Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning.

Area of Science:

• Multiway data analysis
• Machine learning
• Tensor decomposition

Background:

• Tensor-ring (TR) decomposition is effective for low-rank multiway data.
• Existing methods lack parts-based representation and manifold geometry capture.

Purpose of the Study:

• Introduce non-negative TR (NTR) decomposition.
• Propose graph-regularized NTR (GNTR) decomposition.
• Enhance representation learning for non-negative multiway data.

Main Methods:

• Developed non-negative TR (NTR) decomposition by imposing non-negativity on core tensors.
• Introduced graph regularization to NTR for manifold geometry.
• Derived optimization algorithms using accelerated proximal gradient for NTR and GNTR.

Main Results:

• NTR and GNTR provide interpretable, parts-based representations.
• Methods successfully extract meaningful components like color and line patterns.
• Experimental results show superior performance in clustering and classification over state-of-the-art tensor methods.

Conclusions:

• NTR and GNTR are powerful extensions of TR decomposition for non-negative multiway data.
• These models offer improved representation learning capabilities.
• The proposed methods demonstrate significant advantages in downstream tasks like clustering and classification.