The trace ratio optimization (TRO) problem consists of finding an orthonormal basis for the discriminative subspace that maximizes the ratio of two trace operators on two covariance matrices corresponding to two distinctive classes or signal components. The TRO problem is encountered in various signal processing problems such as dimensionality reduction, signal enhancement, and discriminative analysis. In this paper, we propose a distributed and adaptive algorithm for solving the TRO problem in the context of wireless sensor networks (WSNs), where the two matrices involved in the trace ratio operators correspond to the (unknown) spatial correlation of the sensor signals across the nodes in the network. We first focus on fully-connected networks where every node can communicate with each other, but only compressed signals observations can be shared to reduce the communication cost. After showing convergence, we modify the algorithm to operate in WSNs with more general topologies. Simulation results are provided to validate and complement the theoretical results.

中文翻译：

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无线传感器网络中的分布式自适应迹线比优化


迹比优化 (TRO) 问题包括找到判别子空间的标准正交基，以最大化对应于两个不同类别或信号分量的两个协方差矩阵上的两个迹算子的比率。 TRO问题在降维、信号增强、判别分析等各种信号处理问题中都会遇到。在本文中，我们提出了一种分布式自适应算法，用于解决无线传感器网络（WSN）背景下的 TRO 问题，其中迹比算子中涉及的两个矩阵对应于传感器信号的（未知）空间相关性。网络中的节点。我们首先关注全连接网络，其中每个节点都可以相互通信，但只能共享压缩信号观测值以降低通信成本。显示收敛性后，我们修改算法以在具有更通用拓扑的 WSN 中运行。提供仿真结果来验证和补充理论结果。