The second school seminar on 5th November at 2pm, on Teams. If you do not have the Teams link available please contact the organiser, Ian Gent.
Dimensionality Reduction in non-Euclidean Spaces
Deep Learning (ie Convolutional Neural Networks) gives astoundingly good classification over many domains, notably images. Less well known, but perhaps more exciting, are similarity models that can be applied to their inner layers, where there lurk data representations that can give a much more generic notion of similarity. The problem is that these data representations are huge, and so searching a very large space for similar objects is inherently intractable.
If we treat the data as high-dimensional vectors in Euclidean space, then a wealth of approximation techniques is available, most notably dimensionality reduction which can give much smaller forms of the data within acceptable error bounds. However, this data is not inherently a Euclidean space, and there are better ways of measuring similarity using more sophisticated metrics.
The problem now is that existing dimensionality reduction techniques perform analysis over the coordinate space to achieve the size reduction. The more sophisticated metrics give only relative distances and are not amenable to analysis of the coordinates. In this talk, we show a novel technique which uses only the distances among whole objects to achieve a mapping into a low dimensional Euclidean space. As well as being applicable to non-Euclidean metrics, its performance over Euclidean spaces themselves is also interesting.
This is work in progress; anyone interested is more than welcome to collaborate!