扩散中的多核分布式自适应学习 网络

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摘要翻译：
提出了一种自适应的非线性函数分布式学习算法。该算法包括一个局部自适应阶段，利用多个核函数在hyperslabs上进行投影，以及一个在整个网络上实现一致估计的扩散阶段。多个核的结合，以增强函数的逼近与几个高低频成分在实际场景中常见。基于多重再生核Hilbert空间的笛卡尔积度量，我们给出了该格式的全面收敛性分析。为此，我们引入了一个改进的一致性矩阵，并证明了它与普通一致性矩阵的等价性。此外，使用hyperslabs可以大大减少计算需求，而性能只会有很小的损失。用合成数据和实际数据进行了数值评估，表明了所提算法与现有方案相比的有效性。
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英文标题：
《Distributed Adaptive Learning with Multiple Kernels in Diffusion
  Networks》
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作者：
Ban-Sok Shin, Masahiro Yukawa, Renato Luis Garrido Cavalcante, Armin
  Dekorsy
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.
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PDF链接：
https://arxiv.org/pdf/1801.07087

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关键词：分布式 Applications Optimization Application distributed 一致性 全面 格式 学习 kernels