A Tensor Space for Multi-View and Multitask Learning Based on Einstein and Hadamard Products: A Case Study on Vehicle...

Area of Science:

• Computer Science
• Machine Learning
• Artificial Intelligence

Background:

• Multi-view learning enhances model performance by integrating information from diverse feature sets.
• Existing tensor-based data fusion layers (MV-DTF) face exponential growth in parameters and complexity with increasing views.
• This limits the scalability and practical application of multi-view learning in high-dimensional scenarios.

Purpose of the Study:

• To develop a computationally efficient tensor-based data fusion layer for neural networks.
• To address the challenge of exponential parameter growth in Multi-View Data Tensor Fusion (MV-DTF) as the number of views increases.
• To introduce a novel method for approximating the MV-DTF layer using low-rank tensor constraints.

Main Methods:

• Enforced low-rank constraints on subtensors of the MV-DTF layer's tensor A using canonical polyadic decomposition.
• Derived Hadamard factor tensors U(1),...,U(M) from the low-rank decomposition.
• Approximated the Einstein product A⊛MX using a sum of Hadamard products involving Einstein products of Hadamard factor tensors and individual views.

Main Results:

• The proposed low-rank approximation significantly reduces the computational complexity of the MV-DTF layer.
• A novel relationship between low-rank constraints and computational efficiency in tensor fusion was identified.
• In a vehicle traffic surveillance case study, the low-rank MV-DTF layer achieved notable improvements (up to 6-7%) in occlusion detection and vehicle-size classification.

Conclusions:

• The low-rank tensor fusion method offers a computationally efficient alternative for multi-view learning.
• This approach effectively handles data fusion with a large number of views without prohibitive computational cost.
• The method demonstrates practical utility and improved performance in real-world applications such as intelligent transportation systems.