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arXiv 1908.08145cs.LGstat.ML
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流形上的半监督学习神经网络

A Neural Network for Semi-Supervised Learning on Manifolds

Neuroscience Institute, NYU Langone Medical Center(纽约大学朗格尼医学中心神经科学研究所);Flatiron Institute, Simons Foundation(西蒙斯基金会熨斗研究所);Rutgers University(罗格斯大学)

Alexander Genkin, Anirvan M. Sengupta, Dmitri Chklovskii

摘要:

半监督学习算法通常构造数据点的加权图来表示流形。然而,显式的图形表示是有问题的神经网络运行在在线设置。在这里,我们提出了一个前馈神经网络能够半监督学习流形上,而不使用显式的图形表示。我们的算法使用的渠道,代表地方的歧管,使通道之间的相关性表示歧管结构。建议的神经网络有两层。第一层学习在输入数据中构建低维流形的表示,如最近在[8]中提出的。第二个学习使用偶尔的监督和数据的流形表示的相似性来对数据进行分类。承载用于第二层的标签信息的信道被假定为在大部分时间是“静默的”。这两层的学习都是赫布式的,这使得我们的网络设计在生物学上是合理的。我们实验证明了半监督学习对非平凡流形的影响。

英文摘要:

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose a feed-forward neural network capable of semi-supervised learning on manifolds without using an explicit graph representation. Our algorithm uses channels that represent localities on the manifold such that correlations between channels represent manifold structure. The proposed neural network has two layers. The first layer learns to build a representation of low-dimensional manifolds in the input data as proposed recently in [8]. The second learns to classify data using both occasional supervision and similarity of the manifold representation of the data. The channel carrying label information for the second layer is assumed to be "silent" most of the time. Learning in both layers is Hebbian, making our network design biologically plausible. We experimentally demonstrate the effect of semi-supervised learning on non-trivial manifolds.

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