{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:57:06Z","timestamp":1778086626646,"version":"3.51.4"},"reference-count":95,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Analyzing large volumes of high-dimensional data poses significant challenges. Dimensionality reduction aims to reveal the most prominent properties of data by embedding them into a low-dimensional representation. Spectral dimensionality reduction methods using kernel matrices have been proven to yield optimal results. Online versions of those methods are desirable to incrementally project new data without recomputing the whole embedding from the complete dataset. In addition, integrating different spectral methods may have a synergistic effect. This paper presents an online dimensionality reduction method based on deep neural networks that integrates embeddings optimized by statistical approximation of neighborhoods and induced by different spectral methods through stacking ensemble learning. In particular, the proposed method first applies a self-supervised stage in order to train a set of deep encoders based on the embeddings induced by different spectral methods applied to a given input dataset. Those basis encoders are optimized and then integrated through a metamodel constituted by a fully connected network. A supervised and an unsupervised approach have been designed depending on whether the final aim is to enforce topological preservation or cluster induction. The proposed method has been experimentally validated on well-known image datasets and compared to some of the most relevant dimensionality reduction techniques by using widely-used quality measures.<\/jats:p>","DOI":"10.1007\/s10994-024-06715-8","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T11:07:01Z","timestamp":1743160021000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Online dimensionality reduction through stacked generalization of spectral methods with deep networks"],"prefix":"10.1007","volume":"114","author":[{"given":"Juan Carlos","family":"Alvarado-P\u00e9rez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel Angel","family":"Garcia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dom\u00e8nec","family":"Puig","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"6715_CR1","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.neucom.2014.11.078","volume":"169","author":"F Aiolli","year":"2015","unstructured":"Aiolli, F., & Donini, M. (2015). EasyMKL: A scalable multiple kernel learning algorithm. Neurocomputing, 169, 215\u2013224.","journal-title":"Neurocomputing"},{"issue":"7","key":"6715_CR2","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.3390\/sym14071282","volume":"14","author":"M Alswaitti","year":"2022","unstructured":"Alswaitti, M., Siddique, K., Jiang, S., Alomoush, W., & Alrosan, A. (2022). Dimensionality reduction, modelling, and optimization of multivariate problems based on machine learning. Symmetry, 14(7), 1282.","journal-title":"Symmetry"},{"key":"6715_CR3","unstructured":"Amid, E., & Warmuth, M.K. (2019). TriMap: Large-scale dimensionality reduction using triplets. arXiv preprint arXiv:1910.00204."},{"key":"6715_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804779","volume-title":"Bayesian Reasoning and Machine Learning","author":"D Barber","year":"2012","unstructured":"Barber, D. (2012). Bayesian Reasoning and Machine Learning. United Kingdom: Cambridge University Press."},{"key":"6715_CR5","doi-asserted-by":"crossref","unstructured":"Basalaj, W. (1999). Incremental multidimensional scaling method for database visualization. In Visual data exploration and analysis VI (vol. 3643, pp. 149\u2013158). International Society for Optics and Photonics.","DOI":"10.1117\/12.342830"},{"key":"6715_CR6","unstructured":"Belanche\u00a0Mu\u00f1oz, L. A. (2013). Developments in kernel design. In ESANN 2013 proceedings: European symposium on artificial neural networks, computational intelligence and machine learning: Bruges (Belgium) (pp. 369\u2013378)."},{"issue":"6","key":"6715_CR7","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1162\/089976603321780317","volume":"15","author":"M Belkin","year":"2003","unstructured":"Belkin, M., & Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation, 15(6), 1373\u20131396.","journal-title":"Neural Computation"},{"issue":"1","key":"6715_CR8","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1162\/089976698300017953","volume":"10","author":"CM Bishop","year":"1998","unstructured":"Bishop, C. M., Svens\u00e9n, M., & Williams, C. K. (1998). GTM: The generative topographic mapping. Neural Computation, 10(1), 215\u2013234.","journal-title":"Neural Computation"},{"issue":"1","key":"6715_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10994-022-06261-1","volume":"112","author":"A Bj\u00f6rklund","year":"2023","unstructured":"Bj\u00f6rklund, A., M\u00e4kel\u00e4, J., & Puolam\u00e4ki, K. (2023). SLISEMAP: Supervised dimensionality reduction through local explanations. Machine Learning, 112(1), 1\u201343.","journal-title":"Machine Learning"},{"key":"6715_CR10","unstructured":"Blockeel, H., De\u00a0Raedt, L., & Ramon, J. (2000). Top-down induction of clustering trees. arXiv preprint cs\/0011032."},{"key":"6715_CR11","volume-title":"Modern multidimensional scaling: Theory and applications","author":"I Borg","year":"2005","unstructured":"Borg, I., & Groenen, P. J. (2005). Modern multidimensional scaling: Theory and applications. Science & Business Media: Springer."},{"issue":"1","key":"6715_CR12","doi-asserted-by":"crossref","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":"04","key":"6715_CR13","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1142\/S0219530506000838","volume":"4","author":"C Carmeli","year":"2006","unstructured":"Carmeli, C., De Vito, E., & Toigo, A. (2006). Vector valued reproducing kernel Hilbert spaces of integrable functions and mercer theorem. Analysis and Applications, 4(04), 377\u2013408.","journal-title":"Analysis and Applications"},{"key":"6715_CR14","doi-asserted-by":"crossref","unstructured":"Chavula, C., & Suleman, H. (2017). Morphological cluster induction of bantu words using a weighted similarity measure. In Proceedings of the South African institute of computer scientists and information technologists (pp. 1\u20139).","DOI":"10.1145\/3129416.3129453"},{"issue":"6","key":"6715_CR15","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1109\/TIP.2007.896668","volume":"16","author":"T-J Chin","year":"2007","unstructured":"Chin, T.-J., & Suter, D. (2007). Incremental kernel principal component analysis. IEEE Transactions on Image Processing, 16(6), 1662\u20131674.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"8","key":"6715_CR16","doi-asserted-by":"crossref","first-page":"1690","DOI":"10.1073\/pnas.1800256115","volume":"115","author":"D Denisko","year":"2018","unstructured":"Denisko, D., & Hoffman, M. M. (2018). Classification and interaction in random forests. Proceedings of the National Academy of Sciences, 115(8), 1690\u20131692.","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"6715_CR17","doi-asserted-by":"crossref","DOI":"10.1201\/9780429246593","volume-title":"An introduction to the bootstrap","author":"B Efron","year":"1994","unstructured":"Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. CRC Press."},{"key":"6715_CR18","doi-asserted-by":"crossref","first-page":"103618","DOI":"10.1016\/j.scs.2021.103618","volume":"78","author":"E Eskandarnia","year":"2022","unstructured":"Eskandarnia, E., Al-Ammal, H. M., & Ksantini, R. (2022). An embedded deep-clustering-based load profiling framework. Sustainable Cities and Society, 78, 103618.","journal-title":"Sustainable Cities and Society"},{"key":"6715_CR19","doi-asserted-by":"crossref","first-page":"114181","DOI":"10.1016\/j.cma.2021.114181","volume":"388","author":"S Fresca","year":"2022","unstructured":"Fresca, S., & Manzoni, A. (2022). POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDES by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering, 388, 114181.","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"1","key":"6715_CR20","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. https:\/\/doi.org\/10.1006\/jcss.1997.1504","journal-title":"Journal of Computer and System Sciences"},{"key":"6715_CR21","first-page":"2211","volume":"12","author":"M G\u00f6nen","year":"2011","unstructured":"G\u00f6nen, M., & Alpayd\u0131n, E. (2011). Multiple kernel learning algorithms. The Journal of Machine Learning Research, 12, 2211\u20132268.","journal-title":"The Journal of Machine Learning Research"},{"key":"6715_CR22","first-page":"2181","volume":"12","author":"M G\u00f6nen","year":"2011","unstructured":"G\u00f6nen, M., Alpayd\u0131n, E., & Bach, F. (2011). Multiple kernel learning algorithms. The Journal of Machine Learning Research, 12, 2181\u20132238.","journal-title":"The Journal of Machine Learning Research"},{"key":"6715_CR23","doi-asserted-by":"crossref","first-page":"113079","DOI":"10.1016\/j.eswa.2019.113079","volume":"144","author":"J Gou","year":"2020","unstructured":"Gou, J., Yang, Y., Yi, Z., Lv, J., Mao, Q., & Zhan, Y. (2020). Discriminative globality and locality preserving graph embedding for dimensionality reduction. Expert Systems with Applications, 144, 113079.","journal-title":"Expert Systems with Applications"},{"key":"6715_CR24","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.future.2021.09.044","volume":"128","author":"T Guo","year":"2022","unstructured":"Guo, T., Yu, K., Aloqaily, M., & Wan, S. (2022). Constructing a prior-dependent graph for data clustering and dimension reduction in the edge of AIoT. Future Generation Computer Systems, 128, 381\u2013394.","journal-title":"Future Generation Computer Systems"},{"key":"6715_CR25","unstructured":"Hallgren, F., & Northrop, P. (2018). Incremental kernel PCA and the Nystrom method. arXiv preprint arXiv:1802.00043 (2018)"},{"key":"6715_CR26","doi-asserted-by":"publisher","unstructured":"Ham, J., Lee, D., Mika, S., & Sch\u00f6lkopf, B. (2004). A kernel view of the dimensionality reduction of manifolds.[SPACE]https:\/\/doi.org\/10.1145\/1015330.1015417","DOI":"10.1145\/1015330.1015417"},{"key":"6715_CR27","doi-asserted-by":"crossref","unstructured":"Ham, J., Lee, D. D., Mika, S., & Sch\u00f6lkopf, B. (2004). A kernel view of the dimensionality reduction of manifolds. In Proceedings of the twenty-first international conference on machine learning (p. 47). ACM.","DOI":"10.1145\/1015330.1015417"},{"key":"6715_CR28","unstructured":"Hazelzet, J. (2019). Images of LEGO bricks dataset. https:\/\/www.kaggle.com\/joosthazelzet\/lego-brick-images"},{"key":"6715_CR29","unstructured":"Hinton, G. E., & Roweis, S. T. (2002). Stochastic neighbor embedding. In Advances in neural information processing systems (pp. 833\u2013840)."},{"key":"6715_CR30","doi-asserted-by":"publisher","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"GE Hinton","year":"2006","unstructured":"Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science (New York), 313, 504\u2013507. https:\/\/doi.org\/10.1126\/science.1127647","journal-title":"Science (New York)"},{"issue":"5786","key":"6715_CR31","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1126\/science.1127647","volume":"313","author":"GE Hinton","year":"2006","unstructured":"Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504\u2013507.","journal-title":"Science"},{"key":"6715_CR32","unstructured":"Hong, D., Zhang, B., Li, X., Li, Y., Li, C., Yao, J., Yokoya, N., Li, H., Jia, X., & Plaza, A., et al. (2023). Spectralgpt: Spectral foundation model. arXiv preprint arXiv:2311.07113"},{"issue":"4","key":"6715_CR33","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1109\/TIP.2018.2878958","volume":"28","author":"D Hong","year":"2018","unstructured":"Hong, D., Yokoya, N., Chanussot, J., & Zhu, X. X. (2018). An augmented linear mixing model to address spectral variability for hyperspectral unmixing. IEEE Transactions on Image Processing, 28(4), 1923\u20131938.","journal-title":"IEEE Transactions on Image Processing"},{"issue":"6","key":"6715_CR34","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1037\/h0071325","volume":"24","author":"H Hotelling","year":"1933","unstructured":"Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24(6), 417\u2013441. https:\/\/doi.org\/10.1037\/h0071325","journal-title":"Journal of Educational Psychology"},{"key":"6715_CR35","unstructured":"Howard, J., et al. (2020). Imagenette. 2. https:\/\/github.com\/fastai\/imagenette"},{"issue":"3","key":"6715_CR36","doi-asserted-by":"crossref","first-page":"1678","DOI":"10.1287\/mnsc.2021.4020","volume":"68","author":"D Huang","year":"2022","unstructured":"Huang, D., Jiang, F., Li, K., Tong, G., & Zhou, G. (2022). Scaled PCA: A new approach to dimension reduction. Management Science, 68(3), 1678\u20131695.","journal-title":"Management Science"},{"issue":"1","key":"6715_CR37","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1214\/aoms\/1177703732","volume":"35","author":"PJ Huber","year":"1964","unstructured":"Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73\u2013101.","journal-title":"Annals of Mathematical Statistics"},{"key":"6715_CR38","unstructured":"Hull, J. J. (2023). Hand-written digits USPS dataset. Accessed on November 27. https:\/\/www.kaggle.com\/datasets\/andrewmvd\/medical-mnist\/data"},{"issue":"5","key":"6715_CR39","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/34.291440","volume":"16","author":"JJ Hull","year":"1994","unstructured":"Hull, J. J. (1994). A database for handwritten text recognition research. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(5), 550\u2013554.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"6715_CR40","doi-asserted-by":"crossref","unstructured":"Izenman, A. J. (2013). Linear discriminant analysis. In Modern multivariate statistical techniques (pp. 237\u2013280). Springer.","DOI":"10.1007\/978-0-387-78189-1_8"},{"key":"6715_CR41","doi-asserted-by":"crossref","first-page":"108817","DOI":"10.1016\/j.sigpro.2022.108817","volume":"204","author":"L Jiang","year":"2023","unstructured":"Jiang, L., Fang, X., Sun, W., Han, N., & Teng, S. (2023). Low-rank constraint based dual projections learning for dimensionality reduction. Signal Processing, 204, 108817.","journal-title":"Signal Processing"},{"issue":"16","key":"6715_CR42","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1016\/j.patrec.2009.08.005","volume":"30","author":"P Jia","year":"2009","unstructured":"Jia, P., Yin, J., Huang, X., & Hu, D. (2009). Incremental Laplacian eigenmaps by preserving adjacent information between data points. Pattern Recognition Letters, 30(16), 1457\u20131463.","journal-title":"Pattern Recognition Letters"},{"issue":"5","key":"6715_CR43","doi-asserted-by":"crossref","first-page":"43","DOI":"10.5121\/ijdkp.2012.2504","volume":"2","author":"P Joshi","year":"2012","unstructured":"Joshi, P., & Kulkarni, P. (2012). Incremental learning: Areas and methods-a survey. International Journal of Data Mining & Knowledge Management Process, 2(5), 43.","journal-title":"International Journal of Data Mining & Knowledge Management Process"},{"key":"6715_CR44","unstructured":"Kingma, D. P., & Ba, J. (2014). Adam: A method for stochastic optimization. cite arxiv:1412.6980Comment: Published as a conference paper at the 3rd International Conference for Learning Representations, San Diego, 2015. http:\/\/arxiv.org\/abs\/1412.6980"},{"key":"6715_CR45","unstructured":"Kingma, D. P., & Welling, M. (2013). Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114."},{"issue":"4","key":"6715_CR46","first-page":"179","volume":"9","author":"T Kohonen","year":"2001","unstructured":"Kohonen, T. (2001). Self-organizing maps of massive databases. International Journal of Engineering Intelligent Systems for Electrical Engineering and Communications, 9(4), 179\u2013186.","journal-title":"International Journal of Engineering Intelligent Systems for Electrical Engineering and Communications"},{"key":"6715_CR47","doi-asserted-by":"crossref","unstructured":"Kouropteva, O., Okun, O., & Pietik\u00e4inen, M. (2005). Incremental locally linear embedding algorithm. In Scandinavian conference on image analysis (pp. 521\u2013530). Springer.","DOI":"10.1007\/11499145_53"},{"key":"6715_CR48","doi-asserted-by":"crossref","unstructured":"Lauriola, I., Polato, M., & Aiolli, F. (2017). Radius-margin ratio optimization for dot-product Boolean kernel learning. In International conference on artificial neural networks.","DOI":"10.1007\/978-3-319-68612-7_21"},{"key":"6715_CR49","unstructured":"Lauriola, I., Polato, M., & Aiolli, F. (2018). The minimum effort maximum output principle applied to multiple kernel learning. In European symposium on artificial neural networks."},{"key":"6715_CR50","unstructured":"Lee, J. A., Archambeau, C., & Verleysen, M., et al. (2003). Locally linear embedding versus isotop. In ESANN (pp. 527\u2013534)."},{"key":"6715_CR51","doi-asserted-by":"crossref","first-page":"246","DOI":"10.1016\/j.neucom.2014.12.095","volume":"169","author":"JA Lee","year":"2015","unstructured":"Lee, J. A., Peluffo-Ordonez, D. H., & Verleysen, M. (2015). Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing, 169, 246\u2013261.","journal-title":"Neurocomputing"},{"key":"6715_CR52","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.neucom.2012.12.036","volume":"112","author":"JA Lee","year":"2013","unstructured":"Lee, J. A., Renard, E., Bernard, G., Dupont, P., & Verleysen, M. (2013). Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation. Neurocomputing, 112, 92\u2013108.","journal-title":"Neurocomputing"},{"key":"6715_CR53","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-39351-3","volume-title":"Nonlinear Dimensionality Reduction","author":"JA Lee","year":"2007","unstructured":"Lee, J. A., & Verleysen, M. (2007). Nonlinear Dimensionality Reduction. Science & Business Media: Springer."},{"issue":"7","key":"6715_CR54","doi-asserted-by":"crossref","first-page":"1431","DOI":"10.1016\/j.neucom.2008.12.017","volume":"72","author":"JA Lee","year":"2009","unstructured":"Lee, J. A., & Verleysen, M. (2009). Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing, 72(7), 1431\u20131443.","journal-title":"Neurocomputing"},{"issue":"1","key":"6715_CR55","doi-asserted-by":"crossref","first-page":"20028","DOI":"10.1038\/s41598-021-99003-7","volume":"11","author":"Z Luo","year":"2021","unstructured":"Luo, Z., Xu, C., Zhang, Z., & Jin, W. (2021). A topology-preserving dimensionality reduction method for single-cell RNA-SEQ data using graph autoencoder. Scientific Reports, 11(1), 20028.","journal-title":"Scientific Reports"},{"key":"6715_CR56","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/978-3-642-21735-7_7","volume-title":"Artificial neural networks and machine learning\u2013ICANN 2011","author":"J Masci","year":"2011","unstructured":"Masci, J., Meier, U., Cire\u015fan, D., & Schmidhuber, J. (2011). Stacked convolutional auto-encoders for hierarchical feature extraction. In T. Honkela, W. Duch, M. Girolami, & S. Kaski (Eds.), Artificial neural networks and machine learning\u2013ICANN 2011 (pp. 52\u201359). Berlin: Springer."},{"key":"6715_CR57","doi-asserted-by":"crossref","unstructured":"McInnes, L., Healy, J., & Melville, J. (2018). UMAP: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426","DOI":"10.21105\/joss.00861"},{"key":"6715_CR58","doi-asserted-by":"crossref","unstructured":"Menaga, D., & Revathi, S. (2021). Probabilistic principal component analysis (PPCA) based dimensionality reduction and deep learning for cancer classification. In Intelligent computing and applications: Proceedings of ICICA 2019 (pp. 353\u2013368). Springer.","DOI":"10.1007\/978-981-15-5566-4_31"},{"key":"6715_CR59","unstructured":"Misra, D. (2020). Mish: A self regularized non-monotonic neural activation function. In The British machine vision conference."},{"key":"6715_CR60","doi-asserted-by":"publisher","unstructured":"Molina, L. C., Belanche, L., & Nebot, A. (2002). Feature selection algorithms: a survey and experimental evaluation. In 2002 IEEE international conference on data mining, 2002. Proceedings (pp. 306\u2013313). https:\/\/doi.org\/10.1109\/ICDM.2002.1183917","DOI":"10.1109\/ICDM.2002.1183917"},{"key":"6715_CR61","doi-asserted-by":"crossref","unstructured":"Narayan, A., Berger, B., & Cho, H. (2020). Density-preserving data visualization unveils dynamic patterns of single-cell transcriptomic variability. bioRxiv, 2020-05.","DOI":"10.1101\/2020.05.12.077776"},{"key":"6715_CR62","unstructured":"Nene, S. A., Nayar, S. K., & Murase, H. (1996). Columbia object image library (coil-20). Department of Computer Science, Columbia University, New York. http:\/\/www. cs. columbia. edu\/CAVE\/coil-20. html 62"},{"key":"6715_CR63","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.ins.2021.04.066","volume":"570","author":"O \u00d6zdenizci","year":"2021","unstructured":"\u00d6zdenizci, O., & Erdo\u011fmu\u015f, D. (2021). Stochastic mutual information gradient estimation for dimensionality reduction networks. Information Sciences, 570, 298\u2013305.","journal-title":"Information Sciences"},{"key":"6715_CR64","doi-asserted-by":"crossref","first-page":"104461","DOI":"10.1016\/j.imavis.2022.104461","volume":"123","author":"G Pai","year":"2022","unstructured":"Pai, G., Bronstein, A., Talmon, R., & Kimmel, R. (2022). Deep isometric maps. Image and Vision Computing, 123, 104461.","journal-title":"Image and Vision Computing"},{"key":"6715_CR65","unstructured":"Polanco\u00a0Lozano, A. (2017). Medical MNIST. Accessed on November 27, 2023. https:\/\/www.kaggle.com\/datasets\/andrewmvd\/medical-mnist\/data"},{"key":"6715_CR66","unstructured":"Preksha, A. (2023). Indian sign language. Accessed on November 27. https:\/\/www.kaggle.com\/datasets\/prekshapalva\/indian-sign-language"},{"key":"6715_CR67","doi-asserted-by":"crossref","first-page":"115055","DOI":"10.1016\/j.eswa.2021.115055","volume":"180","author":"H Qu","year":"2021","unstructured":"Qu, H., Li, L., Li, Z., & Zheng, J. (2021). Supervised discriminant Isomap with maximum margin graph regularization for dimensionality reduction. Expert Systems with Applications, 180, 115055.","journal-title":"Expert Systems with Applications"},{"key":"6715_CR68","unstructured":"Radford, A., Metz, L., & Chintala, S. (2015). Unsupervised representation learning with deep convolutional generative adversarial networks."},{"key":"6715_CR69","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1214\/aoms\/1177729586","volume":"22","author":"H Robbins","year":"1951","unstructured":"Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 22, 400\u2013407.","journal-title":"The Annals of Mathematical Statistics"},{"key":"6715_CR70","unstructured":"Rosenberg, A., & Hirschberg, J. (2007). V-measure: A conditional entropy-based external cluster evaluation measure. In Proceedings of the 2007 joint conference on empirical methods in natural language processing and computational natural language learning (EMNLP-CoNLL) (pp. 410\u2013420)."},{"issue":"5500","key":"6715_CR71","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"ST Roweis","year":"2000","unstructured":"Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323\u20132326.","journal-title":"Science"},{"issue":"11","key":"6715_CR72","first-page":"2881","volume":"33","author":"T Sainburg","year":"2021","unstructured":"Sainburg, T., McInnes, L., & Gentner, T. Q. (2021). Parametric UMAP embeddings for representation and semisupervised learning. Neural Computation, 33(11), 2881\u20132907.","journal-title":"Neural Computation"},{"key":"6715_CR73","doi-asserted-by":"crossref","first-page":"103802","DOI":"10.1016\/j.imavis.2019.08.006","volume":"90","author":"RK Sanodiya","year":"2019","unstructured":"Sanodiya, R. K., & Mathew, J. (2019). A novel unsupervised globality-locality preserving projections in transfer learning. Image and Vision Computing, 90, 103802.","journal-title":"Image and Vision Computing"},{"key":"6715_CR74","doi-asserted-by":"publisher","first-page":"55","DOI":"10.4236\/ajcm.2014.42006","volume":"04","author":"A Sarveniazi","year":"2014","unstructured":"Sarveniazi, A. (2014). An actual survey of dimensionality reduction. American Journal of Computational Mathematics, 04, 55\u201372. https:\/\/doi.org\/10.4236\/ajcm.2014.42006","journal-title":"American Journal of Computational Mathematics"},{"issue":"5","key":"6715_CR75","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","volume":"10","author":"B Sch\u00f6lkopf","year":"1998","unstructured":"Sch\u00f6lkopf, B., Smola, A. J., & M\u00fcller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299\u20131319.","journal-title":"Neural Computation"},{"key":"6715_CR76","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, 379\u2013423.","journal-title":"The Bell System Technical Journal"},{"key":"6715_CR77","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.apm.2022.09.034","volume":"114","author":"K Shinde","year":"2023","unstructured":"Shinde, K., Itier, V., Mennesson, J., Vasiukov, D., & Shakoor, M. (2023). Dimensionality reduction through convolutional autoencoders for fracture patterns prediction. Applied Mathematical Modelling, 114, 94\u2013113.","journal-title":"Applied Mathematical Modelling"},{"key":"6715_CR78","doi-asserted-by":"publisher","unstructured":"Skocaj, D., & Leonardis, A. (2003). Weighted and robust incremental method for subspace learning. In Proceedings ninth IEEE international conference on computer vision (pp 1494\u201315012). https:\/\/doi.org\/10.1109\/ICCV.2003.1238667","DOI":"10.1109\/ICCV.2003.1238667"},{"key":"6715_CR79","unstructured":"Sovrasov, V. (2018). PTFLOPS: A flops counting tool for neural networks in pytorch framework. https:\/\/github.com\/sovrasov\/flops-counter.pytorch"},{"key":"6715_CR80","doi-asserted-by":"crossref","first-page":"201","DOI":"10.2307\/1412107","volume":"15","author":"C Spearman","year":"1904","unstructured":"Spearman, C. (1904). \u201cGeneral intelligence,\u2019\u2019 objectively determined and measured. American Journal of Psychology, 15, 201\u2013293.","journal-title":"American Journal of Psychology"},{"key":"6715_CR81","doi-asserted-by":"crossref","unstructured":"Strobl, E. V., & Visweswaran, S. (2013). Deep multiple kernel learning. In 2013 12th international conference on machine learning and applications (vol. 1, pp. 414\u2013417).","DOI":"10.1109\/ICMLA.2013.84"},{"issue":"4","key":"6715_CR82","first-page":"3","volume":"100","author":"K Teknomo","year":"2006","unstructured":"Teknomo, K. (2006). K-means clustering tutorial. Medicine, 100(4), 3.","journal-title":"Medicine"},{"issue":"5500","key":"6715_CR83","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"JB Tenenbaum","year":"2000","unstructured":"Tenenbaum, J. B., Silva, V., & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319.","journal-title":"Science"},{"key":"6715_CR84","doi-asserted-by":"crossref","unstructured":"Tian, F., Gao, B., Cui, Q., Chen, E., & Liu, T. -Y. (2014). Learning deep representations for graph clustering. In Proceedings of the AAAI conference on artificial intelligence (vol. 28).","DOI":"10.1609\/aaai.v28i1.8916"},{"key":"6715_CR85","unstructured":"Venna, J., & Kaski, S.: Nonlinear dimensionality reduction as information retrieval. In Artificial intelligence and statistics (pp. 572\u2013579)."},{"key":"6715_CR86","doi-asserted-by":"publisher","DOI":"10.1007\/s40745-020-00253-5","author":"Q Wang","year":"2020","unstructured":"Wang, Q., Ma, Y., Zhao, K., & Tian, Y. (2020). A comprehensive survey of loss functions in machine learning. Annals of Data Science. https:\/\/doi.org\/10.1007\/s40745-020-00253-5","journal-title":"Annals of Data Science"},{"key":"6715_CR87","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.asoc.2018.02.004","volume":"66","author":"L Wang","year":"2018","unstructured":"Wang, L., Wang, Z., Qu, H., & Liu, S. (2018). Optimal forecast combination based on neural networks for time series forecasting. Applied Soft Computing, 66, 1\u201317.","journal-title":"Applied Soft Computing"},{"key":"6715_CR88","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1007\/978-3-540-45080-1_122","volume-title":"Intelligent data engineering and automated learning","author":"J Weng","year":"2003","unstructured":"Weng, J., Zhang, Y., & Hwang, W.-S. (2003). A fast algorithm for incremental principal component analysis. In J. Liu, Y.-M. Cheung, & H. Yin (Eds.), Intelligent data engineering and automated learning (pp. 876\u2013881). Berlin: Springer."},{"key":"6715_CR89","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0893-6080(05)80023-1","volume":"5","author":"DH Wolpert","year":"1992","unstructured":"Wolpert, D. H. (1992). Stacked generalization. Neural Networks, 5, 241\u2013259.","journal-title":"Neural Networks"},{"key":"6715_CR90","doi-asserted-by":"crossref","first-page":"114476","DOI":"10.1016\/j.cma.2021.114476","volume":"390","author":"L Wu","year":"2022","unstructured":"Wu, L., & Noels, L. (2022). Recurrent neural networks (RNNS) with dimensionality reduction and break down in computational mechanics; application to multi-scale localization step. Computer Methods in Applied Mechanics and Engineering, 390, 114476.","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"6715_CR91","unstructured":"Xiao, H., Rasul, K., & Vollgraf, R. (2017). Fashion-MNIST: A novel image dataset for benchmarking machine learning algorithms. arXiv preprint arXiv:1708.07747"},{"key":"6715_CR92","doi-asserted-by":"crossref","unstructured":"Xu, B., & Zhang, G. (2023). Robust parametric UMAP for the analysis of single-cell data. bioRxiv, 2023-11.","DOI":"10.1101\/2023.11.14.567092"},{"key":"6715_CR93","doi-asserted-by":"crossref","unstructured":"Yao, Y., & Doretto, G. (2010). Boosting for transfer learning with multiple sources. In 2010 IEEE computer society conference on computer vision and pattern recognition (pp. 1855\u20131862). IEEE.","DOI":"10.1109\/CVPR.2010.5539857"},{"issue":"6","key":"6715_CR94","doi-asserted-by":"crossref","first-page":"3412","DOI":"10.1214\/09-AOS772","volume":"38","author":"M Yuan","year":"2010","unstructured":"Yuan, M., Cai, T. T., et al. (2010). A reproducing kernel Hilbert space approach to functional linear regression. The Annals of Statistics, 38(6), 3412\u20133444.","journal-title":"The Annals of Statistics"},{"issue":"4","key":"6715_CR95","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1109\/TSMCB.2006.870645","volume":"36","author":"H Zhao","year":"2006","unstructured":"Zhao, H., Yuen, P. C., & Kwok, J. T. (2006). A novel incremental principal component analysis and its application for face recognition. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36(4), 873\u2013886.","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06715-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-024-06715-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-024-06715-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T18:07:33Z","timestamp":1745258853000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-024-06715-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":95,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["6715"],"URL":"https:\/\/doi.org\/10.1007\/s10994-024-06715-8","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,25]]},"assertion":[{"value":"10 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 October 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2025","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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"125"}}