Learning Collaborative Sparsity Structure via Nonconvex Optimization for Feature Recognition

This paper aims to unveil a collaborative sparsity structure for rigorously describing the universal self-similarity property of mechanical feature information, which is an important task in the field of adaptive feature recognition. The self-similarity pattern among all local feature segments is first highlighted by an elaborately designed partition strategy, and then a row-wise group sparsity penalty is enforced under an appropriate dictionary to effectively capture the latent self-similarity features from noisy observations. Incorporating dictionary learning techniques, a collaborative sparsity learning model (CSLM) is further proposed, and meanwhile solved by a nonconvex optimization solver generated from a block proximal gradient descend framework. Moreover, the convergence property and computational complexity of the developed solver are discussed comprehensively. The advantage of this model is to adaptively achieve a satisfying sparse level to concentrate the underlying feature information and simultaneously enforce that all segments share a same active atom set to retain the desired self-similarity pattern. The proposed CSLM is profoundly evaluated through implementing feature detection for wind turbine gearbox, and it shows superior performances to many state-of-the-art feature recognition techniques.