My journey to the area of machine learning started from learning linear transforms from data. The idea of learning linear transforms was further developed to learning nonlinear transforms via deep neural networks.
The data-driven tight frame construction for image denoising is an unsupervised learning approach for image restorations and dictionary learning for sparse coding is a supervised learning approach for classifications. The key feature is to learn a linear transform that has a good sparse approximation of the underline images. The both algorithms are shown to be convergent.
A deep learning framework of nonlinear transform and its inverse is a fully connected neural network between the encoder and decoder and is applied to a wide range of applications in signal/image processing, predictive data science, forward and inverse problems.
- Chenglong Bao, Hui Ji, Zuowei Shen, Convergence analysis for iterative data-driven tight frame construction scheme, Applied and Computational Harmonic Analysis, 38(3), (2015), 510-523. PDF
- Jianfeng Cai, Hui Ji, Zuowei Shen, Guibo Ye, Data-driven tight frame construction and image denoising, Applied and Computational Harmonic Analysis, 37(1), (2014), 89-105. PDF
- Chenglong Bao, Hui Ji, Yuhui Quan, Zuowei Shen, Dictionary learning for sparse coding: Algorithms and convergence analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence, 38(7), (2016), 1356-1369. PDF
- Chenglong Bao, Hui Ji, Yuhui Quan, Zuowei Shen, L0 norm based dictionary learning by proximal methods with global convergence, IEEE Conference Computer Vision and Pattern Recognition (CVPR), Columbus, (2014). PDF
Learning Nonlinear Transform
- Yong Zheng Ong, Zuowei Shen, Haizhao Yang, Integral Autoencoder Network for Discretization-Invariant Learning, Journal of Machine Learning Research, 23, (2022), PDF