Robust Corrupted Data Recovery and Clustering via Generalized Transformed Tensor Low-Rank Representation

Area of Science:

• Data Science
• Machine Learning
• Tensor Analysis

Background:

• High-dimensional tensor data learning is crucial but faces challenges from signal corruptions like missing entries and noise.
• Recovering corrupted tensor data for downstream tasks, such as clustering, remains a significant problem.

Purpose of the Study:

• To propose a novel generalized transformed tensor low-rank representation (TTLRR) model for simultaneous recovery and clustering of corrupted tensor data.
• To develop a robust method capable of handling arbitrary signal corruptions in tensor data.

Main Methods:

• The core methodology involves finding latent low-rank tensor structures using transformed tensor singular value decomposition (SVD).
• The model adaptively learns transformations from data to represent intrinsic subspaces and cluster structures.
• An algorithm based on the alternating direction method of multipliers (ADMMs) framework is employed to solve the proposed model.

Main Results:

• Theoretical guarantees show TTLRR can recover clean tensor data with high probability under mild conditions.
• The TTLRR model accurately represents intrinsic subspaces and identifies cluster structures in corrupted tensor data.
• Experimental results demonstrate the effectiveness and superiority of TTLRR over existing methods in data recovery and clustering tasks.

Conclusions:

• The proposed TTLRR model offers a powerful approach for simultaneously recovering and clustering corrupted high-dimensional tensor data.
• TTLRR shows significant advantages in handling real-world data imperfections and improving clustering performance across various applications.