{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T20:42:58Z","timestamp":1773002578813,"version":"3.50.1"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2025,5,11]],"date-time":"2025-05-11T00:00:00Z","timestamp":1746921600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,5,11]],"date-time":"2025-05-11T00:00:00Z","timestamp":1746921600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"European Union NextGenerationEU\/ PRTR), European Commission, Autonomous Government of Castilla-La Mancha","award":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"],"award-info":[{"award-number":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"]}]},{"name":"European Union NextGenerationEU\/ PRTR), European Commission, Autonomous Government of Castilla-La Mancha","award":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"],"award-info":[{"award-number":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"]}]},{"name":"European Union NextGenerationEU\/ PRTR), European Commission, Autonomous Government of Castilla-La Mancha","award":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"],"award-info":[{"award-number":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"]}]},{"name":"European Union NextGenerationEU\/ PRTR), European Commission, Autonomous Government of Castilla-La Mancha","award":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"],"award-info":[{"award-number":["PDC2021-121197-C22, Grant n. 101120726, SBPLY\/21\/180501\/000025"]}]},{"DOI":"10.13039\/501100007480","name":"Universidad de Castilla la Mancha","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007480","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. &amp; Cyber."],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Deep neural networks (DNNs) have demonstrated strong performance in classification-based applications in the field of machine learning (ML). A DNN model is nonetheless susceptible to adversarial examples (AE), which are created by introducing minor well-designed changes to a regular example. In important security-sensitive systems, these undetectable small perturbations can fool the DNN model into making a mistake. In this work, we suggest a novel model-agnostic adversarial example detection technique using multivariate features based on pre-detector based defense. The suggested approach extracts the generalized alignment index (GALI) and the guided filter (GF) based spatial features (SFs) that offer an effective criteria for distinguishing between adversarial and normal cases. We use space-filling curve (SFC) to vectorize the images of the normal and adversarial instances, and then determine the GALI feature values for the examples using a chaos detection method based on time-series-analysis. The GF is used to determine the values of the local features. On the basis of multivariate feature values, an Isolation Forest classifier (IFC) is lastly trained to recognize adversarial samples. The experimental findings across benchmark datasets show that the suggested strategy can recognize AE with high accuracy using a broad range of attack categories.<\/jats:p>","DOI":"10.1007\/s13042-025-02657-2","type":"journal-article","created":{"date-parts":[[2025,5,11]],"date-time":"2025-05-11T08:01:03Z","timestamp":1746950463000},"page":"7331-7342","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Adversarial Examples Detection with Chaos-Based Multivariate Features"],"prefix":"10.1007","volume":"16","author":[{"given":"Harbinder","family":"Singh","sequence":"first","affiliation":[]},{"given":"Anibal","family":"Pedraza","sequence":"additional","affiliation":[]},{"given":"Oscar","family":"Deniz","sequence":"additional","affiliation":[]},{"given":"Gloria","family":"Bueno","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,11]]},"reference":[{"issue":"6","key":"2657_CR1","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1145\/3065386","volume":"60","author":"A Krizhevsky","year":"2017","unstructured":"Krizhevsky A, Sutskever I, Hinton GE (2017) Imagenet classification with deep convolutional neural networks. Commun. ACM 60(6):84\u201390","journal-title":"Commun. ACM"},{"key":"2657_CR2","doi-asserted-by":"crossref","unstructured":"Mart\u00ednez-D\u00edaz M, Soriguera F (2018) Autonomous vehicles: theoretical and practical challenges. Transportation Research Procedia 33:275\u2013282. XIII Conference on Transport Engineering, CIT2018","DOI":"10.1016\/j.trpro.2018.10.103"},{"key":"2657_CR3","unstructured":"Radford A, Kim JW, Xu T, Brockman G, McLeavey C, Sutskever I (2022) Robust speech recognition via large-scale weak supervision. arXiv preprint arXiv:2212.04356 [eess.AS]"},{"key":"2657_CR4","doi-asserted-by":"publisher","first-page":"93145","DOI":"10.1109\/ACCESS.2020.2993887","volume":"8","author":"H Tang","year":"2020","unstructured":"Tang H, Hu Z (2020) Research on medical image classification based on machine learning. IEEE Access 8:93145\u201393154. https:\/\/doi.org\/10.1109\/ACCESS.2020.2993887","journal-title":"IEEE Access"},{"key":"2657_CR5","unstructured":"Sutskever I, Vinyals O, Le QV (2014) Sequence to sequence learning with neural networks. arXiv preprint arXiv:1409.3215"},{"key":"2657_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cose.2022.102847","volume":"121","author":"T Long","year":"2022","unstructured":"Long T, Gao Q, Xu L, Zhou Z (2022) A survey on adversarial attacks in computer vision: Taxonomy, visualization and future directions. Comput Security 121:102847","journal-title":"Comput Security"},{"key":"2657_CR7","unstructured":"Szegedy C, Zaremba W, Sutskever I, Bruna J, Erhan D, Goodfellow I, Fergus R (2013) Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199"},{"key":"2657_CR8","unstructured":"Goodfellow IJ, Shlens J, Szegedy C (2015) Explaining and harnessing adversarial examples. International Conference on Learning Representations (ICLR)"},{"key":"2657_CR9","unstructured":"Liu Y, Chen X, Liu C, Song D (2017) Delving into transferable adversarial examples and black-box attacks. arXiv preprint arXiv:1611.02770"},{"key":"2657_CR10","unstructured":"Papernot N, McDaniel P, Goodfellow I (2016) Transferability in machine learning: from phenomena to black-box attacks using adversarial samples. arXiv preprint arXiv:1605.07277"},{"key":"2657_CR11","unstructured":"Brendel W, Rauber J, Bethge M (2017) Decision-based adversarial attacks: Reliable attacks against black-box machine learning models. arXiv preprint arXiv:1712.04248"},{"key":"2657_CR12","doi-asserted-by":"crossref","unstructured":"Chen J, Jordan MI, Wainwright MJ (2020) HopSkipJumpAttack: A query-efficient decision-based attack. In: 2020 IEEE Symposium on Security and Privacy (sp), pp. 1277\u20131294. IEEE","DOI":"10.1109\/SP40000.2020.00045"},{"key":"2657_CR13","doi-asserted-by":"publisher","first-page":"155161","DOI":"10.1109\/ACCESS.2021.3127960","volume":"9","author":"N Akhtar","year":"2021","unstructured":"Akhtar N, Mian A, Kardan N, Shah M (2021) Advances in adversarial attacks and defenses in computer vision: A survey. IEEE Access 9:155161\u2013155196. https:\/\/doi.org\/10.1109\/ACCESS.2021.3127960","journal-title":"IEEE Access"},{"key":"2657_CR14","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/j.cose.2019.06.012","volume":"86","author":"AS Hashemi","year":"2019","unstructured":"Hashemi AS, Mozaffari S (2019) Secure deep neural networks using adversarial image generation and training with noise-gan. Comput Security 86:372\u2013387","journal-title":"Comput Security"},{"key":"2657_CR15","unstructured":"Tram\u00e8r F, Kurakin A, Papernot N, Goodfellow I, Boneh D, McDaniel P (2017) Ensemble adversarial training: Attacks and defenses. arXiv preprint arXiv:1705.07204"},{"key":"2657_CR16","unstructured":"Blau T, Ganz R, Kawar B, Bronstein A, Elad M (2022) Threat model-agnostic adversarial defense using diffusion models. arXiv preprint arXiv:2207.08089 [cs.CV]"},{"key":"2657_CR17","doi-asserted-by":"publisher","first-page":"1711","DOI":"10.1109\/TIP.2019.2940533","volume":"29","author":"A Mustafa","year":"2020","unstructured":"Mustafa A, Khan SH, Hayat M, Shen J, Shao L (2020) Image super-resolution as a defense against adversarial attacks. IEEE Transact Image Process 29:1711\u20131724","journal-title":"IEEE Transact Image Process"},{"issue":"9","key":"2657_CR18","doi-asserted-by":"publisher","first-page":"1523","DOI":"10.1109\/JAS.2021.1004108","volume":"8","author":"H Samuel","year":"2021","unstructured":"Samuel H, Fazle K, Houshang D (2021) Generating adversarial samples on multivariate time series using variational autoencoders. IEEE\/CAA J Automatica Sinica 8(9):1523\u20131538","journal-title":"IEEE\/CAA J Automatica Sinica"},{"key":"2657_CR19","unstructured":"Grosse K, Manoharan P, Papernot N, Backes M, McDaniel P (2017) On the (statistical) detection of adversarial examples. arXiv preprint arXiv:1702.06280 [cs.CR]"},{"key":"2657_CR20","unstructured":"Feinman R, Curtin RR, Shintre S, Gardner AB (2017) Detecting adversarial samples from artifacts. arXiv preprint arXiv:1703.00410 [stat.ML]"},{"key":"2657_CR21","unstructured":"Metzen JH, Genewein T, Fischer V, Bischoff B (2017) On detecting adversarial perturbations. arXiv preprint arXiv:1702.04267"},{"key":"2657_CR22","unstructured":"Speakman S, Sridharan S, Remy S, Weldemariam K, McFowland E (2018) Subset scanning over neural network activations. arXiv preprint arXiv:1810.08676 [cs.LG]"},{"key":"2657_CR23","unstructured":"Vacanti G, Looveren AV (2020) Adversarial detection and correction by matching prediction distributions. arXiv preprint arXiv:2002.09364 [cs.LG]"},{"issue":"12","key":"2657_CR24","first-page":"1533","volume":"14","author":"III Em","year":"2013","unstructured":"Em III, Speakman S, Neill DB (2013) Fast generalized subset scan for anomalous pattern detection. J Mach Learning Res 14(12):1533\u20131561","journal-title":"J Mach Learning Res"},{"key":"2657_CR25","unstructured":"Prabhu VU, Desai N, Whaley J (2017) On Lyapunov exponents and adversarial perturbation. Deep Learning Security Workshop (Singapore)"},{"key":"2657_CR26","doi-asserted-by":"publisher","unstructured":"Liu FT, Ting KM, Zhou Z-H (2008) Isolation forest. In: 2008 Eighth IEEE International Conference on Data Mining, pp. 413\u2013422. https:\/\/doi.org\/10.1109\/ICDM.2008.17","DOI":"10.1109\/ICDM.2008.17"},{"key":"2657_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2021.111745","volume":"155","author":"A Pedraza","year":"2022","unstructured":"Pedraza A, Deniz O, Bueno G (2022) Lyapunov stability for detecting adversarial image examples. Chaos, Solitons Fractals 155:111745","journal-title":"Chaos, Solitons Fractals"},{"key":"2657_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2022.112577","volume":"163","author":"O Deniz","year":"2022","unstructured":"Deniz O, Pedraza A, Bueno G (2022) Detecting chaos in adversarial examples. Chaos, Solitons Fractals 163:112577","journal-title":"Chaos, Solitons Fractals"},{"issue":"7","key":"2657_CR29","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1002\/jae.805","volume":"20","author":"F Fern\u00e1ndez-Rodr\u00edguez","year":"2005","unstructured":"Fern\u00e1ndez-Rodr\u00edguez F, Sosvilla-Rivero S, Andrada-F\u00e9lix J (2005) Testing chaotic dynamics via Lyapunov exponents. J Appl Econom 20(7):911\u2013930","journal-title":"J Appl Econom"},{"issue":"11","key":"2657_CR30","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.3390\/e22111201","volume":"22","author":"A Pedraza","year":"2020","unstructured":"Anibal P, Oscar D, Gloria B (2020) Approaching adversarial example classification with chaos theory. Entropy 22(11):1201","journal-title":"Entropy"},{"issue":"1","key":"2657_CR31","first-page":"157","volume":"36","author":"G Peano","year":"1980","unstructured":"Peano G (1980) Sur une courbe, qui remplit toute une aire plane. IEEE Transact Image Process 36(1):157\u2013160","journal-title":"IEEE Transact Image Process"},{"key":"2657_CR32","doi-asserted-by":"crossref","unstructured":"Hilbert D (1935) \u00dcber die stetige abbildung einer linie auf ein fl\u00e4chenst\u00fcck. Dritter Band: Analysis$$\\cdot$$ Grundlagen der Mathematik$$\\cdot$$ Physik Verschiedenes: Nebst Einer Lebensgeschichte, 1\u20132","DOI":"10.1007\/978-3-662-38452-7_1"},{"key":"2657_CR33","first-page":"71","volume":"23","author":"H Tropf","year":"1981","unstructured":"Tropf H, Herzog H (1981) Multimensional range search in dynamically balanced trees. Angew Inform 23:71\u201377","journal-title":"Angew Inform"},{"issue":"1","key":"2657_CR34","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.physd.2007.04.004","volume":"231","author":"C Skokos","year":"2007","unstructured":"Skokos C, Bountis TC, Antonopoulos C (2007) Geometrical properties of local dynamics in hamiltonian systems: The generalized alignment index (GALI) method. Physica D: Nonlinear Phenomena 231(1):30\u201354","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"2657_CR35","first-page":"1","volume-title":"Comput Vision - ECCV 2010","author":"K He","year":"2010","unstructured":"He K, Sun J, Tang X (2010) Guided image filtering. In: Daniilidis K, Maragos P, Paragios N (eds) Comput Vision - ECCV 2010. Springer, Berlin, Heidelberg, pp 1\u201314"},{"key":"2657_CR36","unstructured":"Goldsmith M (2009) The maximal Lyapunov exponent of a time series. A Thesis in The Department of Computer Science, Concordia University, Montreal, Canada"},{"issue":"1","key":"2657_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0167-2789(97)00306-0","volume":"114","author":"M Bask","year":"1998","unstructured":"Bask M, Gen\u00e7ay R (1998) Testing chaotic dynamics via Lyapunov exponents. Physica D: Nonlinear Phenomena 114(1):1\u20132","journal-title":"Physica D: Nonlinear Phenomena"},{"key":"2657_CR38","doi-asserted-by":"crossref","unstructured":"Bottou L, Cortes C, Denker JS, Drucker H, Guyon I, Jackel LD, Le Cun Y, Muller UA, S\u00e4ckinger E, Simard P, Vapnik V (1994) Comparison of classifier methods: a case study in handwritten digit recognition. In: Proceedings of the 12th IAPR International Conference on Pattern Recognition, Conference B: Computer Vision & Image Processing., vol. 2, pp. 77\u201382. IEEE, Jerusalem","DOI":"10.1109\/ICPR.1994.576879"},{"key":"2657_CR39","unstructured":"S Charalampos H, G Georg A, Jacques L (2016) Chaos Detection and Predictability vol. 915. Springer, Heidelberg"},{"key":"2657_CR40","doi-asserted-by":"crossref","unstructured":"Xie C, Wu Y, Maaten L, Yuille AL, He K (2019) Feature denoising for improving adversarial robustness. In: 2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 501\u2013509. IEEE Computer Society, Los Alamitos, CA, USA","DOI":"10.1109\/CVPR.2019.00059"},{"issue":"7","key":"2657_CR41","doi-asserted-by":"publisher","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","volume":"26","author":"K Zhang","year":"2017","unstructured":"Zhang K, Zuo W, Chen Y, Meng D, Zhang L (2017) Beyond a gaussian denoiser: Residual learning of deep CNN for image denoising. IEEE Transact Image Process 26(7):3142\u20133155","journal-title":"IEEE Transact Image Process"},{"key":"2657_CR42","doi-asserted-by":"crossref","unstructured":"Singh H, Kumar V, Bhooshan S (2014) A novel approach for detail-enhanced exposure fusion using guided filter. The Scientific World Journal, Hindawi, 1\u20138","DOI":"10.1155\/2014\/659217"},{"key":"2657_CR43","doi-asserted-by":"publisher","DOI":"10.1002\/9781118625590","volume-title":"Appl Regression Anal","author":"NR Draper","year":"1998","unstructured":"Draper NR, Smith H (1998) Appl Regression Anal, vol 326. John Wiley & Sons, New Jersey"},{"key":"2657_CR44","unstructured":"Xiao H, Rasul K, Vollgraf R (2017) Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms. CoRR arXiv:1708.07747"},{"key":"2657_CR45","unstructured":"Krizhevsky A, Hinton G, et al (2009) Learning multiple layers of features from tiny images. Technical Report TR-2009"},{"key":"2657_CR46","unstructured":"Nicolae M, Sinn M, Minh TN, Rawat A, Wistuba M, Zantedeschi V, Molloy IM, Edwards B (2018) Adversarial robustness toolbox v0.2.2. CoRR arXiv:1807.01069"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-025-02657-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-025-02657-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-025-02657-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T16:57:44Z","timestamp":1760547464000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-025-02657-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,11]]},"references-count":46,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["2657"],"URL":"https:\/\/doi.org\/10.1007\/s13042-025-02657-2","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"value":"1868-8071","type":"print"},{"value":"1868-808X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,11]]},"assertion":[{"value":"4 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}