Improving KPCA Online Extraction by Orthonormalization in the Feature Space.

Area of Science:

• Machine Learning
• Data Science
• Computational Statistics

Background:

• Online Kernel Principal Component Analysis (KPCA) methods, utilizing the generalized Hebbian algorithm (GHA), have been developed for analyzing large datasets.
• These methods extract kernel components using dictionaries automatically derived from the data.

Purpose of the Study:

• To introduce two novel online KPCA algorithms.
• To enhance the performance of existing GHA-based KPCA techniques.

Main Methods:

• Development of two new online KPCA algorithms based on orthogonalized versions of the GHA rule.
• Integration of low-complexity orthogonalization steps into the kernel Hebbian algorithm without significant computational overhead.

Main Results:

• The proposed methods demonstrate improved convergence speed compared to current state-of-the-art online KPCA algorithms.
• Enhanced accuracy in the extraction of kernel components was observed.

Conclusions:

• The novel orthogonalized GHA-based online KPCA algorithms offer superior performance in terms of speed and accuracy.
• These methods provide an efficient approach for kernel component extraction in large-scale data analysis.