LAMINAR 自适应生成数据结构距离度量，提升复杂数据表征
Learning Locally Adaptive Metrics that Enhance Structural Representation with $\texttt{LAMINAR}$
- 基于连续归一化流与逆变换采样构建黎曼流形
- 输出局部自适应度量，生成更具结构信息的密度距离
- 无需预先设定度量，适合复杂数据几何分析
我们提出 LAMINAR，一种新颖的无监督机器学习流程，通过生成更具信息量的距离度量来增强数据中的结构表征。物理科学中的分析方法常依赖标准度量定义数据的几何关系，但可能无法捕捉复杂数据集的底层结构。LAMINAR 通过连续归一化流与逆变换采样，在数据空间中定义黎曼流形，无需用户预先指定度量。结果是一个局部自适应度量，可产生具有结构信息的基于密度的距离。我们通过将 LAMINAR 输出与欧氏度量在结构化数据集上的表现进行比较，验证了其有效性。
原文摘要 · Abstract (English)
We present $\texttt{LAMINAR}$, a novel unsupervised machine learning pipeline designed to enhance the representation of structure within data via producing a more-informative distance metric. Analysis methods in the physical sciences often rely on standard metrics to define geometric relationships in data, which may fail to capture the underlying structure of complex data sets. $\texttt{LAMINAR}$ addresses this by using a continuous-normalising-flow and inverse-transform-sampling to define a Riemannian manifold in the data space without the need for the user to specify a metric over the data a-priori. The result is a locally-adaptive-metric that produces structurally-informative density-based distances. We demonstrate the utility of $\texttt{LAMINAR}$ by comparing its output to the Euclidean metric for structured data sets.
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