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Section 2.2 Data Geometry Map

Note Id: 202607310002 | Tags: data analysis geometry

Big Idea: The computational methods and mathematical tools used to evaluate a dataset should be determined based on the geometry of the data.

Table 2.2.1. Data Geometry Map

Data structure	Natural geometry	Representation	Analysis tools
Measurements and signals	Euclidean vector space	Feature vectors	PCA, SVD, regression
Compositions	Simplex geometry	CLR / log-ratio coordinates	PCA, clustering
Probability distributions	Statistical manifold	Information geometry coordinates	KL divergence, Fisher metrics
Quantum states	Hilbert space	State vectors / density matrices	Spectral analysis, tomography
Networks	Graph space	Adjacency / Laplacian matrices	Spectral graph theory
Nonlinear systems	Manifold	Learned embeddings	Diffusion maps, autoencoders

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