Deep-RLS: A Model-Inspired Deep Learning Approach to Nonlinear PCA

2020/11/15 by Zahra Esmaeilbeig, Esmaeilbeig, Zahra, Shahin Khobahi +3
Computer Science · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Signal Processing (eess.SP) #Speech and Audio Processing #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2011.07458

openalex publication_date 2020/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we consider the application of model-based deep learning in nonlinear principal component analysis (PCA). Inspired by the deep unfolding methodology, we propose a task-based deep learning approach, referred to as Deep-RLS, that unfolds the iterations of the well-known recursive least squares (RLS) algorithm into the layers of a deep neural network in order to perform nonlinear PCA. In particular, we formulate the nonlinear PCA for the blind source separation (BSS) problem and show through numerical analysis that Deep-RLS results in a significant improvement in the accuracy of recovering the source signals in BSS when compared to the traditional RLS algorithm.

Citations

• Adam: A Method for Stochastic Optimization
• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing

Related

• Deep Unrolling for Nonconvex Robust Principal Component Analysis
• On the achievability of blind source separation for high-dimensional nonlinear source mixtures
• Deep Kernel Principal Component Analysis for Multi-level Feature Learning
• A PCA-Based Convolutional Network
• Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization