{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:33:03Z","timestamp":1740123183861,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T00:00:00Z","timestamp":1720483200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T00:00:00Z","timestamp":1720483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["SFB 1074 project Z1","SFB 1506","project B6"],"award-info":[{"award-number":["SFB 1074 project Z1","SFB 1506","project B6"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Bildung und Forschung","doi-asserted-by":"publisher","award":["TRANSCAN VI - PMTR-pNET","ID 01KT1901B"],"award-info":[{"award-number":["TRANSCAN VI - PMTR-pNET","ID 01KT1901B"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008977","name":"Universit\u00e4t Ulm","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008977","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Invariant concept classes form the backbone of classification algorithms immune to specific data transformations, ensuring consistent predictions regardless of these alterations. However, this robustness can come at the cost of limited access to the original sample information, potentially impacting generalization performance. This study introduces an addition to these classes\u2014the permutation-invariant linear classifiers. Distinguished by their structural characteristics, permutation-invariant linear classifiers are unaffected by permutations on feature vectors, a property not guaranteed by other non-constant linear classifiers. The study characterizes this new concept class, highlighting its constant capacity, independent of input dimensionality. In practical assessments using linear support vector machines, the permutation-invariant classifiers exhibit superior performance in permutation experiments on artificial datasets and real mutation profiles. Interestingly, they outperform general linear classifiers not only in permutation experiments but also in permutation-free settings, surpassing unconstrained counterparts. Additionally, findings from real mutation profiles support the significance of tumor mutational burden as a biomarker.<\/jats:p>","DOI":"10.1007\/s10994-024-06561-8","type":"journal-article","created":{"date-parts":[[2024,7,9]],"date-time":"2024-07-09T18:09:16Z","timestamp":1720548556000},"page":"7195-7221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Permutation-invariant linear classifiers"],"prefix":"10.1007","volume":"113","author":[{"given":"Ludwig","family":"Lausser","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robin","family":"Szekely","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4759-5254","authenticated-orcid":false,"given":"Hans A.","family":"Kestler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,9]]},"reference":[{"key":"6561_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-098-4","volume-title":"Support vector machines for pattern classification","author":"S Abe","year":"2010","unstructured":"Abe, S. (2010). Support vector machines for pattern classification. Berlin: Springer."},{"key":"6561_CR2","volume-title":"Computational learning theory","author":"MHG Anthony","year":"1997","unstructured":"Anthony, M. H. G., & Biggs, N. (1997). Computational learning theory (Vol. 30). Cambridge: Cambridge University Press."},{"key":"6561_CR3","volume-title":"Pattern recognition and machine learning (information science and statistics)","author":"CM Bishop","year":"2006","unstructured":"Bishop, C. M. (2006). Pattern recognition and machine learning (information science and statistics). Berlin: Springer."},{"issue":"1","key":"6561_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1010933404324","volume":"45","author":"L Breiman","year":"2001","unstructured":"Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5\u201332.","journal-title":"Machine Learning"},{"issue":"2","key":"6561_CR5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1023\/A:1009715923555","volume":"2","author":"CJC Burges","year":"1998","unstructured":"Burges, C. J. C. (1998). A tutorial on support vector machines for pattern recognition. Data Mining and Knowledge Discovery, 2(2), 121\u2013167.","journal-title":"Data Mining and Knowledge Discovery"},{"issue":"1","key":"6561_CR6","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1186\/s13073-017-0424-2","volume":"9","author":"ZR Chalmers","year":"2017","unstructured":"Chalmers, Z. R., Connelly, C. F., Fabrizio, D., et al. (2017). Analysis of 100,000 human cancer genomes reveals the landscape of tumor mutational burden. Genome Medicine, 9(1), 34.","journal-title":"Genome Medicine"},{"key":"6561_CR7","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1109\/PGEC.1965.264137","volume":"3","author":"TM Cover","year":"1965","unstructured":"Cover, T. M. (1965). Geometrical and statistical properties of systems of linear inequalities with applications in pattern recognition. IEEE Transactions on Electronic Computers, 3, 326\u2013334.","journal-title":"IEEE Transactions on Electronic Computers"},{"issue":"2","key":"6561_CR8","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1111\/j.1469-1809.1936.tb02137.x","volume":"7","author":"RA Fisher","year":"1936","unstructured":"Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179\u2013188.","journal-title":"Annals of Eugenics"},{"key":"6561_CR9","doi-asserted-by":"crossref","unstructured":"Fix, E., & Hodges, J. L. (1951). Discriminatory analysis: Nonparametric discrimination: Consistency properties. Tech. Rep. Project 21-49-004, Report Number 4, USAF School of Aviation Medicine, Randolf Field, Texas.","DOI":"10.1037\/e471672008-001"},{"key":"6561_CR10","doi-asserted-by":"crossref","unstructured":"Forbes, S. A., Bindal, N., & Bamford, S., et\u00a0al. (2010). Cosmic: mining complete cancer genomes in the catalogue of somatic mutations in cancer. Nucleic Acids Research 39(suppl_1):D945\u2013D950.","DOI":"10.1093\/nar\/gkq929"},{"issue":"1","key":"6561_CR11","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1006\/jcss.1997.1504","volume":"55","author":"Y Freund","year":"1997","unstructured":"Freund, Y., & Schapire, R. E. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55(1), 119\u2013139.","journal-title":"Journal of Computer and System Sciences"},{"issue":"1","key":"6561_CR12","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/s10994-007-5009-7","volume":"68","author":"B Haasdonk","year":"2007","unstructured":"Haasdonk, B., & Burkhardt, H. (2007). Invariant kernel functions for pattern analysis and machine learning. Machine Learning, 68(1), 35\u201361.","journal-title":"Machine Learning"},{"key":"6561_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21606-5","volume-title":"The elements of statistical learning","author":"T Hastie","year":"2001","unstructured":"Hastie, T., Tibshirani, R., & Friedman, J. H. (2001). The elements of statistical learning. New York: Springer."},{"key":"6561_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511921803","volume-title":"Evaluating learning algorithms: A classification perspective","author":"N Japkowicz","year":"2011","unstructured":"Japkowicz, N., & Shah, M. (2011). Evaluating learning algorithms: A classification perspective. New York: Cambridge University Press."},{"key":"6561_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1904-8","volume-title":"Principal component analysis","author":"I Jolliffe","year":"1986","unstructured":"Jolliffe, I. (1986). Principal component analysis. New York: Springer."},{"issue":"2","key":"6561_CR16","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s00180-011-0243-7","volume":"26","author":"HA Kestler","year":"2011","unstructured":"Kestler, H. A., Lausser, L., Lindner, W., et al. (2011). On the fusion of threshold classifiers for categorization and dimensionality reduction. Computational Statistics, 26(2), 321\u2013340.","journal-title":"Computational Statistics"},{"issue":"3","key":"6561_CR17","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/s41060-018-0095-0","volume":"6","author":"JM Kraus","year":"2018","unstructured":"Kraus, J. M., Lausser, L., Kuhn, P., et al. (2018). Big data and precision medicine: Challenges and strategies with healthcare data. International Journal of Data Science and Analytics, 6(3), 241\u2013249.","journal-title":"International Journal of Data Science and Analytics"},{"issue":"1","key":"6561_CR18","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1007\/s10044-002-0173-7","volume":"6","author":"LI Kuncheva","year":"2003","unstructured":"Kuncheva, L. I., Whitaker, C. J., Shipp, C. A., et al. (2003). Limits on the majority vote accuracy in classifier fusion. Pattern Analysis & Applications, 6(1), 22\u201331.","journal-title":"Pattern Analysis & Applications"},{"key":"6561_CR19","doi-asserted-by":"crossref","unstructured":"Lausser, L., & Kestler, H. A. (2010). Robustness analysis of eleven linear classifiers in extremely high-dimensional feature spaces. In: Schwenker, F., Gayar, N. E. (Eds.), Artificial neural networks in pattern recognition (Vol LNAI 5998, pp. 72\u201383).","DOI":"10.1007\/978-3-642-12159-3_7"},{"key":"6561_CR20","doi-asserted-by":"crossref","unstructured":"Lausser, L., & Kestler, H. A. (2014). Fold change classifiers for the analysis for the analysis of gene expression profiles. In: Gaul, W., Geyer-Schulz, A., Baba, Y., et\u00a0al. (Eds.), proceedings volume of the German\/Japanese workshops in 2010 (Karlsruhe) and 2012 (Kyoto), studies in classification, data analysis, and knowledge organization (pp. 193\u2013202).","DOI":"10.1007\/978-3-319-01264-3_17"},{"issue":"1","key":"6561_CR23","doi-asserted-by":"publisher","first-page":"11746","DOI":"10.1038\/s41598-019-48150-z","volume":"9","author":"L Lausser","year":"2019","unstructured":"Lausser, L., Sch\u00e4fer, L. M., Schirra, L. R., et al. (2019). Assessing phenotype order in molecular data. Scientific Reports, 9(1), 11746.","journal-title":"Scientific Reports"},{"issue":"4","key":"6561_CR21","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1007\/s11634-016-0277-3","volume":"12","author":"L Lausser","year":"2018","unstructured":"Lausser, L., Schmid, F., Schirra, L. R., et al. (2018). Rank-based classifiers for extremely high-dimensional gene expression data. Advances in Data Analysis and Classification, 12(4), 917\u2013936.","journal-title":"Advances in Data Analysis and Classification"},{"issue":"163","key":"6561_CR24","doi-asserted-by":"publisher","first-page":"20190612","DOI":"10.1098\/rsif.2019.0612","volume":"17","author":"L Lausser","year":"2020","unstructured":"Lausser, L., Szekely, R., Klimmek, A., et al. (2020). Constraining classifiers in molecular analysis: Invariance and robustness. Journal of the Royal Society Interface, 17(163), 20190612.","journal-title":"Journal of the Royal Society Interface"},{"issue":"2","key":"6561_CR22","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1007\/s11063-017-9706-3","volume":"48","author":"L Lausser","year":"2018","unstructured":"Lausser, L., Szekely, R., Schirra, L. R., et al. (2018). The influence of multi-class feature selection on the prediction of diagnostic phenotypes. Neural Processing Letters, 48(2), 863\u2013880.","journal-title":"Neural Processing Letters"},{"key":"6561_CR25","doi-asserted-by":"publisher","first-page":"7776","DOI":"10.1109\/ACCESS.2017.2696365","volume":"5","author":"A L\u2019Heureux","year":"2017","unstructured":"L\u2019Heureux, A., Grolinger, K., Elyamany, H. F., et al. (2017). Machine learning with big data: Challenges and approaches. IEEE Access, 5, 7776\u20137797.","journal-title":"IEEE Access"},{"key":"6561_CR26","unstructured":"Meyer, D., Dimitriadou, E., & Hornik, K., et\u00a0al. (2020). e1071: Misc functions of the department of statistics, probability theory group (Formerly: E1071), TU Wien. https:\/\/CRAN.R-project.org\/package=e1071, r package version 1.7-4."},{"key":"6561_CR27","volume-title":"Perceptrons: An introduction to computational geometry","author":"M Minsky","year":"1988","unstructured":"Minsky, M., & Papert, S. A. (1988). Perceptrons: An introduction to computational geometry. Cambridge: MIT Press."},{"issue":"5","key":"6561_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v046.i05","volume":"46","author":"C M\u00fcssel","year":"2012","unstructured":"M\u00fcssel, C., Lausser, L., Maucher, M., et al. (2012). Multi-objective parameter selection for classifiers. Journal of Statistical Software, 46(5), 1\u201327.","journal-title":"Journal of Statistical Software"},{"issue":"10","key":"6561_CR29","doi-asserted-by":"publisher","first-page":"1345","DOI":"10.1109\/TKDE.2009.191","volume":"22","author":"SJ Pan","year":"2010","unstructured":"Pan, S. J., & Yang, Q. (2010). A survey on transfer learning. IEEE Transactions on Knowledge and Data Engineering, 22(10), 1345\u20131359.","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"issue":"6","key":"6561_CR30","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1037\/h0042519","volume":"65","author":"F Rosenblatt","year":"1958","unstructured":"Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386.","journal-title":"Psychological Review"},{"issue":"2","key":"6561_CR31","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1038\/s41588-018-0312-8","volume":"51","author":"RM Samstein","year":"2019","unstructured":"Samstein, R. M., Lee, C. H., Shoushtari, A. N., et al. (2019). Tumor mutational load predicts survival after immunotherapy across multiple cancer types. Nature Genetics, 51(2), 202\u2013206.","journal-title":"Nature Genetics"},{"key":"6561_CR32","doi-asserted-by":"crossref","unstructured":"Schmid, F., Lausser, L., & Kestler, H. A. (2014). Linear contrast classifiers in high-dimensional spaces. In El\u00a0Gayar, N., Schwenker, F., Suen, C. (Eds.), IAPR workshop on artificial neural networks in pattern recognition (pp. 141\u2013152).","DOI":"10.1007\/978-3-319-11656-3_13"},{"issue":"105","key":"6561_CR33","first-page":"524","volume":"97","author":"D Singh","year":"2020","unstructured":"Singh, D., & Singh, B. (2020). Investigating the impact of data normalization on classification performance. Applied Soft Computing, 97(105), 524.","journal-title":"Applied Soft Computing"},{"issue":"8","key":"6561_CR34","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1002\/gcc.22733","volume":"58","author":"A Stenzinger","year":"2019","unstructured":"Stenzinger, A., Allen, J. D., Maas, J., et al. (2019). Tumor mutational burden standardization initiatives: Recommendations for consistent tumor mutational burden assessment in clinical samples to guide immunotherapy treatment decisions. Genes, Chromosomes and Cancer, 58(8), 578\u2013588.","journal-title":"Genes, Chromosomes and Cancer"},{"key":"6561_CR35","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/3717.001.0001","volume-title":"Independent component analysis: A tutorial introduction","author":"J Stone","year":"2004","unstructured":"Stone, J. (2004). Independent component analysis: A tutorial introduction. Cambridge: MIT Press."},{"key":"6561_CR36","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/j.ebiom.2016.08.037","volume":"12","author":"S Taudien","year":"2016","unstructured":"Taudien, S., Lausser, L., Giamarellos-Bourboulis, E. J., et al. (2016). Genetic factors of the disease course after sepsis: Rare deleterious variants are predictive. EBioMedicine, 12, 227\u2013238.","journal-title":"EBioMedicine"},{"key":"6561_CR37","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1515\/jib-2015-281","volume":"12","author":"E Valente","year":"2015","unstructured":"Valente, E., & Rocha, M. (2015). Integrating data from heterogeneous DNA microarray platforms. Journal of Integrative Bioinformatics, 12, 281.","journal-title":"Journal of Integrative Bioinformatics"},{"issue":"11","key":"6561_CR38","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1145\/1968.1972","volume":"27","author":"LG Valiant","year":"1984","unstructured":"Valiant, L. G. (1984). A theory of the learnable. Communications of the ACM, 27(11), 1134\u20131142.","journal-title":"Communications of the ACM"},{"key":"6561_CR39","volume-title":"Statistical learning theory","author":"V Vapnik","year":"1998","unstructured":"Vapnik, V. (1998). Statistical learning theory. New York: Wiley."}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06561-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-024-06561-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06561-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T21:06:59Z","timestamp":1729199219000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-024-06561-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,9]]},"references-count":39,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["6561"],"URL":"https:\/\/doi.org\/10.1007\/s10994-024-06561-8","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"type":"print","value":"0885-6125"},{"type":"electronic","value":"1573-0565"}],"subject":[],"published":{"date-parts":[[2024,7,9]]},"assertion":[{"value":"30 November 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 January 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare not conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not applicable.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}]}}