摘要翻译：
寻找高维多模态数据的适当的低维表示可能是一个挑战，因为每个模态都体现了独特的变形和干扰。本文利用流形学习的方法来解决这个问题，其中每个模态的数据都假设位于某个流形上。在这种背景下，目标是通过研究它们的潜在流形来描述不同模态之间的关系。我们提出了两种新的扩散算子，允许以数据驱动的方式隔离、增强和衰减多模态数据的隐藏分量。基于这些新算子，可以为这些数据构造高效的低维表示，这些表示表征了不同模态下流形的共同结构和差异。所提出的操作员的能力在3D形状和胎儿心率监测应用程序上进行了演示。
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英文标题：
《Recovering Hidden Components in Multimodal Data with Composite Diffusion
  Operators》
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作者：
Tal Shnitzer, Mirela Ben-Chen, Leonidas Guibas, Ronen Talmon,
  Hau-Tieng Wu
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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：
  Finding appropriate low dimensional representations of high-dimensional multi-modal data can be challenging, since each modality embodies unique deformations and interferences. In this paper, we address the problem using manifold learning, where the data from each modality is assumed to lie on some manifold. In this context, the goal is to characterize the relations between the different modalities by studying their underlying manifolds. We propose two new diffusion operators that allow to isolate, enhance and attenuate the hidden components of multi-modal data in a data-driven manner. Based on these new operators, efficient low-dimensional representations can be constructed for such data, which characterize the common structures and the differences between the manifolds underlying the different modalities. The capabilities of the proposed operators are demonstrated on 3D shapes and on a fetal heart rate monitoring application.
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PDF链接：
https://arxiv.org/pdf/1808.07312