DuSK: A Dual Structure-preserving Kernel for Supervised Tensor Learning with Applications to Neuroimages.

Area of Science:

• Machine Learning
• Data Mining
• Computational Neuroscience

Background:

• Tensor data is increasingly prevalent across various applications.
• Supervised tensor learning is crucial for extracting insights from complex tensor datasets.
• Existing methods often lose structural information by vectorizing or matrix-flattening tensors.

Purpose of the Study:

• To develop a novel kernel for supervised tensor learning that preserves the inherent structure of tensor data.
• To encode prior knowledge into the kernel by leveraging the natural structure within tensorial representations.
• To improve the performance of tensor classification tasks, particularly in scenarios with limited sample sizes.

Main Methods:

• Proposed a new scheme for designing structure-preserving kernels for supervised tensor learning.
• Introduced a dual-tensorial mapping function to map tensor instances while preserving their structure.
• Integrated the novel tensor kernel with Support Vector Machines (SVM) for classification.

Main Results:

• The proposed dual-tensorial mapping kernel effectively preserves tensor structures.
• The novel kernel, when used with SVM, demonstrated improved performance in real-world tensor classification problems.
• Significant performance boosts were observed in brain fMRI classification for diseases like Alzheimer's, ADHD, and HIV-related brain damage, especially with small sample sizes.

Conclusions:

• The developed structure-preserving tensor kernel offers a significant advancement in supervised tensor learning.
• This approach extends conventional kernel methods to the tensor space, maintaining crucial structural information.
• The method shows strong potential for applications in medical diagnosis and other fields dealing with high-dimensional tensor data.