Abstract
It is noted that the rank of input data matrix has a critical impact on the performance of a trained classifier model. This paper presents a study on the rank of input data matrix based on a classification model of extreme learning machine which is a single hidden layer feed-forward neural network with non-iterative training. The changing tendency of model accuracy with the increase of input data matrix rank is experimentally investigated and the relationship between the input matrix rank and classification problem complexity is addressed. The analysis and experiments show some meaningful results.
Similar content being viewed by others
References
Huang G, Huang GB, Song S (2015) Trends in extreme learning machines: a review. Neural Netw Off J Int Neural Netw Soc 61:32–48
Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70(1–3):489–501
Huang GB, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neuro-computing 71(16–18):3460–3468
Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892
Huang GB, Chen YQ, Babri HA (2000) Classification ability of single hidden layer feedforward neural networks.[J]. IEEE Trans Neural Netw 11(3):799–801
Li MB, Huang GB, Saratchandran P (2005) Fully complex extreme learning machine. Neurocomputing 68(1):306–314
Liang NY, Huang GB, Saratchandran P (2006) A fast and accurate online sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 17(6):1411–1423
Heeswijk MV, Miche Y, Lindh-Knuutila T (2009) Adaptive Ensemble models of extreme learning machines for time series prediction, artificial neural networks—ICANN. Springer, Berlin, pp 305–314
Rong HJ, Ong YS, Tan AH (2008) A fast pruned-extreme learning machine for classification problem. Neurocomputing 72(1–3):359–366
Deng W, Zheng Q, Chen L (2009) Regularized extreme learning machine //computational intelligence and data mining. CIDM ‘09. IEEE Symposium on. IEEE, pp 389–395
Soria-Olivas E, Gómez-Sanchis J, Martín JD (2011) BELM: Bayesian extreme learning machine. IEEE Trans Neural Netw 22(3):505–509
Lan Y, Soh YC, Huang GB (2010) Two-stage extreme learning machine for regression. Neurocomputing 73(16):3028–3038
Deng WY, Bai Z, Huang GB (2016) A fast SVD-hidden-nodes based extreme learning machine for large-scale data analytics. Neural Netw Off J Int Neural Netw Soc 77:14–28
Zhou H, Huang GB, Lin Z (2014) Stacked extreme learning machines. IEEE Trans Cybern 45(9):1
Liu X, Wang L, Huang GB (2013) Multiple kernel extreme learning machine. Neurocomputing 149(PA):253–264
Fu AM, Wang XZ, He YL (2014) A study on residence error of training an extreme learning machine and its application to evolutionary algorithms. Neurocomputing 146(C):75–82
Huang GB, Zhou H, Ding X (2012) Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern Part B Cybern Publ IEEE Syst Man Cybern Soc 42(2):513–529
Lu SX, Wang XZ, Zhang GQ, Zhou X (2015) Effective algorithms of the Moore-Penrose inverse matrices for extreme learning machine. Intell Data Anal 19(4):743–760
Yuan Y, Wang Y, Cao F (2011) Optimization approximation solution for regression problem based on extreme learning machine. Neurocomputing 74(16):2475–2482
Michie D, Spiegelhalter D, Taylor C (1994) Machine learning, neural and statistical classification. Prentice Hall, Englewood Cliffs
Sohn SY (1999) Meta analysis of classification algorithms for pattern recognition. IEEE Trans Pattern Anal Mach Intell 21(11):1137–1144
Ho TK, Basu M (2002) Complexity measures of supervised classification problems. Pattern Anal Mach Intell IEEE Trans 24(3):289–300
Hoekstra A, Duin RPW (1996) On the nonlinearity of pattern classifiers//International Conference on Pattern Recognition IV. IEEE Computer Society p 271
Huang GB (2014) An insight into extreme learning machines: random neurons, random features and kernels. Cogn Comput 6(3):376–390
Alencar ASC, Neto ARR, Gomes JPP (2016) A new pruning method for extreme learning machines via genetic algorithms. Appl Soft Comput 44:101–107
Zhai JH, Shao QY, Wang XZ (2015) Architecture selection of ELM networks based on sensitivity of hidden nodes. Neural Process Lett 1–19
Zhai JH, Xu HY, Wang XZ (2012) Dynamic ensemble extreme learning machine based on sample entropy. Soft Comput 16(9):1493–1502
Zhong HM, Miao CY, Shen ZQ, Feng YH (2013) Comparing the learning effectiveness of BP, ELM, I-ELM, and SVM for corparate credit ratings. Neurocomputing 128(5):285–295
You ZH, Lei YK, Zhu L, Xia JF, Wang B (2013) Prediction of protein-protein interactions from amino acid sequences with ensemble extreme learning machines and principal component analysis. BMC Bioinformatics 14(8):1–11
Acknowledgements
The first author, Miss Xingmin Zhao, would like to thank her supervisor Professor Xizhao Wang for his guidance and suggestion to improve this paper. This study was supported by Basic Research Project of Knowledge Innovation Program in Shenzhen (JCYJ20150324140036825), and National Natural Science Foundations of China (71371063, 61672358).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, X., Cao, W., Zhu, H. et al. An initial study on the rank of input matrix for extreme learning machine. Int. J. Mach. Learn. & Cyber. 9, 867–879 (2018). https://doi.org/10.1007/s13042-016-0615-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-016-0615-y