I dedicate this work to my son ' BERGHOUT Loukmane '.
Sparse_AE: the function allows to train an Auto encoder In Sparse domain by solving L1 norm optimization problem. Optimization problem: min_B ||B||_1 subject to : H*B = X.
Where H: is the Sparse version hidden layer, B: is output weights matrix and X:is the Input.
the white gaussian noise generated from a random distribution must be added during training , To make the sparse hidden layer a full rank matrix otherwise, L1 norm optimization will never achieved (check the Sparse_AE function .
for any references you can use these ones:
 R. G. Baraniuk, “<Compressive Sensing(lecture notes).pdf>,” no. July, pp. 118–121, 2007.
 M. W. Fakhr, E. N. S. Youssef, and M. S. El-Mahallawy, “L1-regularized least squares sparse extreme learning machine for classification,” 2015 Int. Conf. Inf. Commun. Technol. Res. ICTRC 2015, no. April, pp. 222–225, 2015.
 G. Huang, S. Member, H. Zhou, X. Ding, and R. Zhang, “Extreme Learning Machine for Regression and Multiclass Classification,” vol. 42, no. 2, pp. 513–529, 2012.
 C. justin Romberg and Jrom@acm.caltech.edu, “L1 magic toolbox.”
 A. Makhzani and B. Frey, “k-Sparse Autoencoders,” 2013.
 L. le Cao, W. bing Huang, and F. chun Sun, “Building feature space of extreme learning machine with sparse denoising stacked-autoencoder,” Neurocomputing, vol. 174, pp. 60–71, 2016.
you can also learn from this video tutorial:
BERGHOUT Tarek (2019). Sparse Autoencoder (https://www.mathworks.com/matlabcentral/fileexchange/72102-sparse-autoencoder), MATLAB Central File Exchange. Retrieved .