A Neural Network for Semi-Supervised Learning on Manifolds
This work addresses a domain-specific challenge in machine learning for semi-supervised learning on manifolds, but it is incremental as it builds on existing methods for manifold representation.
The authors tackled the problem of semi-supervised learning on manifolds without explicit graph representations, proposing a feed-forward neural network with Hebbian learning that achieves competitive performance on non-trivial manifolds.
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.