scholarly journals On the expectation of a persistence diagram by the persistence weighted kernel

2019 ◽  
Vol 36 (3) ◽  
pp. 861-892
Author(s):  
Genki Kusano
2017 ◽  
Vol 4 (2) ◽  
Author(s):  
Elizabeth Munch

Topological data analysis (TDA) is a collection of powerful tools that can quantify shape and structure in data in order to answer questions from the data’s domain. This is done by representing some aspect of the structure of the data in a simplified topological signature. In this article, we introduce two of the most commonly used topological signatures. First, the persistence diagram represents loops and holes in the space by considering connectivity of the data points for a continuum of values rather than a single fixed value. The second topological signature, the mapper graph, returns a 1-dimensional structure representing the shape of the data, and is particularly good for exploration and visualization of the data. While these techniques are based on very sophisticated mathematics, the current ubiquity of available software means that these tools are more accessible than ever to be applied to data by researchers in education and learning, as well as all domain scientists.


Sensors ◽  
2020 ◽  
Vol 20 (15) ◽  
pp. 4081
Author(s):  
Chuljoong Kim ◽  
Hanseok Ko

Visual object tracking is an important component of surveillance systems and many high-performance methods have been developed. However, these tracking methods tend to be optimized for the Red/Green/Blue (RGB) domain and are thus not suitable for use with the infrared (IR) domain. To overcome this disadvantage, many researchers have constructed datasets for IR analysis, including those developed for The Thermal Infrared Visual Object Tracking (VOT-TIR) challenges. As a consequence, many state-of-the-art trackers for the IR domain have been proposed, but there remains a need for reliable IR-based trackers for anti-air surveillance systems, including the construction of a new IR dataset for this purpose. In this paper, we collect various anti-air thermal-wave IR (TIR) images from an electro-optical surveillance system to create a new dataset. We also present a framework based on an end-to-end convolutional neural network that learns object tracking in the IR domain for anti-air targets such as unmanned aerial vehicles (UAVs) and drones. More specifically, we adopt a Siamese network for feature extraction and three region proposal networks for the classification and regression branches. In the inference phase, the proposed network is formulated as a detection-by-tracking method, and kernel filters for the template branch that are continuously updated for every frame are introduced. The proposed network is able to learn robust structural information for the targets during offline training, and the kernel filters can robustly track the targets, demonstrating enhanced performance. Experimental results from the new IR dataset reveal that the proposed method achieves outstanding performance, with a real-time processing speed of 40 frames per second.


2020 ◽  
Vol 4 (4) ◽  
pp. 509-523
Author(s):  
Jacek Cyranka ◽  
Konstantin Mischaikow ◽  
Charles Weibel

Abstract This work is motivated by the following question in data-driven study of dynamical systems: given a dynamical system that is observed via time series of persistence diagrams that encode topological features of snapshots of solutions, what conclusions can be drawn about solutions of the original dynamical system? We address this challenge in the context of an N dimensional system of ordinary differential equation defined in $${\mathbb {R}}^N$$ R N . To each point in $${\mathbb {R}}^N$$ R N (e.g. an initial condition) we associate a persistence diagram. The main result of this paper is that under this association the preimage of every persistence diagram is contractible. As an application we provide conditions under which multiple time series of persistence diagrams can be used to conclude the existence of a fixed point of the differential equation that generates the time series.


2012 ◽  
Vol 27 ◽  
pp. 424-442 ◽  
Author(s):  
Mohammad Hossein Zangooei ◽  
Saeed Jalili

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