This paper presents a novel approach for structure extraction of the cluster sparse system identification. Different from adopting \(\ell _1\)-norm constraint to regularize the sparsity in the improved proportionate normalized least mean square (IPNLMS) algorithm, we directly work with the block sparse structure via \(\ell _{1,0}\)-norm constraint. In particular, we develop a cluster sparse IPNLMS by the block \(\ell _0\) norm regularization, named IPNLMS-BL0 method. The cluster sparse constraint is regarded as an extended version for the sparse constraint term. On the other hand, the iterations of IPNLMS-BL0 are derived by the steepest descent strategy. Then, we provide the analysis of block size choices of the cluster sparse constraint, computational complexity, and steady-state error of the proposed method. Various simulations are designed to test the performance of the IPNLMS-BL0 algorithm and its counterparts to identify and track the unknown sparse systems. The results are provided and analyzed to confirm the effectiveness and superiority of the proposed IPNLMS-BL0 algorithm.

本文提出了一种新的聚类稀疏系统识别结构提取方法。与在改进的比例归一化最小均方 (IPNLMS) 算法中采用\(\ell _1\) -norm 约束对稀疏进行正则化不同，我们通过\(\ell _{1,0}\ ) -范数约束。特别是，我们通过块\(\ell _0\)开发了一个集群稀疏 IPNLMS范数正则化，命名为 IPNLMS-BL0 方法。簇稀疏约束被认为是稀疏约束项的扩展版本。另一方面，IPNLMS-BL0 的迭代是通过最速下降策略导出的。然后，我们分析了所提出方法的簇稀疏约束、计算复杂度和稳态误差的块大小选择。设计了各种模拟来测试 IPNLMS-BL0 算法及其对应算法的性能，以识别和跟踪未知的稀疏系统。提供并分析结果以确认所提出的 IPNLMS-BL0 算法的有效性和优越性。