Arabian Journal for Science and Engineering (2021) 46:9237–9251 https://doi.org/10.1007/s13369-021-05674-9 RESEARCH ARTICLE-COMPUTER ENGINEERING AND COMPUTER SCIENCE Hybrid Contractive Auto-encoder with Restricted Boltzmann Machine For Multiclass Classification Muhammad Aamir 1,2 · Nazri Mohd Nawi 1,3 · Fazli Wahid 4 · Muhammad Sadiq Hasan Zada 2 · M. Z. Rehman 1 · Muhammad Zulqarnain 1 Received: 19 April 2020 / Accepted: 13 April 2021 / Published online: 23 June 2021 © King Fahd University of Petroleum & Minerals 2021 Abstract Contractive auto-encoder (CAE) is a type of auto-encoders and a deep learning algorithm that is based on multilayer training approach. It is considered as one of the most powerful, efficient and robust classification techniques, more specifically feature reduction. The problem independence, easy implementation and intelligence of solving sophisticated problems make it distinct from other deep learning approaches. However, CAE fails in data dimensionality reduction that cause difficulty to capture the useful information within the features space. In order to resolve the issues of CAE, restricted Boltzmann machine (RBM) layers have been integrated with CAE to enhance the dimensionality reduction and a randomized factor for hidden layer parameters. The proposed model has been evaluated on four benchmark variant datasets of MNIST. The results have been compared with four well-known multiclass class classification approaches including standard CAE, RBM, AlexNet and artificial neural network. A considerable amount of improvement has been observed in the performance of proposed model as compared to other classification techniques. The proposed CAE–RBM showed an improvement of 2–4% on MNIST(basic), 9–12% for MNIST(rot), 7–12% for MNIST(bg-rand) and 7–10% for MNIST(bg-img) dataset in term of final accuracy. Keywords Contractive auto-encoder · Restricted Boltzmann machine · Classification · Mnist variants B Muhammad Aamir aamir@uthm.edu.my; m.aamir@derby.ac.uk B Fazli Wahid fazli.wahid@uoh.edu.pk Nazri Mohd Nawi nazri@uthm.edu.my Muhammad Sadiq Hasan Zada m.hassanzada@derby.ac.uk M. Z. Rehman syedzubair@uthm.edu.my Muhammad Zulqarnain zulqarnainmalik321@gmail.com 1 Faculty of Computer Science and Information Technology, Universiti Tun Hussein Onn, Parit Raja, Malaysia 2 School of Electronics, Computing and Mathematics, University of Derby, Derby, UK 3 Soft Computing and Data Mining Center, Universiti Tun Hussein Onn, Parit Raja, Malaysia 4 Department of Information Technology, The University of Haripur, Haripur, Khyber Pakhtunkhwa, Pakistan Abbreviations AE Auto-encoder RBM Restricted Boltzmann machine CAE Contractive auto-encoder CAE–RBM Hybrid contractive auto-encoder–restricted Boltzmann machine ANN Artificial neural network SVM Support vector machine kNN k-Nearest neighbor CNN Convolution neural network DL Deep learning ML Machine learning ROC Receiver operating characteristic CM Confusion matrix MNIST Modified National Institute of Standards and Technology (database) rot MNIST random rotation digits bg-rand Random noise background digits bg-img Random background digits 123