Spread and Sparse: Learning Interpretable Transforms for Bandlimited Signals on Directed Graphs
Spread and Sparse: Learning Interpretable Transforms for Bandlimited Signals on Directed Graphs
复制标题
DOI：
10.1109/acssc.2018.8645419
复制
发表时间：
2018-10
期刊：
影响因子：
--
通讯作者：
Rasoul Shafipour;G. Mateos
中科院分区：
文献类型：
--
作者：
Rasoul Shafipour;G. Mateos
我们解决的问题，学习稀疏图傅立叶变换（GFT）的可压缩信号的有向图（有向图）。混合傅立叶和字典学习表示的优点，我们的目标是获得一个正交的基础上，捕获信号变化的传播模式相对于底层网络拓扑结构，并产生简约的表示带限信号。因此，我们通过在可实现的频率范围内最小化频谱分散标准来学习数据自适应字典，沿着训练信号的GFT系数上的稀疏促进正则化项。开发了一种迭代算法，该算法在Stiefel流形上最小化平滑目标和训练集中信号的图谱域表示的软阈值之间交替。对美国邻近地区记录的温度测量结果进行频率分析，说明了新型GFT设计的优点。
We address the problem of learning a sparsifying graph Fourier transform (GFT) for compressible signals on directed graphs (digraphs). Blending the merits of Fourier and dictionary learning representations, the goal is to obtain an orthonormal basis that captures spread modes of signal variation with respect to the underlying network topology, and yields parsimonious representations of bandlimited signals. Accordingly, we learn a data-adapted dictionary by minimizing a spectral dispersion criterion over the achievable frequency range, along with a sparsity-promoting regularization term on the GFT coefficients of training signals. An iterative algorithm is developed which alternates between minimizing a smooth objective over the Stiefel manifold, and soft-thresholding the graph-spectral domain representations of the signals in the training set. A frequency analysis of temperature measurements recorded across the contiguous United States illustrates the merits of the novel GFT design.