Abstract
The combination of K-SVD classifiers has been proved to be an effective tool for improving the performance in recognition applications. The rationale of this method follows from the observation that the diverse K-SVD classifiers are weighted by the recognition rates in confusion matrix (CM). Unfortunately, in the case of small samples, the recognition rate is not suitable to quantify the performance of K-SVD classifier, thus reducing the performance obtainable with any combination strategy. In this paper, we propose an improved CM that tries to address this problem, by calculating the joint probability distribution of the difference of K-SVD reconstruction errors, in order to capture the probability of classifying a sample to different patterns. Based on the improved CM and Dempster-Shafer evidence, the proposed method combines the K-SVD classifiers obtained from different feature vectors of different sensed signals. The analysis results of experiments performed on the axle box bearing and rolling ball bearing demonstrated the efficacy and advantages of proposed method.
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References
Kim M, Han DK, Ko H (2016) Joint patch clustering-based dictionary learning for multimodal image Fusion. Inf Fusion 27:198–214
Nejati M, Samavi S, Shirani S (2015) Multi-focus image fusion using dictionary-based sparse representation. Inf Fusion 25:72–84
Sun XP, Wang J, She MFH, Kong LX (2013) Scale invariant texture classification via sparse representation. Neurocomputing 122:338–348. https://doi.org/10.1016/j.neucom.2013.06.016
Yazdi SV, Douzal-Chouakria A (2018) Time warp invariant k-SVD: sparse coding and dictionary learning for time series under time warp. Pattern Recogn Lett 112:1–8. https://doi.org/10.1016/j.patrec.2018.05.017
Zhao ZB, Qiao BJ, Wang SB, Shen ZX, Chen XF (2019) A weighted multi-scale dictionary learning model and its applications on bearing fault diagnosis. J Sound Vib 446:429–452. https://doi.org/10.1016/j.jsv.2019.01.042
Zhao C, Feng ZP, Wei XK, Qin Y (2018) Sparse classification based on dictionary learning for planet bearing fault identification. Expert Syst Appl 108:233–245. https://doi.org/10.1016/j.eswa.2018.05.012
Zhang QA, Li BX (2010) Discriminative K-SVD for dictionary learning in face recognition, in CVPR, San Francisco, CA, USA, Jun. 13–18, pp. 2691–2698, https://doi.org/10.1109/CVPR.2010.5539989
Jiang ZL, Lin Z, Davis LS (2013) Label consistent K-SVD: learning a discriminative dictionary for recognition. IEEE Trans Pattern Anal Mach Intell 35(11):2651–2664. https://doi.org/10.1109/TPAMI.2013.88
Yang M, Zhang L, Feng XC, Zhang D (2011) Fisher discrimination dictionary learning for sparse representation, In ICCV, Barcelona, SPAIN, Nov. 06–13, pp. 543–550
Aharon M, Elad M, Bruckstein A (2006) K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322. https://doi.org/10.1109/TSP.2006.881199
Chen ZY, Li WH (2017) Multisensor feature fusion for bearing fault diagnosis using sparse autoencoder and deep belief network. IEEE T Instrum Meas 66(7):1693–1702. https://doi.org/10.1109/TIM.2017.2669947
Parikh CR, Pont MJ, Jones NB (2001) Application of Dempster-Shafer theory in condition monitoring applications: a case study. Pattern Recog Lett 22(6–7):777–785. https://doi.org/10.1016/S0167-8655(01)00014-9
Altincay H (2006) On the independence requirement in Dempster-Shafer theory for combining classifiers providing statistical evidence. Appl Intell 25(1):73–90. https://doi.org/10.1007/s10489-006-8867-y
Deng XY, Liu Q, Deng Y, Mahadevan S (2016) An improved method to construct basic probability assignment based on the confusion matrix for classification problem. Inf Sci 340:250–261. https://doi.org/10.1016/j.ins.2016.01.033
Trajdos P, Kurzynski M (2018) Weighting scheme for a pairwise multi-label classifier based on the fuzzy confusion matrix, Pattern Recogn Lett, pp. 60–67
Kurzynski M, Krysmann M, Trajdos P et al (2016) Multiclassifier system with hybrid learning applied to the control of bioprosthetic hand. Comput Biol Med 69:286–297
Liu ZG, Pan Q, Dezert J et al (2018) Combination of classifiers with optimal weight based on evidential reasoning. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2017.2718483
Ivo Düntsch, Günther Gediga, “Confusion matrices and rough set data analysis”, Proceedings of the 2019 International Conference on Pattern Recognition and Intelligent Systems (PRIS 2019) https://arxiv.org/abs/1902.01487v1
Yuan KJ, Deng Y (2019) Conflict evidence management in fault diagnosis. Int J Mach Learn Cyb 10(1):121–130. https://doi.org/10.1007/s13042-017-0704-6
Ye F, Chen J, Li YB (2017) Improvement of DS evidence theory for multi-sensor conflicting information. Symmetry-Basel. https://doi.org/10.3390/sym9050069
Li JC, Nehorai A (2018) Gaussian mixture learning via adaptive hierarchical clustering. Signal Process 150:116–121. https://doi.org/10.1016/j.sigpro.2018.04.013
Angelis AD, Angelis GD, Carbone P (2015) Using Gaussian-Uniform mixture models for robust time-interval measurement. IEEE T Instrum Meas 64(12):3545–3554. https://doi.org/10.1109/TIM.2015.2469434
Wan XJ, Liu LC, Xu ZB, Xu ZG, Li QL, Xu FX (2018) Fault diagnosis of rolling bearing based on optimized soft competitive learning Fuzzy ART and similarity evaluation technique. Adv Eng Inform 38:91–100. https://doi.org/10.1016/j.aei.2018.06.006
Jiang W, Xie CH, Zhuang MY, Shou YH, Tang YC (2016) Sensor data fusion with Z-numbers and its application in fault diagnosis. Sensors. https://doi.org/10.3390/s16091509
Bijalwan A, Chand N, Pilli ES, Krishna CR (2016) Botnet analysis using ensemble classifier. Perspect Sci 8:502–504. https://doi.org/10.1016/j.pisc.2016.05.008
Hassan MF, Abdel-Qader L (2016) Improving pattern classification by nonlinearly combined classifiers, In ICCI*CC, Stanford Univ., Stanford, CA, USA, Aug. 22-23, pp. 489–495
Lilliefors HW (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62(318):399. https://doi.org/10.2307/2283970
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This work was supported by the National Science Foundation of China (Grant No. 51975067 and No. 52175077).
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Liu, X., Liu, W., Huang, H. et al. An improved confusion matrix for fusing multiple K-SVD classifiers. Knowl Inf Syst 64, 703–722 (2022). https://doi.org/10.1007/s10115-022-01655-y
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DOI: https://doi.org/10.1007/s10115-022-01655-y