A Fused CP Factorization Method for Incomplete Tensors

Area of Science:

• Multimode data analysis
• Machine learning
• Signal processing

Background:

• Low-rank tensor completion is crucial for modeling sparse, multi-structured data.
• Existing low-rank priors may not adequately interpret general tensor factors.
• Current regularization methods for tensor completion are often inefficient and lack systematic evaluation.

Purpose of the Study:

• To develop an advanced tensor factorization framework integrating multiple regularization techniques.
• To address the limitations of existing methods in handling complex multiway data.
• To provide experimental insights into the effectiveness of various regularizations for tensor completion.

Main Methods:

• Proposed a modified CP tensor factorization framework.
• Fused l2 norm, l1 norm (sparseness), manifold, and smooth information.
• Employed Nesterov's optimal gradient descent and block coordinate descent.
• Utilized projected gradient method with Lipschitz constant for step size determination.

Main Results:

• Demonstrated the efficiency of the proposed method on simulation, visual, intelligent transportation, and GPS data.
• Successfully completed various types of multiway data.
• Confirmed the effectiveness of the fused regularization approach.

Conclusions:

• The novel framework effectively completes multiway data by integrating diverse regularizations.
• The study provides valuable experimental guidance on selecting and utilizing regularizations for tensor completion.
• Offers a more robust approach compared to single or limited regularization techniques.