Department of Applied Physics, Stanford University, Stanford, California 94305, USA.
Annu Rev Neurosci. 2012;35:485-508. doi: 10.1146/annurev-neuro-062111-150410. Epub 2012 Apr 5.
The curse of dimensionality poses severe challenges to both technical and conceptual progress in neuroscience. In particular, it plagues our ability to acquire, process, and model high-dimensional data sets. Moreover, neural systems must cope with the challenge of processing data in high dimensions to learn and operate successfully within a complex world. We review recent mathematical advances that provide ways to combat dimensionality in specific situations. These advances shed light on two dual questions in neuroscience. First, how can we as neuroscientists rapidly acquire high-dimensional data from the brain and subsequently extract meaningful models from limited amounts of these data? And second, how do brains themselves process information in their intrinsically high-dimensional patterns of neural activity as well as learn meaningful, generalizable models of the external world from limited experience?
维度的诅咒给神经科学的技术和概念进展都带来了严峻的挑战。特别是，它困扰着我们获取、处理和建模高维数据集的能力。此外，神经系统必须应对在高维空间中处理数据的挑战，以便在复杂的世界中成功地学习和运作。我们回顾了最近的数学进展，这些进展为在特定情况下对抗维度提供了方法。这些进展揭示了神经科学中的两个双重问题。首先，作为神经科学家，我们如何从大脑中快速获取高维数据，然后从这些有限的数据中提取有意义的模型？其次，大脑本身如何处理其固有高维神经活动模式中的信息，以及如何从有限的经验中学习到外部世界有意义的、可推广的模型？
