When the distribution of unlabeled data in feature space lies along a manifold, the information it provides may be used by a learner to assist classification in a semi-supervised setting. While manifold learning is well-known in machine learning, the use of manifolds in human learning is largely unstudied. We perform a set of experiments which test a human’s ability to use a manifold in a semis...

We propose the Hierarchical Flow (HF) model constrained by isometric regularizations for manifold learning that combines goals such as dimensionality reduction, inference, sampling, projection and density estimation into one unified framework. Our proposed HF is regularized to not only produce embeddings preserving geometric structure of manifold, but also project samples onto in a manner confo...

Energy landscapes provide a conceptual framework for structure prediction, and detailed understanding of their topological features is necessary to develop efficient methods exploration. The ability visualise these surfaces essential, but the high dimensionality corresponding configuration spaces makes this difficult. Here we present Stochastic Hyperspace Embedding Projection (SHEAP), method en...

In this paper we propose to combine two powerful ideas, boosting and manifold learning. On the one hand, we improve ADABOOST by incorporating knowledge on the structure of the data into base classifier design and selection. On the other hand, we use ADABOOST’s efficient learning mechanism to significantly improve supervised and semi-supervised algorithms proposed in the context of manifold lear...

Manifold learning is an approach for nonlinear dimensionality reduction and has been a hot research topic in the field of computer science. A disadvantage of manifold learning methods is, however, that there are no explicit mappings from the high-dimensional feature space to the low-dimensional representation space. It restricts the application of manifold learning methods in many practical pro...

The term manifold learning encompasses a class of machine learning techniques that convert data from a high to lower dimensional representation while respecting the intrinsic geometry of the data. The intuition underlying the use of manifold learning in the context of image analysis is that, while each image may be viewed as a single point in a very high-dimensional space, a set of such points ...