A Neural Network for Semi-Supervised Learning on Manifolds

TL;DR

This paper introduces a biologically plausible neural network that performs semi-supervised learning on data manifolds without explicit graph representations, suitable for online learning scenarios.

Contribution

It proposes a two-layer neural network that learns manifold representations and classification using Hebbian learning, avoiding explicit graph construction.

Findings

Effective semi-supervised learning on complex manifolds

Biologically plausible Hebbian learning implementation

Demonstrated on non-trivial manifold datasets

Abstract

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.