Multi-Branch Tensor Network Structure for Tensor-Train Discriminant Analysis.

Area of Science:

• Computer Science
• Data Science
• Machine Learning

Background:

• High-dimensional data, common in computer vision and medical imaging, poses storage and computational challenges for tensor-based supervised learning.
• Existing tensor decomposition methods like Tucker and tensor-train (TT) struggle with efficiency and complexity.
• Tensors are natural tools for representing higher-order, high-dimensional datasets.

Purpose of the Study:

• To address the storage complexity and computational inefficiency of current tensor-based supervised learning algorithms.
• To introduce a flexible and general tensor decomposition structure for improved performance.
• To develop a novel supervised learning approach for high-dimensional tensor data.

Main Methods:

• Introduction of a multi-branch tensor network structure, a generalized tensor decomposition.
• Implementation of tensor-train discriminant analysis (TTDA) using the multi-branch tensor network.
• Comparison of multi-branch TTDA with Tucker and TT-based supervised learning methods.

Main Results:

• The multi-branch tensor network offers a flexible balance between storage and computational complexity.
• Multi-branch implementations of TTDA demonstrate reduced storage and computational requirements.
• TTDA using the multi-branch structure achieved superior classification performance compared to Tucker and TT methods.

Conclusions:

• The proposed multi-branch tensor network structure effectively mitigates storage and computational challenges in tensor learning.
• Tensor-train discriminant analysis (TTDA) implemented with multi-branch networks provides an efficient and high-performing solution for high-dimensional data analysis.
• This approach offers significant advantages for applications involving complex, high-dimensional datasets such as medical imaging and video analytics.