This paper traces how the same design question has led to task-specific methods built from graphs, graph-based ranks, kernels, and dissimilarity profiles for testing, change-point detection, covariate-balance assessment, clustering, classification, and generative-model evaluation.
Abstract
Modern data are increasingly high-dimensional or non-Euclidean. As dimension grows, new statistical patterns can emerge in the relations among observations, while a conventional statistical summary may fail to retain the signal they carry. This paper names and organizes a research program around this observation, calling it Cursive. Cursive asks which relational information is lost when the summary is formed and how the analysis should be redesigned around that information. The canonical example is the generalized edge-count test, which keeps the two within-sample edge counts whose opposing deviations can cancel in the classical between-sample count. This paper traces how the same design question has led to task-specific methods built from graphs, graph-based ranks, kernels, and dissimilarity profiles for testing, change-point detection, covariate-balance assessment, clustering, classification, and generative-model evaluation.
The objective is not to construct a low-rank projection, but to retain an interpretable subset of the original coordinates that preserves the distributional information distinguishing the clusters that preserves the distributional information distinguishing the clusters.
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