Distributed Trace Ratio Optimization in Fully-Connected Sensor Networks

Abstract

The trace ratio optimization problem consists of maximizing a ratio between two trace operators and often appears in dimensionality reduction problems for denoising or discriminant analysis. In this paper, we propose a distributed and adaptive algorithm to solve the trace ratio optimization problem over network-wide covariance matrices, which capture the spatial correlation across sensors in a wireless sensor network. We focus on fully-connected network topologies, in which case the distributed algorithm reduces the communication bottleneck by only sharing a compressed version of the observed signals at each given node. Despite this compression, the algorithm can be shown to converge to the maximal trace ratio as if all nodes would have access to all signals in the network. We provide simulation results to demonstrate the convergence and optimality properties of the proposed algorithm.

Energy-Efficient Deep Neural Networks for EEG Signal Noise Reduction in Next-Generation Green Wireless Networks and Industrial IoT Applications

“…High-density sensing modalities, such as HD-EEG, HD-sEMG, and HD-ECG, are often deployed in mini-scale homogeneous WBANs, which can act as sub-networks within larger heterogeneous WBAN systems. Such systems are particularly useful for long-term neuromonitoring of diseases such as epilepsy, Parkinson's, and Alzheimer's, owing to their low power consumption and potential for miniaturization [50][51][52][53].…”

Distributed Adaptive Trace Ratio Optimization in Wireless Sensor Networks

“…T HE trace ratio optimization (TRO) problem is the maximization of the ratio between two quadratic forms, where the optimization variable X is required to have orthonormal columns. Mathematically, it can be expressed as: maximize X tr(X T AX) tr(X T BX) subject to X T X = I, (1) where A and B are positive definite matrices, I is the identity matrix and "tr" and "T " denote the trace and transpose operators respectively. Note that Problem (1) is different from a standard generalized Rayleigh quotient optimization, due to the presence of additional orthogonality constraints on X, and therefore the solution is not provided by a generalized eigenvalue decomposition (GEVD).…”

“…Musluoglu Leuven, Belgium and with Leuven.AI -KU Leuven institute for AI. e-mail: cemates.musluoglu, alexander.bertrand @esat.kuleuven.be A conference precursor of this manuscript has been published in [1].…”

“…It was however mentioned in [2] that this latter technique suffers from separability issues on the projected set of vectors. Therefore, the generalized Foley-Sammon transform was defined in [2] as maximizing the ratio of two trace operators, which led to the TRO problem (1). Several methods to solve the general TRO problem have been described in the literature, using the Grassmann manifold [5], by semi-definite programming [7], and using an iterative method related to the Rayleigh quotient iteration [2]- [4].…”

“…The distributed TRO (DTRO) algorithm is proven to converge to the solution of the centralized TRO problem, as if each node would have access to all sensor data in the network without the need to explicitly estimate the full network-wide correlation structure. A conference precursor describing the DTRO algorithm for fully-connected WSNs has been published in [1]. In this paper, we provide a more detailed analysis, a proof of convergence, an extension to arbitrary topologies, and more extensive experimental analyses.…”