Parallelized Tensor Train Learning of Polynomial Classifiers.

Area of Science:

• Machine Learning
• Pattern Recognition
• Computational Mathematics

Background:

• Polynomial classifiers are effective for complex decision surfaces but struggle with high-dimensional data.
• The curse of dimensionality limits the practical application of multivariate polynomials in machine learning.
• Existing methods often rely on kernel tricks, which can be computationally intensive.

Purpose of the Study:

• To overcome the curse of dimensionality in polynomial classifiers.
• To introduce a novel tensor train (TT) based approach for polynomial classification.
• To develop efficient learning algorithms for TT-represented polynomial classifiers.

Main Methods:

• Representing polynomial classifiers using the tensor train (TT) format.
• Developing two learning algorithms based on the TT structure, involving low-complexity optimization problems.
• Incorporating regularization for overfitting prevention and parallelization for large datasets.

Main Results:

• Successfully demonstrated the ability to represent polynomial classifiers in the TT format.
• Proposed and implemented two computationally efficient learning algorithms.
• Showcased the effectiveness and efficiency of the TT-based polynomial classifier on benchmark datasets (USPS and NIST).

Conclusions:

• The tensor train format effectively overcomes the curse of dimensionality for polynomial classifiers.
• The proposed TT-based polynomial classifier offers an efficient and scalable solution for pattern classification.
• This method holds promise for applications involving high-dimensional data in pattern recognition.