The connections in a graph generate a structure that is independent of a coordinate system. This visual metaphor allows creating a more flexible representation of data than a two-dimensional scatterplot. In this article, we present STAD (Simplified Topological Abstraction of Data), a parameter-free dimensionality reduction method that projects high-dimensional data into a graph. STAD generates an abstract representation of high-dimensional data by giving each data point a location in a graph which preserves the approximate distances in the original high-dimensional space. The STAD graph is built upon the Minimum Spanning Tree (MST) to which new edges are added until the correlation between the distances from the graph and the original dataset is maximized. Additionally, STAD supports the inclusion of additional functions to focus the exploration and allow the analysis of data from new perspectives, emphasizing traits in data which otherwise would remain hidden. We demonstrate the effectiveness of our method by applying it to two real-world datasets: traffic density in Barcelona and temporal measurements of air quality in Castile and León in Spain.

中文翻译：

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生成树作为数据结构的近似

图中的连接生成独立于坐标系的结构。这种视觉隐喻允许创建比二维散点图更灵活的数据表示。在本文中，我们介绍了 STAD（数据的简化拓扑抽象），这是一种无参数的降维方法，可将高维数据投影到图中。STAD 通过为每个数据点在图中保留原始高维空间中的近似距离的位置来生成高维数据的抽象表示。STAD 图建立在最小生成树 (MST) 上，在该树上添加新边，直到图与原始数据集的距离之间的相关性最大化。此外，STAD 支持包含附加功能以集中探索并允许从新的角度分析数据，强调数据中否则将保持隐藏的特征。我们通过将其应用于两个真实世界的数据集来证明我们的方法的有效性：巴塞罗那的交通密度和西班牙卡斯蒂利亚和莱昂的空气质量时间测量。