612","volume":"41","author":"SF Tan","year":"1995","unstructured":"Tan SF, Mavrovouniotis ML (1995) Reducing data dimensionality through optimizing neural-network inputs. AIChE J 41:1471\u20131480","journal-title":"AIChE J"},{"key":"5641_CR28","doi-asserted-by":"publisher","unstructured":"Tang J, Jia M, Liu Z, Chai T, Yu W (2015) Modeling high dimensional frequency spectral data based on virtual sample generation technique. In: IEEE International Conference on Information and Automation, IEEE, Lijiang, China, pp 1090\u20131095. http:\/\/doi.org\/https:\/\/doi.org\/10.1109\/ICInfA.2015.7279449","DOI":"10.1109\/ICInfA.2015.7279449"},{"key":"5641_CR29","doi-asserted-by":"publisher","first-page":"1915","DOI":"10.1002\/bit.26605","volume":"115","author":"A Tulsyan","year":"2018","unstructured":"Tulsyan A, Garvin C, Undey C (2018) Advances in industrial biopharmaceutical batch process monitoring: Machine-learning methods for small data problems. Biotechnol Bioeng 115:1915\u20131924","journal-title":"Biotechnol Bioeng"},{"key":"5641_CR30","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/S1474-6670(17)39729-X","volume":"33","author":"J Van Gorp","year":"2000","unstructured":"Van Gorp J, Rolain Y (2000) An interpolation technique for learning with sparse Data. IFAC Proc Vol 33:73\u201378","journal-title":"IFAC Proc Vol"},{"key":"5641_CR31","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1038\/s41524-018-0081-z","volume":"4","author":"Y Zhang","year":"2018","unstructured":"Zhang Y, Ling C (2018) A strategy to apply machine learning to small datasets in materials science. NPJ Comput Mater 4:25","journal-title":"NPJ Comput Mater"},{"key":"5641_CR32","doi-asserted-by":"publisher","unstructured":"Zhao Y, Ma R, Wen X (2011) Construct virtual samples for improving kernel PCA. In: International Conference on Multimedia and Signal Processing, IEEE, Guilin, China, pp 325\u2013328. http:\/\/doi.org\/https:\/\/doi.org\/10.1109\/CMSP.2011.72","DOI":"10.1109\/CMSP.2011.72"},{"key":"5641_CR33","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.chemolab.2016.12.012","volume":"161","author":"B Zhu","year":"2017","unstructured":"Zhu B, Chen ZS, He YL, Yu LA (2017a) A novel nonlinear functional expansion based PLS (FEPLS) and its soft sensor application. Chemom Intell Lab Syst 161:108\u2013117","journal-title":"Chemom Intell Lab Syst"},{"key":"5641_CR34","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1016\/j.neucom.2018.02.099","volume":"328","author":"FY Zhu","year":"2019","unstructured":"Zhu FY, Ma ZY, Li XX, Chen G, Chien JT, Xue JH, Guo J (2019) Image-text dual neural network with decision strategy for small-sample image classification. Neurocomputing 328:182\u2013188","journal-title":"Neurocomputing"},{"key":"5641_CR35","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.arcontrol.2018.09.003","volume":"46","author":"JL Zhu","year":"2018","unstructured":"Zhu JL, Ge ZQ, Song ZH, Gao FR (2018) Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data. Annu Rev Control 46:107\u2013133","journal-title":"Annu Rev Control"},{"issue":"9","key":"5641_CR36","doi-asserted-by":"publisher","first-page":"6889","DOI":"10.1007\/s00500-019-04326-3","volume":"24","author":"Q Zhu","year":"2020","unstructured":"Zhu Q, Chen Z, Zhang X, Abbas R, Xu Y, Chen Y (2020) Dealing with small sample size problems in process industry using virtual sample generation: a Kriging-based approach. Soft Comput 24(9):6889\u20136902","journal-title":"Soft Comput"},{"key":"5641_CR37","doi-asserted-by":"publisher","unstructured":"Zhu QX, Gong HF, Xu Y, He YL (2017) A bootstrap based virtual sample generation method for improving the accuracy of modeling complex chemical processes using small datasets. In: 6th Data Driven Control and Learning Systems, IEEE, Chongqing, China. http:\/\/doi.org\/https:\/\/doi.org\/10.1109\/DDCLS.2017.8068049","DOI":"10.1109\/DDCLS.2017.8068049"},{"key":"5641_CR38","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/S1004-9541(06)60121-3","volume":"14","author":"QX Zhu","year":"2006","unstructured":"Zhu QX, Li CF (2006) Dimensionality reduction with input training neural network and its application in chemical process modelling. Chin J Chem Eng 14:597\u2013603","journal-title":"Chin J Chem Eng"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-05641-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-021-05641-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-05641-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T14:24:00Z","timestamp":1616768640000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-021-05641-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,27]]},"references-count":38,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["5641"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-05641-4","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"type":"print","value":"1432-7643"},{"type":"electronic","value":"1433-7479"}],"subject":[],"published":{"date-parts":[[2021,2,27]]},"assertion":[{"value":"28 January 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"No individual participants are included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}