Multivariate analyses

Modern data often comprises of the collection of multiple characteristics for each individual observation, to provide a holistic perspective of the properties of each datum. Due to the high dimensionality of such data, the task of modelling and drawing inferences from such data requires specialized methodology. These methods are grouped together under the umbrella of multivariate analysis. We shall describe some fundamental problems that are considered in multivariate analysis and provide some examples regarding the appearance of these problems in scientific investigations. A concise collection of tools from multivariate analysis will be introduced and their applications will be demonstrated.

现代数据通常包含对每个个体观测的多项特征集合，以提供每个数据点属性的整体视角。由于此类数据的高维度特性，对其进行建模和推断的任务需要专门的方法论。这些方法统称为多元分析（multivariate analysis）。我们将阐述多元分析中涉及的若干基本问题，并提供这些问题在科学研究中出现的实例。同时，我们还将介绍多元分析中的一系列核心工具，并展示其应用场景。