PI-Net：一种提取拓扑持久图像的深度学习方法
PI-Net: A Deep Learning Approach to Extract Topological Persistence Images
摘要：
拓扑特征，如持久性图和它们的函数近似，如持久性图像（PI），已经显示出机器学习和计算机视觉应用的实质性前景。这在很大程度上归因于拓扑表示提供的鲁棒性，以对抗现实世界数据中看到的不同类型的物理干扰变量，例如视点，照明等。然而，它们大规模采用的关键瓶颈是计算支出和难以将它们纳入可区分的架构中。在本文中，我们采取了重要的一步，以减轻这些瓶颈，提出了一种新的一步的方法来生成PI直接从输入数据。我们设计了两个独立的卷积神经网络架构，一个设计为接受多变量时间序列信号作为输入，另一个接受多通道图像作为输入。我们分别将这些网络称为信号PI网络和图像PI网络。据我们所知，我们是第一个提出使用深度学习直接从数据中计算拓扑特征的人。我们探讨了两个应用程序中使用的建议PI-网络架构：人类活动识别使用三轴加速度传感器数据和图像分类。我们展示了在监督式深度学习架构中PI融合的容易性，并从数据中提取PI的速度提高了几个数量级。我们的代码可在https://github.com/anirudhsom/PI-Net上获得。
英文摘要：
Topological features such as persistence diagrams and their functional approximations like persistence images (PIs) have been showing substantial promise for machine learning and computer vision applications. This is greatly attributed to the robustness topological representations provide against different types of physical nuisance variables seen in real-world data, such as view-point, illumination, and more. However, key bottlenecks to their large scale adoption are computational expenditure and difficulty incorporating them in a differentiable architecture. We take an important step in this paper to mitigate these bottlenecks by proposing a novel one-step approach to generate PIs directly from the input data. We design two separate convolutional neural network architectures, one designed to take in multi-variate time series signals as input and another that accepts multi-channel images as input. We call these networks Signal PI-Net and Image PI-Net respectively. To the best of our knowledge, we are the first to propose the use of deep learning for computing topological features directly from data. We explore the use of the proposed PI-Net architectures on two applications: human activity recognition using tri-axial accelerometer sensor data and image classification. We demonstrate the ease of fusion of PIs in supervised deep learning architectures and speed up of several orders of magnitude for extracting PIs from data. Our code is available at https://github.com/anirudhsom/PI-Net.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
