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Visualizing probabilistic models and data with Intensive Principal Component Analysis
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DOI：10.1073/pnas.1817218116.png)
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Abstract
En 中文
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the curse of dimensionality in high dimensions. Inspired by replica theory from statistical mechanics, we consider replicas of the system to tune the dimensionality and take the limit as the number of replicas goes to zero. The result is intensive embedding, which not only is isometric (preserving local distances) but also allows global structure to be more transparently visualized. We develop the Intensive Principal Component Analysis (InPCA) and demonstrate clear improvements in visualizations of the !sing model of magnetic spins, a neural network, and the dark energy cold dark matter (ACDM) model as applied to the cosmic microwave background.
Keywords:
manifold learning
information theory
probabilistic models
probabilistic data
visualization
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