Generalization performance of Fisher linear discriminant based on Markov sampling

Area of Science:

• Machine Learning
• Statistical Pattern Recognition
• Dimensionality Reduction

Background:

• Fisher linear discriminant (FLD) is a standard technique for dimensionality reduction and classification.
• Previous analyses of FLD generalization relied on independent and identically distributed (i.i.d.) samples.
• A need exists to explore FLD performance under more general sampling conditions.

Purpose of the Study:

• To investigate the generalization ability of Fisher linear discriminant (FLD) using Markov sampling.
• To establish theoretical bounds for FLD performance with uniformly ergodic Markov chain (u.e.M.c.) samples.
• To introduce a practical Markov sampling algorithm for FLD.

Main Methods:

• Theoretical analysis of FLD generalization bounds for u.e.M.c. samples.
• Development of a Markov sampling algorithm inspired by Markov chain Monte Carlo methods.
• Empirical validation using simulation studies and benchmark datasets.

Main Results:

• FLD based on u.e.M.c. samples is proven to be consistent.
• The proposed Markov sampling algorithm generates u.e.M.c. samples effectively.
• FLD utilizing u.e.M.c. samples achieved lower misclassification rates than FLD with i.i.d. samples.

Conclusions:

• Fisher linear discriminant (FLD) demonstrates consistent generalization performance with Markov sampling.
• Markov sampling offers a viable alternative to i.i.d. assumptions for FLD, potentially enhancing classification accuracy.
• The developed Markov sampling algorithm provides a practical method for improving FLD in real-world applications.