Visualizing probabilistic models and data with Intensive Principal Component Analysis

Katherine N. Quinn

doi:10.1073/pnas.1817218116

2019-06-24

Katherine N. Quinn *

Colin B. Clement

Francesco De Bernardis

Michael D. Niemack

James P. Sethna

DOI：10.1073/pnas.1817218116

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摘要

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.

Keyword:

manifold learning

information theory

probabilistic models

probabilistic data

visualization

AI总结

对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。

期刊

Proceedings of the National Academy of Sciences of the United States of America

IF:

9.1

论文数:

10.8W

被引数:

73.5W

机构

Cornell University

学者数:

6.3W

论文数: 5.4W

被引数: 10.9W

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