BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features

该项目开发了一套来自拓扑数据分析(TDA)的新技术，以丰富大数据问题的分析工具包。特别是，TDA非常适合于提取存在于数据集内许多不同尺度级别的重复(甚至是准重复)模式。所开发的技术可应用于多种多媒体应用。例如，一个可以从大量监控数据中正确识别某些运动模式的系统可以帮助在出现威胁情况时进行识别。或者，一种获取短歌曲片段并提取流派相似性指标的方法最终可能被用来建议新的声音模式。这个项目构建了一个分析管道，用于对多媒体研究社区中已经使用的特征使用TDA-ML(机器学习)方法。拓扑数据分析(TDA)已有近十五年的历史。它的关键工具之一是持久性图(PD)，它是对高维点云中低维多尺度拓扑和几何信息的紧凑和健壮的总结。重要的是，无需降维即可提取该信息。在过去的几年里，两项令人振奋的发展丰富了TDA。首先，在算法和实现方面的理论和实践工作使大量PD的快速计算成为可能。其次，发展了一种连贯的方法来进行以PD为特征的机器学习(ML)，几个例子表明，人们可以用PD特征来扩充更多的标准特征集，并找到以前不明显的有趣信号。这项研究在这些特征中发现了令人信服的信号，这些信号以前并不明显，但由于特征的选择，这些信号立即就能被理解。研究小组对视频和音频功能进行了调查。ML方法被用来进一步衡量特征在给定上下文中的重要性。

This project develops a new set of techniques from topological data analysis (TDA) to enrich the analytical toolkit for big data problems. In particular, TDA is well-suited at picking up repetitive (even quasi-repetitive) patterns that exist at many different scale levels within a dataset. The developed techniques can be applied to many multimedia applications. For example, a system that can correctly recognize certain motion patterns from a large set of surveillance data can help to identify threatening situations as they arise. Or a methodology that takes short song snippets and extract indicators of genre similarity may eventually be used to suggest new sound patterns. This project constructs an analytical pipeline for using TDA-ML (machine-learning) methods on features already in use in the multimedia research communities. Topological Data Analysis (TDA) is almost fifteen years old. One of its key tools is the persistence diagram (PD), a compact and robust summary of the low-dimensional multi-scale topological and geometric information in a high-dimensional point cloud. Crucially, this information is extracted without need for dimension reduction. Over the last few years, two exciting developments have enriched TDA. First, theoretical and practical work on algorithms and implementations has enabled the fast computation of large numbers of PDs. Second, a coherent methodology has developed to do machine-learning (ML) with PDs as features, with several examples showing that one can augment more-standard feature sets with PD features, and find interesting signal that was not apparent before. This research discovers compelling signals in these features which are not previously apparent, but are immediately understandable because of the choice of features. The research team investigates both video and audio features. The ML methods are used to further measure importance of the features in a given context.