A Generalized Graph Regularized Non-Negative Tucker Decomposition Framework for Tensor Data Representation.

Area of Science:

• Multivariate statistics
• Machine learning
• Data mining

Background:

• Non-negative Tucker decomposition (NTD) is a widely used technique for tensor data representation.
• Existing methods often struggle to incorporate intrinsic cues like manifold structure and supervisory information effectively.
• There is a need for advanced tensor decomposition methods that leverage both unsupervised and semi-supervised learning paradigms.

Purpose of the Study:

• To propose a generalized graph regularized non-negative Tucker decomposition (GNTD) framework.
• To enhance tensor representation by integrating manifold structure and supervisory information.
• To develop effective unsupervised and semi-supervised tensor decomposition methods.

Main Methods:

• Developed unsupervised GNTD (UGNTD) by constructing a nearest neighbor graph to preserve tensor data's intrinsic manifold structure.
• Formulated semi-supervised GNTD (SGNTD) by propagating constraints and building a semi-supervised graph weight matrix.
• Employed a fast, efficient alternating proximal gradient-based algorithm for optimization, demonstrating convergence and correctness.

Main Results:

• The proposed UGNTD effectively maintains the intrinsic manifold structure of tensor data.
• SGNTD successfully leverages limited must-link and cannot-link constraints for improved representation.
• Experimental results on four image datasets show superior performance in unsupervised and semi-supervised clustering tasks.

Conclusions:

• The generalized graph regularized NTD framework offers a powerful approach for tensor data representation.
• Both unsupervised and semi-supervised variants (UGNTD and SGNTD) demonstrate significant effectiveness and efficiency.
• The proposed methods provide a robust solution for complex tensor decomposition and clustering problems.