VPNET: Variable Projection Networks

In this paper, we introduce VPNet, a novel model-driven neural network architecture based on variable projection (VP). Applying VP operators to neural networks results in learnable features, interpretable parameters, and compact network structures. This paper discusses the motivation and mathematical background of VPNet and presents experiments. The VPNet approach was evaluated in the context of signal processing, where we classified a synthetic dataset and real electrocardiogram (ECG) signals. Compared to fully connected and one-dimensional convolutional networks, VPNet offers fast learning ability and good accuracy at a low computational cost of both training and inference. Based on these advantages and the promising results obtained, we anticipate a profound impact on the broader field of signal processing, in particular on classification, regression and clustering problems.

An Improved Tikhonov-Regularized Variable Projection Algorithm for Separable Nonlinear Least Squares

In this work, we investigate the ill-conditioned problem of a separable, nonlinear least squares model by using the variable projection method. Based on the truncated singular value decomposition method and the Tikhonov regularization method, we propose an improved Tikhonov regularization method, which neither discards small singular values, nor treats all singular value corrections. By fitting the Mackey–Glass time series in an exponential model, we compare the three regularization methods, and the numerically simulated results indicate that the improved regularization method is more effective at reducing the mean square error of the solution and increasing the accuracy of unknowns.