期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2019
卷号：116
期号：28
页码：13762-13767
DOI：10.1073/pnas.1817218116
出版社：The National Academy of Sciences of the United States of America
摘要：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 Ising model of magnetic spins, a neural network, and the dark energy cold dark matter ( Λ CDM ) model as applied to the cosmic microwave background.
关键词：manifold learning ; information theory ; probabilistic models ; probabilistic data ; visualization
