{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T10:43:38Z","timestamp":1776681818755,"version":"3.51.2"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T00:00:00Z","timestamp":1654128000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T00:00:00Z","timestamp":1654128000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Classif"],"published-print":{"date-parts":[[2022,11]]},"DOI":"10.1007\/s00357-022-09414-y","type":"journal-article","created":{"date-parts":[[2022,6,2]],"date-time":"2022-06-02T06:03:41Z","timestamp":1654149821000},"page":"410-431","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Network-Based Discriminant Analysis for Multiclassification"],"prefix":"10.1007","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5440-5036","authenticated-orcid":false,"given":"Li-Pang","family":"Chen","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,2]]},"reference":[{"key":"9414_CR1","unstructured":"Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In N. Petrov F. Czaki (Eds.) 2nd International Symposium on Information Theory (pp. 267\u2013281). Bydapest: Akademiai Kaido."},{"key":"9414_CR2","doi-asserted-by":"publisher","first-page":"1443","DOI":"10.1214\/14-AOAS722","volume":"8","author":"V Baladanddayuthapani","year":"2014","unstructured":"Baladanddayuthapani, V., Talluri, R., Ji, Y., Coombes, K.R., Lu, Y., Hennessy, B.T., Davies, M.A., & Mallick, B.K. (2014). Bayesian sparse graphical models for classification with application to protein expression data. The Annals of Applied Statistics, 8, 1443\u20131468.","journal-title":"The Annals of Applied Statistics"},{"key":"9414_CR3","doi-asserted-by":"publisher","first-page":"1800","DOI":"10.1093\/bioinformatics\/btg238","volume":"19","author":"AM Bagirov","year":"2003","unstructured":"Bagirov, A.M., Ferguson, B., Ivkovic, S., Saunders, G., & Yearwood, J. (2003). New algorithms for multi-class cancer diagnosis using tumor gene expression signatures. Bioinformatics, 19, 1800\u20131807.","journal-title":"Bioinformatics"},{"key":"9414_CR4","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1093\/bioinformatics\/btg051","volume":"19","author":"S Bicciato","year":"2003","unstructured":"Bicciato, S., Luchini, A., & Bello, C.D. (2003). PCA disjoint models for multiclass cancer analysis using gene expression data. Bioinformatics, 19, 571\u2013578.","journal-title":"Bioinformatics"},{"key":"9414_CR5","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1016\/j.ijar.2011.01.007","volume":"52","author":"C Bielza","year":"2011","unstructured":"Bielza, C., Li, G., & Larra\u00f1aga, P. (2011). Multi-dimensional classification with Bayesian networks. International Journal of Approximate Reasoning, 52, 705\u2013727.","journal-title":"International Journal of Approximate Reasoning"},{"key":"9414_CR6","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.csda.2017.07.007","volume":"117","author":"W Cai","year":"2018","unstructured":"Cai, W., Guan, G., Pan, R., Zhu, X., & Wang, H. (2018). Network linear discriminant analysis. Computational Statistics and Data Analysis, 117, 32\u201344.","journal-title":"Computational Statistics and Data Analysis"},{"key":"9414_CR7","doi-asserted-by":"publisher","first-page":"555","DOI":"10.5705\/ss.2010.216","volume":"22","author":"J Chen","year":"2012","unstructured":"Chen, J., & Chen, Z. (2012). Extended BIC for small-n-large-P spases GLM. Statistica Sinica, 22, 555\u2013574.","journal-title":"Statistica Sinica"},{"key":"9414_CR8","doi-asserted-by":"publisher","first-page":"555751","DOI":"10.19080\/BBOAJ.2018.09.555751","volume":"9","author":"L-P Chen","year":"2018","unstructured":"Chen, L.-P. (2018). Multiclassification to gene expression data with some complex features. Biostatistics and Biometrics Open Access Journal, 9, 555751. https:\/\/doi.org\/10.19080\/BBOAJ.2018.09.555751.","journal-title":"Biostatistics and Biometrics Open Access Journal"},{"key":"9414_CR9","unstructured":"Chen, L.-P. (2019). Survival Analysis of Complex Featured Data with Measurement Error. UWSpace. http:\/\/hdl.handle.net\/10012\/14927."},{"key":"9414_CR10","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1186\/s40488-019-0094-2","volume":"6","author":"L-P Chen","year":"2019","unstructured":"Chen, L.-P., Yi, G.Y., Zhang, Q., & He, W. (2019). Multiclass analysis and prediction with network structured covariates. Journal of Statistical Distributions and Applications, 6, 6. https:\/\/doi.org\/10.1186\/s40488-019-0094-2.","journal-title":"Journal of Statistical Distributions and Applications"},{"key":"9414_CR11","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1111\/biom.13331","volume":"77","author":"L-P Chen","year":"2021","unstructured":"Chen, L.-P., & Yi, G.Y. (2021). Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics, 77, 956\u2013969.","journal-title":"Biometrics"},{"key":"9414_CR12","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1198\/TECH.2011.08118","volume":"53","author":"L Clemmensen","year":"2011","unstructured":"Clemmensen, L., Hastie, T., Witten, D., & Ersb\u00f8ll, B. (2011). Sparse discriminant analysis. Technometrics, 53, 406\u2013413.","journal-title":"Technometrics"},{"key":"9414_CR13","doi-asserted-by":"publisher","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"J Fan","year":"2001","unstructured":"Fan, J., & Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 1348\u20131360.","journal-title":"Journal of the American Statistical Association"},{"key":"9414_CR14","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1093\/biostatistics\/kxm045","volume":"9","author":"J Friedman","year":"2008","unstructured":"Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9, 432\u2013441.","journal-title":"Biostatistics"},{"key":"9414_CR15","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1093\/biostatistics\/kxj035","volume":"8","author":"Y Guo","year":"2007","unstructured":"Guo, Y., Hastie, T., & Tibshirani, R. (2007). Regularized linear discriminant analysis and its application in microarrays. Biostatistics, 8, 86\u2013100.","journal-title":"Biostatistics"},{"key":"9414_CR16","volume-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"T Hastie","year":"2008","unstructured":"Hastie, T., Tibshirani, R., & Friedman, J. (2008). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer."},{"key":"9414_CR17","doi-asserted-by":"publisher","DOI":"10.1201\/b18401","volume-title":"Statistical Learning with Sparsity: The Lasso and Generalizations","author":"T Hastie","year":"2015","unstructured":"Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical Learning with Sparsity: The Lasso and Generalizations. New York: CRC press."},{"key":"9414_CR18","unstructured":"He, W., Yi, G.Y., & Chen, L.-P. (2019). Support vector machine with graphical network structures in features. In Proceedings, Machine Learning and Data Mining in Pattern Recognition, 15th International Conference on Machine Learning and Data Mining, MLDM 2019, (Vol. II pp. 557\u2013570)."},{"key":"9414_CR19","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/BF01908075","volume":"2","author":"L Hubert","year":"1985","unstructured":"Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193\u2013218.","journal-title":"Journal of Classification"},{"key":"9414_CR20","volume-title":"An Introduction to Statistical Learning: With Applications in R","author":"G James","year":"2017","unstructured":"James, G., Witten, D., Hastie, T., & Tibshirani, R. (2017). An Introduction to Statistical Learning: With Applications in R. New York: Springer."},{"key":"9414_CR21","doi-asserted-by":"publisher","first-page":"2691","DOI":"10.1093\/bioinformatics\/bti419","volume":"21","author":"JJ Liu","year":"2005","unstructured":"Liu, J.J., Cutler, G., Li, W., Pan, Z., Peng, S., Hoey, T., Chen, L., & Ling, X.B. (2005). Multiclass cancer classification and biomarker discovery using GA-based algorithms. Bioinformatics, 21, 2691\u20132697.","journal-title":"Bioinformatics"},{"key":"9414_CR22","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1214\/009053606000000281","volume":"34","author":"N Meinshausen","year":"2006","unstructured":"Meinshausen, N., & B\u00fchlmann, P. (2006). High-dimensional graphs and variable selection with the lasso. Annals of Statistics, 34, 1436\u20131462.","journal-title":"Annals of Statistics"},{"key":"9414_CR23","doi-asserted-by":"publisher","first-page":"886","DOI":"10.1016\/j.patcog.2010.10.016","volume":"44","author":"J Miguel Hern\u00e1ndez-Lobato","year":"2011","unstructured":"Miguel Hern\u00e1ndez-Lobato, J., Hern\u00e1ndez-Lobato, D., & Su\u00e1rez, A. (2011). Network-based sparse Bayesian classification. Pattern Recognition, 44, 886\u2013900.","journal-title":"Pattern Recognition"},{"key":"9414_CR24","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1002\/sim.6792","volume":"35","author":"CB Peterson","year":"2015","unstructured":"Peterson, C.B., Stingo, F.C., & Vannucci, M. (2015). Joint Bayesian variable and graph selection for regression models with network-structured predictors. Statistics in Medicine, 35, 1017\u20131031.","journal-title":"Statistics in Medicine"},{"key":"9414_CR25","doi-asserted-by":"publisher","first-page":"1287","DOI":"10.1214\/09-AOS691","volume":"38","author":"P Ravikumar","year":"2010","unstructured":"Ravikumar, P., Wainwright, M.J., & Lafferty, J. (2010). High-Dimensional Ising Model Selection Using \u21131-Regularized Logistic Regression. The Annals of Statistics, 38, 1287\u20131319.","journal-title":"The Annals of Statistics"},{"key":"9414_CR26","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/j.csda.2016.01.011","volume":"99","author":"SE Safo","year":"2016","unstructured":"Safo, S.E., & Ahn, J. (2016). General sparse multi-class linear discriminant analysis. Computational Statistics and Data Analysis, 99, 81\u201390.","journal-title":"Computational Statistics and Data Analysis"},{"key":"9414_CR27","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz, G. (1978). Estimating the dimension of model. Annals of Statistics, 6, 461\u2013464.","journal-title":"Annals of Statistics"},{"key":"9414_CR28","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"R Tibshirani","year":"1996","unstructured":"Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B, 58, 267\u2013288.","journal-title":"Journal of the Royal Statistical Society. Series B"},{"key":"9414_CR29","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1093\/biomet\/asm053","volume":"94","author":"H Wang","year":"2007","unstructured":"Wang, H., Li, R., & Tsai, C. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika, 94, 553\u2013568.","journal-title":"Biometrika"},{"issue":"Suppl 3","key":"9414_CR30","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1186\/s12918-016-0313-0","volume":"10","author":"Y-W Wan","year":"2016","unstructured":"Wan, Y.-W., Allen, G.I., Baker, Y., Yang, E., Ravikumar, P., Anderson, M., & Liu, Z. (2016). XMRF: an R package to fit Markov Networks to high-throughput genetics data. BMC Systems Biology, 10(Suppl 3), 69.","journal-title":"BMC Systems Biology"},{"key":"9414_CR31","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1111\/j.1467-9868.2011.00783.x","volume":"73","author":"DM Witten","year":"2011","unstructured":"Witten, D.M., & Tibshirani, R. (2011). Penalized classification using Fisher\u2019s linear discriminant. Journal of the Royal Statistical Society, Series B, 73, 753\u2013772.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"9414_CR32","first-page":"3813","volume":"16","author":"E Yang","year":"2015","unstructured":"Yang, E., Ravikumar, P., Allen, G.I., & Liu, Z. (2015). Graphical models via univariate exponential family distribution. Journal of Machine Learning Research, 16, 3813\u20133847.","journal-title":"Journal of Machine Learning Research"},{"key":"9414_CR33","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1002\/cjs.11268","volume":"43","author":"GY Yi","year":"2015","unstructured":"Yi, G.Y., Tan, X., & Li, R. (2015). Variable selection and inference procedures for marginal analysis of longitudinal data with missing observations and covariate measurement error. The Canadian Journal of Statistics, 43, 498\u2013518.","journal-title":"The Canadian Journal of Statistics"},{"key":"9414_CR34","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1093\/biomet\/asm018","volume":"94","author":"M Yuan","year":"2007","unstructured":"Yuan, M., & Lin, Y. (2007). Model selection and estimation in the Gaussian graphical model. Biometrika, 94, 19\u201335.","journal-title":"Biometrika"},{"key":"9414_CR35","first-page":"1059","volume":"13","author":"T Zhao","year":"2012","unstructured":"Zhao, T., Liu, H., Roeder, K., Lafferty, J., & Wasserman, L. (2012). The huge package for high-dimensional undirected graph estimation in R. Journal of Machine Learning Research, 13, 1059\u20131062.","journal-title":"Journal of Machine Learning Research"},{"key":"9414_CR36","doi-asserted-by":"publisher","first-page":"1418","DOI":"10.1198\/016214506000000735","volume":"101","author":"H Zou","year":"2006","unstructured":"Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418\u20131429.","journal-title":"Journal of the American Statistical Association"}],"container-title":["Journal of Classification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-022-09414-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00357-022-09414-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-022-09414-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,26]],"date-time":"2024-09-26T08:33:19Z","timestamp":1727339599000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00357-022-09414-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,2]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,11]]}},"alternative-id":["9414"],"URL":"https:\/\/doi.org\/10.1007\/s00357-022-09414-y","relation":{},"ISSN":["0176-4268","1432-1343"],"issn-type":[{"value":"0176-4268","type":"print"},{"value":"1432-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,2]]},"assertion":[{"value":"30 March 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"This research does not contain any studies with human participants or animals performed by any of the authors.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"The author declares no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of Interest"}}]}}