主成分分析
降维
维数之咒
函数主成分分析
数学证明
校长(计算机安全)
成像体模
计算机科学
口译(哲学)
简单(哲学)
功能数据分析
模式识别(心理学)
数学
人工智能
统计物理学
数据挖掘
物理
机器学习
哲学
几何学
认识论
光学
程序设计语言
操作系统
标识
DOI:10.1101/2023.06.20.545619
摘要
Abstract Principal component analysis (PCA) is a dimensionality reduction technique that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional data. However, this simple interpretation of PCA relies on several unstated assumptions that are difficult to satisfy. When these assumptions are violated, non-oscillatory data may have oscillatory principal components. Here, we show that two common properties of data violate these assumptions and cause oscillatory principal components: smooth-ness, and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations that they produce, which we call “phantom oscillations”, impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.
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