{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T23:57:34Z","timestamp":1784419054081,"version":"3.55.0"},"reference-count":65,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,21]],"date-time":"2018-01-21T00:00:00Z","timestamp":1516492800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2016YFB1200203"],"award-info":[{"award-number":["2016YFB1200203"]}]},{"DOI":"10.13039\/501100005023","name":"State Key Laboratory of Rail Traffic Control and Safety","doi-asserted-by":"publisher","award":["RCS2016ZQ003"],"award-info":[{"award-number":["RCS2016ZQ003"]}],"id":[{"id":"10.13039\/501100005023","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005023","name":"State Key Laboratory of Rail Traffic Control and Safety","doi-asserted-by":"publisher","award":["RCS2016ZT018"],"award-info":[{"award-number":["RCS2016ZT018"]}],"id":[{"id":"10.13039\/501100005023","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Rotating machineries often work under severe and variable operation conditions, which brings challenges to fault diagnosis. To deal with this challenge, this paper discusses the concept of adaptive diagnosis, which means to diagnose faults under variable operation conditions with self-adaptively and little prior knowledge or human intervention. To this end, a novel algorithm is proposed, information geometrical extreme learning machine with kernel (IG-KELM). From the perspective of information geometry, the structure and Riemannian metric of Kernel-ELM is specified. Based on the geometrical structure, an IG-based conformal transformation is created to improve the generalization ability and self-adaptability of KELM. The proposed IG-KELM, in conjunction with variation mode decomposition (VMD) and singular value decomposition (SVD) is utilized for adaptive diagnosis: (1) VMD, as a new self-adaptive signal processing algorithm is used to decompose the raw signals into several intrinsic mode functions (IMFs). (2) SVD is used to extract the intrinsic characteristics from the matrix constructed with IMFs. (3) IG-KELM is used to diagnose faults under variable conditions self-adaptively with no requirement of prior knowledge or human intervention. Finally, the proposed method was applied on fault diagnosis of a bearing and hydraulic pump. The results show that the proposed method outperforms the conventional method by up to 7.25% and 7.78% respectively, in percentages of accuracy.<\/jats:p>","DOI":"10.3390\/e20010073","type":"journal-article","created":{"date-parts":[[2018,1,22]],"date-time":"2018-01-22T04:51:13Z","timestamp":1516596673000},"page":"73","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Adaptive Diagnosis for Rotating Machineries Using Information Geometrical Kernel-ELM Based on VMD-SVD"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3039-7582","authenticated-orcid":false,"given":"Zhipeng","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Limin","family":"Jia","sequence":"additional","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Qin","sequence":"additional","affiliation":[{"name":"State Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China"},{"name":"National Engineering Laboratory for System Safety and Operation Assurance of Urban Rail Transit, Guangzhou 510000, China"},{"name":"Beijing Research Center of Urban Traffic Information Sensing and Service Technologies, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1016\/j.asoc.2012.06.020","article-title":"A flexible algorithm for fault diagnosis in a centrifugal pump with corrupted data and noise based on ANN and support vector machine with hyper-parameters optimization","volume":"13","author":"Azadeh","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1016\/j.asoc.2012.01.020","article-title":"Fuzzy lattice classifier and its application to bearing fault diagnosis","volume":"12","author":"Li","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_3","unstructured":"Grebenik, J., Zhang, Y., Bingham, C., and Srivastava, S. (2016, January 7\u20139). Roller element bearing acoustic fault detection using smartphone and consumer microphones comparing with vibration techniques. Proceedings of the 17th International Conference on Mechatronics\u2014Mechatronika (ME), Prague, Czech Republic."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rzeszucinski, P., Orman, M., Pinto, C.T., Tkaczyk, A., and Sulowicz, M. (2015, January 1\u20134). A signal processing approach to bearing fault detection with the use of a mobile phone. Proceedings of the 2015 IEEE 10th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), Guarda, Portugal.","DOI":"10.1109\/DEMPED.2015.7303707"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Belfiore, N.P., and Rudas, I.J. (2014, January 19\u201321). Applications of computational intelligence to mechanical engineering. Proceedings of the 2014 IEEE 15th International Symposium on Computational Intelligence and Informatics (CINTI), Budapest, Hungary.","DOI":"10.1109\/CINTI.2014.7028702"},{"key":"ref_6","unstructured":"Wanbin, W., and Tse, P.W. (2006, January 11\u201314). Remote Machine Monitoring Through Mobile Phone, Smartphone or PDA. Proceedings of the 1st World Congress on Engineering Asset Management (WCEAM), Gold Coast, Australia."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1177\/014233129802000303","article-title":"A quantitative fault detection method for a class of nonlinear systems","volume":"20","author":"Shields","year":"1998","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.asoc.2011.08.053","article-title":"Automatic rule learning using roughset for fuzzy classifier in fault categorization of mono-block centrifugal pump","volume":"12","author":"Sakthivel","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Shengqiang, W., Yuru, M., Wanlu, J., and Sheng, Z. (2011, January 17\u201320). Kernel principal component analysis fault diagnosis method based on sound signal processing and its application in hydraulic pump. Proceedings of the 2011 International Conference on Fluid Power and Mechatronics, Beijing, China.","DOI":"10.1109\/FPM.2011.6045737"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4041","DOI":"10.1016\/j.asoc.2011.03.026","article-title":"A hybrid feature selection scheme and self-organizing map model for machine health assessment","volume":"11","author":"Yu","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.ymssp.2015.02.002","article-title":"Rolling bearing fault diagnosis based on LCD\u2013TEO and multifractal detrended fluctuation analysis","volume":"60\u201361","author":"Liu","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_12","unstructured":"Tian, Y., Wang, Z., and Lu, C. (2016). Self-adaptive bearing fault diagnosis based on permutation entropy and manifold-based dynamic time warping. Mech. Syst. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.mechmachtheory.2015.03.014","article-title":"Rolling bearing fault diagnosis under variable conditions using LMD-SVD and extreme learning machine","volume":"90","author":"Tian","year":"2015","journal-title":"Mech. Mach. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.eswa.2010.06.099","article-title":"An engine fault diagnosis system using intake manifold pressure signal and Wigner-Ville distribution technique","volume":"38","author":"Wu","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1006\/mssp.2000.1338","article-title":"A comparative study of acoustic and vibration signals in detection of gear failures using wigner\u2013ville distribution","volume":"15","author":"Baydar","year":"2001","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2017.07.017","article-title":"A convolutional neural network based feature learning and fault diagnosis method for the condition monitoring of gearbox","volume":"111","author":"Jing","year":"2017","journal-title":"Measurement"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10000","DOI":"10.1016\/j.eswa.2011.02.008","article-title":"A new feature extraction and selection scheme for hybrid fault diagnosis of gearbox","volume":"38","author":"Li","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1016\/S0888-3270(03)00077-3","article-title":"Bearing fault diagnosis based on wavelet transform and fuzzy inference","volume":"18","author":"Lou","year":"2004","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.ndteint.2005.09.002","article-title":"Continuous wavelet transform technique for fault signal diagnosis of internal combustion engines","volume":"39","author":"Wu","year":"2006","journal-title":"NDT & E Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1458","DOI":"10.1016\/j.ymssp.2009.11.011","article-title":"Rolling element bearing faults diagnosis based on optimal Morlet wavelet filter and autocorrelation enhancement","volume":"24","author":"Su","year":"2010","journal-title":"Mech. Syst.Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jsv.2003.07.002","article-title":"A comparative study on time\u2013frequency feature of cracked rotor by Wigner\u2013Ville distribution and wavelet transform","volume":"276","author":"Zou","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.rcim.2004.10.005","article-title":"An efficient approach to machine health diagnosis based on harmonic wavelet packet transform","volume":"21","author":"Yan","year":"2005","journal-title":"Robot Comput. Manuf."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1016\/j.jsv.2003.09.031","article-title":"Machine fault diagnosis through an effective exact wavelet analysis","volume":"277","author":"Tse","year":"2004","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"4568","DOI":"10.1016\/j.eswa.2009.12.051","article-title":"Application of mother wavelet functions for automatic gear and bearing fault diagnosis","volume":"37","author":"Rafiee","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4862","DOI":"10.1016\/j.eswa.2008.05.052","article-title":"A novel technique for selecting mother wavelet function using an intelligent fault diagnosis system","volume":"36","author":"Rafiee","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.ymssp.2005.09.011","article-title":"Research on the intrinsic mode function (IMF) criterion in EMD method","volume":"20","author":"Junsheng","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/asmb.501","article-title":"Applications of Hilbert\u2013Huang transform to non-stationary financial time series analysis","volume":"19","author":"Huang","year":"2003","journal-title":"Appl. Stoch. Models Bus. Ind."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. Math. Phys. Eng. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0888-3270(03)00099-2","article-title":"Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings","volume":"19","author":"Yu","year":"2005","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.ymssp.2004.11.002","article-title":"A fault diagnosis approach for roller bearings based on EMD method and AR model","volume":"20","author":"Junsheng","year":"2006","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1016\/j.measurement.2012.10.026","article-title":"Gear fault identification based on Hilbert\u2013Huang transform and SOM neural network","volume":"46","author":"Cheng","year":"2013","journal-title":"Measurement"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2607","DOI":"10.1016\/j.ymssp.2006.12.004","article-title":"Bearing fault diagnosis using FFT of intrinsic mode functions in Hilbert\u2013Huang transform","volume":"21","author":"Rai","year":"2007","journal-title":"Mech.Syst. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational mode decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.ymssp.2015.02.020","article-title":"Research on variational mode decomposition and its application in detecting rub-impact fault of the rotor system","volume":"60\u201361","author":"Wang","year":"2015","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1155\/2009\/519502","article-title":"Application of SVM and SVD technique based on EMD to the fault diagnosis of the rotating machinery","volume":"16","author":"Cheng","year":"2009","journal-title":"Shock Vib."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1277","DOI":"10.1109\/5.237536","article-title":"Subspace-based signal analysis using singular value decomposition","volume":"81","author":"Veen","year":"1993","journal-title":"Proc. IEEE"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ymssp.2012.12.014","article-title":"Fault diagnosis of rolling bearings based on multifractal detrended fluctuation analysis and Mahalanobis distance criterion","volume":"38","author":"Lin","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"7828","DOI":"10.1016\/j.eswa.2010.12.122","article-title":"The application of rough set and Mahalanobis distance to enhance the quality of OSA diagnosis","volume":"38","author":"Wang","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"798","DOI":"10.1177\/0142331212472929","article-title":"Fault diagnosis and health assessment for bearings using the Mahalanobis\u2013Taguchi system based on EMD-SVD","volume":"35","author":"Wang","year":"2013","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1016\/j.eswa.2007.11.043","article-title":"Improved kernel fisher discriminant analysis for fault diagnosis","volume":"36","author":"Li","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"959","DOI":"10.1016\/j.asoc.2017.09.019","article-title":"Fault diagnosis and classification framework using multi-scale classification based on kernel Fisher discriminant analysis for chemical process system","volume":"61","author":"Hussain","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1650","DOI":"10.1016\/j.asoc.2012.02.011","article-title":"Support Vector Machines for classification and locating faults on transmission lines","volume":"12","author":"Ekici","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"2023","DOI":"10.1016\/j.asoc.2012.03.021","article-title":"A comparative study of naive bayes classifier and Bayes net classifier for fault diagnosis of monoblock centrifugal pump using wavelet analysis","volume":"12","author":"Muralidharan","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1016\/j.asoc.2012.03.015","article-title":"Attribute selection method based on a hybrid BPNN and PSO algorithms","volume":"12","author":"Jin","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2896","DOI":"10.1016\/j.asoc.2012.04.026","article-title":"Sensor deployment for fault diagnosis using a new discrete optimization algorithm","volume":"13","author":"Koupaei","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"2867","DOI":"10.1016\/j.asoc.2012.04.003","article-title":"Gear dynamics monitoring using discrete wavelet transformation and multi-layer perceptron neural networks","volume":"12","author":"Sanz","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3191","DOI":"10.1016\/j.asoc.2013.01.027","article-title":"Cluster analysis by self-organizing maps: An application to the modelling of water quality in a treatment process","volume":"13","author":"Juntunen","year":"2013","journal-title":"Appl. Soft Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1186\/1687-6180-2011-49","article-title":"Fault detection for hydraulic pump based on chaotic parallel RBF network","volume":"1","author":"Lu","year":"2011","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.ymssp.2015.10.025","article-title":"Deep neural networks: A promising tool for fault characteristic mining and intelligent diagnosis of rotating machinery with massive data","volume":"72\u201373","author":"Jia","year":"2016","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"4113","DOI":"10.1016\/j.eswa.2013.12.026","article-title":"An approach to fault diagnosis of reciprocating compressor valves using Teager\u2013Kaiser energy operator and deep belief networks","volume":"41","author":"Tran","year":"2014","journal-title":"Expert Syst. Appl."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.ymssp.2017.09.026","article-title":"A novel method for intelligent fault diagnosis of rolling bearings using ensemble deep auto-encoders","volume":"102","author":"Shao","year":"2018","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","article-title":"Extreme learning machine: Theory and applications","volume":"70","author":"Huang","year":"2006","journal-title":"Neurocomputing"},{"key":"ref_53","unstructured":"Huang, G.B., Zhu, Q.Y., and Siew, C.K. (2004, January 25\u201329). Extreme learning machine: A new learning scheme of feedforward neural networks. Proceedings of the 2004 IEEE International Joint Conference on Neural Networks, Budapest, Hungary."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.neunet.2014.10.001","article-title":"Trends in extreme learning machines: A review","volume":"61","author":"Huang","year":"2015","journal-title":"Neural Netw."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.neucom.2017.04.036","article-title":"Twin extreme learning machines for pattern classification","volume":"260","author":"Wan","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_56","first-page":"16","article-title":"Extreme learning machine with randomly assigned RBF kernels","volume":"11","author":"Huang","year":"2005","journal-title":"Int. J. Inf. Technol."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Rodriguez, N., Cabrera, G., Lagos, C., and Cabrera, E. (2017). Stationary wavelet singular entropy and kernel extreme learning for bearing multi-fault diagnosis. Entropy, 19.","DOI":"10.3390\/e19100541"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1007\/978-3-642-00826-9_4","article-title":"Information geometry and its applications: Convex function and dually flat manifold","volume":"5416","author":"Amari","year":"2009","journal-title":"Emerg. Trends Vis. Comput."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s11460-010-0101-3","article-title":"Information geometry in optimization, machine learning and statistical inference","volume":"5","author":"Amari","year":"2010","journal-title":"Front. Electr. Electron. Eng."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/0893-6080(91)90040-C","article-title":"Dualistic geometry of the manifold of higher-order neurons","volume":"4","author":"Amari","year":"1991","journal-title":"Neural Netw."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1379","DOI":"10.1016\/0893-6080(95)00003-8","article-title":"Information geometry of the EM and em algorithms for neural networks","volume":"8","author":"Amari","year":"1995","journal-title":"Neural Netw."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ics.2004.05.143","article-title":"Information geometry of multilayer perceptron","volume":"1269","author":"Amari","year":"2004","journal-title":"Int. Congr. Ser."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/0167-2789(94)00175-P","article-title":"Gradient systems in view of information geometry","volume":"80","author":"Fujiwara","year":"1995","journal-title":"Phys. D Nonlinear Phenomena"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0024-3795(94)00348-3","article-title":"Dualistic differential geometry of positive definite matrices and its applications to related problems","volume":"247","author":"Ohara","year":"1996","journal-title":"Linear Algebra Appl."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1023\/A:1013848912046","article-title":"Conformal transformation of kernel functions: A data-dependent way to improve support vector machine classifiers","volume":"15","author":"Wu","year":"2002","journal-title":"Neural Process. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/73\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:52:02Z","timestamp":1760194322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/73"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,21]]},"references-count":65,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["e20010073"],"URL":"https:\/\/doi.org\/10.3390\/e20010073","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,21]]}}}