Abstract Localization of sensor nodes is becoming an interesting research area in wireless sensor networks(WSNs). In recent years, some localization algorithms are presented based on manifold learning which can achieve good performance. In this paper, based on the need of practical application and the development of manifold learning theory in WSNs, the localization problem is considered for fast determining the locations of unknown nodes in large scale WSNs. For this purpose, a new semi-supervised manifold learning algorithm is proposed based on polynomial mapping which is the combination of Gaussian kernel embedding and polynomial kernel embedding algorithms. This method is to compute a polynomial mapping function between the high dimensional location data space and the low dimensional physical space, which can obtain an explicit nonlinear feature mapping and has a high discriminative ability. At last, comparing with some related localization approaches, the performance of the proposed algorithm is evaluated and analyzed under different signal noise, anchor nodes, and communication range, respectively. In terms of the root-mean-square error and computational complexity, the experiment results demonstrate that the proposed algorithm has faster speed for large scale sensor nodes and higher accuracy with a small amount of known nodes.

中文翻译：

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基于多项式映射的无线传感器网络定位半监督流形学习

摘要 传感器节点定位正在成为无线传感器网络（WSNs）中一个有趣的研究领域。近年来，提出了一些基于流形学习的定位算法，可以获得良好的性能。在本文中，基于实际应用的需要和流形学习理论在 WSN 中的发展，考虑定位问题以快速确定大规模 WSN 中未知节点的位置。为此，提出了一种新的基于多项式映射的半监督流形学习算法，该算法是高斯核嵌入和多项式核嵌入算法的结合。该方法是计算高维位置数据空间和低维物理空间之间的多项式映射函数，可以得到显式的非线性特征映射，并且具有很高的判别能力。最后，与一些相关的定位方法进行比较，分别在不同的信号噪声、锚节点和通信范围下对所提算法的性能进行了评估和分析。在均方根误差和计算复杂度方面，实验结果表明，该算法对于大规模传感器节点具有更快的速度，在已知节点数量较少的情况下具有更高的精度。