Lifted proximal operator machine-based deep nonlinear dictionary learning with multilayer regularization

doi:10.1016/j.neucom.2025.129390

2025-03-01

PRE

DOI：10.1016/j.neucom.2025.129390

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Nonlinear dictionary learning (NLDL) can mine nonlinear information in data better than linear models. Mainstream NLDL methods are based on kernel methods; however, their large storage requirements pose computational challenges and are difficult to scalability. Moreover, the single-layer NLDL framework cannot capture deep features and requires the reversibility of nonlinear functions, leaving room for improving nonlinear signal representation. Inspired by deep dictionary learning, we design a generalized deep nonlinear dictionary learning model called DNLDL_Sp. This model features deep and nonlinear structures. In the proposed model, data are decomposed into nonlinear mappings of several dictionary layers, and the coefficients of the deeper layers are learned via dictionary learning in the preceding layers. We impose sparsity constraints on the coefficients of each layer of DNLDL_Sp to achieve a concise and accurate representation of the data, and this representation proves to be more effective than single-layer structures in capturing deep nonlinear representations. To optimize DNLDL_Sp and prevent issues such as loss of accuracy due to the inverse operation of the nonlinear function, we employ the lifted proximal operator machine (LPOM) technology to transform the nonlinear function into an equivalent proximal operator, which is then incorporated into the model as a penalty. This method converts the nonconvex optimization problem into a series of convex subproblems, allowing us to obtain the optimal dictionaries and coefficients through alternating updates. We demonstrate the effectiveness of our algorithm via image classification and denoising experiments involving different nonlinear functions and sparse constraints.

Keyword:

Nonlinear dictionary learning

Sparse regularization

Deep features

Lifted proximal operator machine

Image classification and denoising