A kernel-based framework to tensorial data analysis.

Area of Science:

• Machine Learning
• Data Science
• Applied Mathematics

Background:

• Tensor-based learning exploits data structure, beneficial for small datasets in biosignal processing and chemometrics.
• Existing tensor models have limitations in discriminative power.
• Kernel methods offer flexibility but don't utilize tensor structure.

Purpose of the Study:

• Introduce non-parametric tensor-based models to overcome limitations of existing methods.
• Enhance the discriminative power of supervised tensor models.
• Exploit structural information within data tensors.

Main Methods:

• Introduce a feature space using multilinear functionals, the infinite-dimensional analogue of tensors.
• Develop kernels that exploit the algebraic structure of data tensors for implicit mapping.
• Utilize a framework compatible with Support Vector Machine (SVM)-like algorithms.

Main Results:

• Proposed tensorial kernel links to Multilinear Singular Value Decomposition (MLSVD).
• The approach exhibits an invariance property.
• The framework results in convex optimization problems.

Conclusions:

• The novel framework effectively integrates tensor structure with kernel methods.
• Achieves improved discriminative power for tensor-based learning.
• Offers a flexible and powerful approach for analyzing structured data.