Abstract
Contractive auto encoder (CAE) is on of the most robust variant of standard Auto Encoder (AE). The major drawback associated with the conventional CAE is its higher reconstruction error during encoding and decoding process of input features to the network. This drawback in the operational procedure of CAE leads to its incapability of going into finer details present in the input features by missing the information worth consideration. Resultantly, the features extracted by CAE lack the true representation of all the input features and the classifier fails in solving classification problems efficiently. In this work, an improved variant of CAE is proposed based on layered architecture following feed forward mechanism named as deep CAE. In the proposed architecture, the normal CAEs are arranged in layers and inside each layer, the process of encoding and decoding take place. The features obtained from the previous CAE are given as inputs to the next CAE. Each CAE in all layers are responsible for reducing the reconstruction error thus resulting in obtaining the informative features. The feature set obtained from the last CAE is given as input to the softmax classifier for classification. The performance and efficiency of the proposed model has been tested on five MNIST variant-datasets. The results have been compared with standard SAE, DAE, RBM, SCAE, ScatNet and PCANet in term of training error, testing error and execution time. The results revealed that the proposed model outperform the aforementioned models.
Similar content being viewed by others
References
Aamir M, Mohd Nawi N, Mahdin HB, Naseem R, Zulqarnain M (2020) Auto-encoder variants for solving handwritten digits classification problem. Int J Fuzzy Logic Intell Syst 20(1):8–16
Hosseini-Asl E, Zurada JM, Nasraoui O (2016) Deep learning of part-based representation of data using sparse autoencoders with nonnegativity constraints. IEEE Trans Neural Netw Learn Syst 27(12):2486–2498
Bengio Y, Yao L, Alain G, Vincent P (2013) Generalized denoising auto-encoders as generative models. In: Advances in neural information processing systems pp 899–907
Jia K, Sun L, Gao S, Song Z, Shi BE (2015) Laplacian auto-encoders: an explicit learning of nonlinear data manifold. Neurocomputing 160:250–260
Zhang N, Ding S, Shi Z (2016) Denoising Laplacian multi-layer extreme learning machine. Neurocomputing 171:1066–1074
Wang W, Cui Z, Chang H, Shan S, Chen X (2014) Deeply coupled auto-encoder networks for cross-view classification. arXiv preprint arXiv:14022031
Liu W, Ma T, Tao D, You J (2016) HSAE: a Hessian regularized sparse auto-encoders. Neurocomputing 187:59–65
Chorowski J, Zurada JM (2015) Learning understandable neural networks with nonnegative weight constraints. IEEE Trans Neural Netw Learn Syst 26(1):62–69
Hong C, Yu J, Wan J, Tao D, Wang M (2015) Multimodal deep autoencoder for human pose recovery. IEEE Trans Image Process 24(12):5659–5670
Nishino K, Inaba M (2016) Bayesian AutoEncoder: generation of Bayesian networks with hidden nodes for features. In: AAAI pp 4244–4245
Rifai S, Mesnil G, Vincent P, Muller X, Bengio Y, Dauphin Y, et al. (2011) Higher order contractive auto-encoder. In: Joint European conference on machine learning and knowledge discovery in databases. Springer. pp 645–660
Vincent P, Larochelle H, Lajoie I, Bengio Y, Manzagol PA (2010) Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. J Mach Learn Res 11:3371–3408
Qi Y, Wang Y, Zheng X, Wu Z (2014) Robust feature learning by stacked autoencoder with maximum correntropy criterion. In: 2014 IEEE international conference on acoustics, speech and signal processing (ICASSP). IEEE. pp 6716–6720
Lemme A, Reinhart RF, Steil JJ (2010) Efficient online learning of a non-negative sparse autoencoder. In: ESANN. Citeseer
Wu P, Hoi SC, Xia H, Zhao P, Wang D, Miao C (2013) Online multimodal deep similarity learning with application to image retrieval. In: Proceedings of the 21st ACM international conference on multimedia. ACM, pp 153–162
Mescheder L, Nowozin S, Geiger A (2017) Adversarial variational bayes: Unifying variational autoencoders and generative adversarial networks. arXiv preprint arXiv:1701.04722
Liu Y, Feng X, Zhou Z (2016) Multimodal video classification with stacked contractive autoencoders. Sig Process 120:761–766
Rifai S, Vincent P, Muller X, Glorot X, Bengio Y (2011) Contractive auto-encoders: explicit invariance during feature extraction. In: Proceedings of the 28th international conference on international conference on machine learning. Omnipress, pp 833–840
Nawi NM, Ransing RS, Salleh MNM, Ghazali R, Hamid NA (2010) An improved back propagation neural network algorithm on classification problems. In: Database theory and application, bio-science and bio-technology. Springer, pp 177–188
Wahid F, Ismail LH, Ghazali R, Aamir M (2019) An efficient artificial intelligence hybrid approach for energy management in intelligent buildings. KSII Trans Internet Inf Syst 13(12):5904–5927
Mohd Nawi N, Hamzah F, Hamid NA, Rehman MZ, Aamir M, Azhar AR (2017) An optimized back propagation learning algorithm with adaptive learning rate. Int J Adv Sci Eng Inf Technol 7(5):1693–1700
Snášel V, Nowaková J, Xhafa F, Barolli L (2017) Geometrical and topological approaches to Big Data. Future Gener Comput Syst 67:286–296
Wahid F, Ghazali R (2018) Hybrid of firefly algorithm and pattern search for solving optimization problems. Evol Intel 1–10
Izenman AJ (2013) Linear discriminant analysis. In: Modern multivariate statistical techniques. Springer, pp 237–280
Wahid F, Ghazali R, Fayaz M, Shah AS (2017) Statistical features based approach (SFBA) for hourly energy consumption prediction using neural network. Networks 8:9
Aamir M, Mohd Nawi N, Wahid F, Mahdin H (2019) An efficient normalized restricted Boltzmann machine for solving multiclassclassification problems. Int J Adv Comput Sci Appl 10(8):416–426
Wahid F, Ghazali R, Shah H (2018) An improved hybrid firefly algorithm for solving optimization problems. In: International conference on soft computing and data mining. Springer, pp 14–23
Larochelle H, Erhan D, Courville A, Bergstra J, Bengio Y (2007) An empirical evaluation of deep architectures on problems with many factors of variation. In: Proceedings of the 24th international conference on Machine learning. ACM, pp 473–480
Chollet F, et al (2018) Keras: the python deep learning library. Astrophysics Source Code Library
Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, et al (2016) Tensorflow: a system for large-scale machine learning. In: OSDI. vol 16, pp 265–283
Montavon G, Müller KR, Cuturi M (2016) Wasserstein training of restricted Boltzmann machines. In: Advances in neural information processing systems, pp 3718–3726
Liang J, Liu R (2015) Stacked denoising autoencoder and dropout together to prevent overfitting in deep neural network. In: 2015 8th International congress on image and signal processing (CISP). IEEE, pp 697–701
Sankaran A, Vatsa M, Singh R, Majumdar A (2017) Group sparse autoencoder. Image Vis Comput 60:64–74
Chan TH, Jia K, Gao S, Lu J, Zeng Z, Ma Y (2015) PCANet: A simple deep learning baseline for image classification? IEEE Trans Image Process 24(12):5017–5032
Zi Y, Xie F, Jiang Z (2018) A cloud detection method for Landsat 8 images based on PCANet. Remote Sens 10(6):877
Zhu W, Miao J, Qing L, Huang GB (2015) Hierarchical extreme learning machine for unsupervised representation learning. In: 2015 International joint conference on neural networks (IJCNN). IEEE, pp 1–8
Liu R, Lu T (2016) Character recognition based on PCANet. In: 2016 15th International symposium on parallel and distributed computing (ISPDC). IEEE, pp 364–367
Lee JN, Byeon YH, Pan SB, Kwak KC (2018) An EigenECG network approach based on PCANet for personal identification from ECG Signal. Sensors. https://doi.org/10.3390/s18114024
Wang Z, Chang S, Ling Q, Huang S, Hu X, Shi H, et al (2016) Stacked approximated regression machine: a simple deep learning approach. arXiv preprint arXiv:1608.04062.
Soon FC, Khaw HY, Chuah JH, Kanesan J (2018) PCANet-Based Convolutional Neural Network Architecture For a Vehicle Model Recognition System. IEEE Trans Intell Transp Syst 99:1–11
Liao L, Jin W, Pavel R (2016) Enhanced restricted Boltzmann machine with prognosability regularization for prognostics and health assessment. IEEE Trans Industr Electron 63(11):7076–7083
Biglari F, Ebadian A (2015) Limited memory BFGS method based on a high-order tensor model. Comput Optim Appl 60(2):413–422
Jae-Neung Lee YHB, Kwak KC (2018) An EigenECG network approach based on PCANet for personal identification from ECG signal. Micromachines 9(4):411
Lee JN, Byeon YH, Kwak KC (2018) Design of ensemble stacked auto-encoder for classification of horse gaits with MEMS inertial sensor technology. Micromachines 9(8):411
Acknowledgements
The authors would like to thank Universiti Tun Hussein Onn Malaysia (UTHM) and Ministry of Higher Education (MOHE) Malaysia for supporting this Research.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aamir, M., Mohd Nawi, N., Wahid, F. et al. A deep contractive autoencoder for solving multiclass classification problems. Evol. Intel. 14, 1619–1633 (2021). https://doi.org/10.1007/s12065-020-00424-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12065-020-00424-6