Adaptive Diffusion Pairwise Fused Lasso LMS Algorithm Over Networks.

Area of Science:

• Adaptive filtering
• Signal processing
• Machine learning

Background:

• Sparse vector identification is crucial in adaptive filtering.
• Existing methods often rely on clustered components, limiting applicability.
• The pairwise fused lasso technique promotes similarity among non-negligible components, regardless of their distribution.

Purpose of the Study:

• To propose a novel algorithm for identifying sparse vectors in a distributed manner.
• To address the challenge of randomly scattered non-negligible components in sparse vectors.
• To enhance the performance of sparse parameter identification and tracking.

Main Methods:

• Development of the pairwise fused lasso diffusion least mean-square (PFL-DLMS) algorithm.
• Construction of an objective function including mean-square error, component sparsity, and pairwise component difference sparsity.
• Theoretical analysis of mean stability conditions for mean-square behavior.
• Implementation of a variable regularizing coefficients strategy.

Main Results:

• The proposed PFL-DLMS algorithm demonstrates effectiveness in identifying sparse vectors.
• Numerical experiments validate the algorithm's capability in tracking sparse parameter vectors.
• The pairwise fused lasso approach proves beneficial for non-uniformly distributed sparse components.

Conclusions:

• The PFL-DLMS algorithm offers a robust solution for sparse vector identification in adaptive filtering.
• The variable regularizing coefficients strategy effectively handles unknown optimal coefficients.
• The method is particularly advantageous when sparse components are randomly scattered.