Kernel map compression for speeding the execution of kernel-based methods.

Area of Science:

• Machine Learning
• Statistical Learning Theory
• Computational Complexity

Background:

• Mercer kernel methods, including kernel principal component analysis (KPCA) and support vector machines (SVM), are powerful tools in statistical learning.
• A significant drawback is the high computational complexity during execution, scaling linearly with the training set size.

Purpose of the Study:

• To develop a computationally efficient execution procedure for Mercer kernel methods.
• To address the scalability limitations of kernel-based algorithms in large-scale applications.

Main Methods:

• A novel two-step procedure is proposed for kernel execution.
• Generalized radial basis function (RBF) neural networks are employed to approximate kernel map projections.
• The RBF network replaces computationally intensive kernel computations after the initial learning phase.

Main Results:

• The proposed method achieves significant compression of the kernel representation.
• The generalized RBF neural network effectively approximates the empirical kernel map.
• Applications demonstrate a reduction in computational complexity with acceptable performance degradation.

Conclusions:

• The two-step procedure offers a computationally efficient alternative for executing Mercer kernel methods.
• Generalized RBF neural networks provide a viable method for approximating kernel maps, enhancing scalability.
• This approach balances computational efficiency with learning performance for practical applications.