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A Novel Hierarchical Deep Matrix Completion Method
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DOI：10.1109/ACCESS.2021.3049297.png)
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摘要
En 中文
The matrix completion technique based on matrix factorization for recovering missing items is widely used in collaborative filtering, image restoration, and other applications. We proposed a new matrix completion model called hierarchical deep matrix completion (HDMC), where we assume that the variables lie in hierarchically organized groups. HDMC explicitly expresses either shallow or high-level hierarchical structures, such as taxonomy trees, by embedding a series of so-called structured sparsity penalties in a framework to encourage hierarchical relations between compact representations and reconstructed data. Moreover, HDMC considers the group-level sparsity of neurons in a neural network to obtain a pruning effect and compact architecture by enhancing the relevance of within-group neurons while neglecting the between-group neurons. Since the optimization of HDMC is a nonconvex problem, to avoid converting the framework of the HDMC models into separate optimized formulations, we unify a generic optimization by applying a smoothing proximal gradient strategy in dual space. HDMC is compared with state-of-the-art matrix completion methods on applications with simulated data, MRI image datasets, and gene expression datasets. The experimental results verify that HDMC achieves higher matrix completion accuracy.
Keyword:
Neurons
Taxonomy
Matrix converters
Optimization
Indexes
Image reconstruction
Diseases
Matrix completion
hierarchical relation
structured sparsity
regulation
neural network
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