Efficient Learning of Transform-Domain LMS Filter Using Graph Laplacian.

Area of Science:

• Signal Processing
• Machine Learning
• Adaptive Filters

Background:

• Transform-domain Least Mean Squares (TDLMS) adaptive filters use data-independent transforms for preprocessing.
• Conventional transforms offer limited convergence improvement for Least Mean Squares (LMS) filters, especially when input data characteristics are unknown.
• A data-dependent transformation is needed to optimize filter performance across diverse datasets.

Purpose of the Study:

• To develop a learning framework for adaptively obtaining preconditioning transformations.
• To investigate the hypothesis that data topology influences the choice of transformation.
• To introduce Preconditioning using Graph (PrecoG) for learning data-specific transforms.

Main Methods:

• Input data is modeled as a weighted finite graph.
• The PrecoG method adaptively learns the transformation by recursively estimating the graph Laplacian matrix.
• The learned transform is evaluated as a generalized split preconditioner for linear systems and Hebbian-LMS models.

Main Results:

• PrecoG effectively learns data-dependent transformations.
• The method demonstrates significant improvement in the condition number after transformation.
• PrecoG outperforms existing state-of-the-art techniques using both unitary and nonunitary transforms.

Conclusions:

• PrecoG provides an effective approach to learn optimal preconditioning transformations for adaptive filters.
• The graph-based modeling captures data topology crucial for transformation selection.
• This adaptive strategy enhances the convergence and performance of LMS-based learning models.