Joining the dots: from data to insight

数据的数量、种类、可用性和变化率的不断增长，已经深刻地改变了人类生活的方方面面。大数据革命创造了一个悖论：虽然我们创造和收集的数据比以往任何时候都多，但要解锁其中包含的信息并不总是那么容易。为了将数据的易获得性转化为重大的科学和经济优势，我们必须创建能够应对现代数据复杂性所带来的挑战的分析工具。近年来，拓扑数据分析和机器学习方面的突破为创建高效可靠的工具从数据中提取信息铺平了道路。我们的提案旨在解决为了"将产生的大量数据转换为可理解的、可操作的信息"，我们将创建一个强大的机器学习、统计和拓扑数据分析的融合。这种统计洞察力与机器学习的计算能力以及拓扑结构的灵活性、可扩展性和可视化工具的结合，将大大降低所研究数据的复杂性。结果将以最适合预期应用或手头科学问题的形式输出。通过这种方式，我们将创建一个从数据分析到实施的无缝路径，这将使我们能够控制这个过程的每一步。特别是，预期的最终用户将能够查询分析结果，以提取与他们相关的信息。总之，我们的工作将提供工具，从复杂的数据集提取信息，以支持用户的调查或决策。现在已经确定，大数据的主要挑战是如何“有效地和智能地从异构的，分布式的数据中提取知识，同时保留其解释所需的上下文”。这将首先通过开发处理异质数据的技术来解决。拓扑学的一个主要优点是它能够识别复杂系统中的简单组件。它还可以提供有关如何组合联合收割机元素以创建复杂系统模型的指导原则。它还提供数值技术来控制生成模型的整体形状，以确保其符合原始约束。我们将利用机器学习、统计学和拓扑学的特殊优势来识别数据的主要属性，然后将这些属性结合起来，对数据进行全面分析。例如，可以使用机器学习技术来分析文本文档的集合，以创建以拓扑方式捕获文档之间的相似性的图。这是一种根据所需的关键字集对文档语料库进行分类的有效方法。我们研究的一个重要部分将是开发强大的数据融合技术。这在许多应用中很重要。我们的一个主要应用程序将解决创建一组描述符来诊断和治疗哮喘的问题。哮喘的临床诊断有五种主要途径，每种途径都有数据支持。为了创建一个连贯的疾病图片，我们需要了解如何将这些单独的数据集中包含的信息联合收割机组合起来，以创建所谓的"哮喘手印"，这是医学这一部分的一个主要挑战。每一种新的数据分析方法都必须证明其"技术是现实的，与真实的世界服务和硬件系统兼容和可扩展的"。要做到这一点，最好的方法是从一开始就参与具有挑战性的应用，并确保理论和建模解决方案能够很好地适应预期的应用。我们提供理论和建模之间的独特协同作用，以及世界一流的医学和化学设施，这将为我们的想法和结果提供严格的测试。

The relentless growth of the amount, variety, availability, and the rate of change of data has profoundly transformed essentially all aspects of human life. The Big Data revolution has created a paradox: While we create and collect more data than ever before, it is not always easy to unlock the information it contains. To turn the easy availability of data into a major scientific and economic advantage, it is imperative that we create analytic tools that would be equal to the challenge presented by the complexity of modern data.In recent years, breakthroughs in topological data analysis and machine learning have paved the way for significant progress towards creating efficient and reliable tools to extract information from data.Our proposal has been designed to address the scope of the call as follows.To 'convert the vast amounts of data produced into understandable, actionable information' we will create a powerful fusion of machine learning, statistics, and topological data analysis. This combination of statistical insight, with computational power of machine learning with the flexibility, scalability, and visualisation tools of topology will allow a significant reduction of complexity of the data under study. The results will be output in a form that is best suited to the intended application or a scientific problem at hand. This way, we will create a seamless pathway from data analysis to implementation, which will allow us to control every step of this process. In particular, the intended end user will be able to query the results of the analysis to extract the information relevant to them. In summary, our work will provide tools to extract information from complex data sets to support user investigations or decisions.It is now well established that a main challenge of Big Data is how 'to efficiently and intelligently extract knowledge from heterogeneous, distributed data while retaining the context necessary for its interpretation'. This will be addressed first of all by developing techniques for dealing with heterogenous data. A main strength of topology is its ability to identify simple components in complex systems. It can also provide guiding principles on how to combine elements to create a model of a complex system. It also provides numerical techniques to control the overall shape of the resulting model to ensure that it fits with the original constraints. We will use the particular strengths of machine learning, statistics and topology to identify the main properties of data, which will then be combined to provide an overall analysis of the data. For example, a collection of text documents can be analysed using machine learning techniques to create a graph which captures similarities between documents in a topological way. This is an efficient way to classify a corpus of documents according to a desired set of keywords. An important part of our investigation will be to develop robust techniques of data fusion. This is important in many applications. One of our main applications will address the problem of creating a set of descriptors to diagnose and treat asthma. There are five main pathways for clinical diagnosis of asthma, each supported by data. To create a coherent picture of the disease we need to understand how to combine the information contained in these separate data sets to create the so called 'asthma handprint' which is a major challenge in this part of medicine.Every novel methodology of data analysis has to prove that its 'techniques are realistic, compatible and scalable with real- world services and hardware systems'. The best way to do that is to engage from the outset with challenging applications , and to ensure that theoretic and modelling solutions fit well the intended applications. We offer a unique synergy between theory and modelling as well as world-class facilities in medicine and chemistry which will provide a strict test for our ideas and results.