Dimensionality Reduction Mappings

A wealth of powerful dimensionality reduction methods has been established which can be used for data visualization and preprocessing. These are accompanied by formal evaluation schemes, which allow a quantitative evaluation along general principles and which even lead to further visualization schemes based on these objectives. Most methods, however, provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based on a simple global linear mapping as well as prototype-based local linear mappings.

Mapping the conformations of biological assemblies

Mapping conformational heterogeneity of macromolecules presents a formidable challenge to X-ray crystallography and cryo-electron microscopy, which often presume its absence. This has severely limited our knowledge of the conformations assumed by biological systems and their role in biological function, even though they are known to be important. We propose a new approach to determining to high resolution the three-dimensional conformations of biological entities such as molecules, macromolecular assemblies, and ultimately cells, with existing and emerging experimental techniques. This approach may also enable one to circumvent current limits due to radiation damage and solution purification.Comment: 14 pages, 6 figure

Representation Learning: A Review and New Perspectives

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning

Advances in dissimilarity-based data visualisation

Gisbrecht A. Advances in dissimilarity-based data visualisation. Bielefeld: Universitätsbibliothek Bielefeld; 2015

Some steps towards a general principle for dimensionality reduction mappings

In the past years, many dimensionality reduction methods have been established which allow to visualize high dimensional data sets. Recently, also formal evaluation schemes have been proposed for data visualization, which allow a quantitative evaluation along general principles. Most techniques provide a mapping of a priorly given finite set of points only, requiring additional steps for out-of-sample extensions. We propose a general view on dimensionality reduction based on the concept of cost functions, and, based on this general principle, extend dimensionality reduction to explicit mappings of the data manifold. This offers the possibility of simple out-of-sample extensions. Further, it opens a way towards a theory of data visualization taking the perspective of its generalization ability to new data points. We demonstrate the approach based in a simple example