  Most Machine Learning (ML) methods, from clustering to classification, rely
on a distance function to describe relationships between datapoints. For
complex datasets it is hard to avoid making some arbitrary choices when
defining a distance function. To compare images, one must choose a spatial
scale, for signals, a temporal scale. The right scale is hard to pin down and
it is preferable when results do not depend too tightly on the exact value one
picked. Topological data analysis seeks to address this issue by focusing on
the notion of neighbourhood instead of distance. It is shown that in some cases
a simpler solution is available. It can be checked how strongly distance
relationships depend on a hyperparameter using dimensionality reduction. A
variant of dynamical multi-dimensional scaling (MDS) is formulated, which
embeds datapoints as curves. The resulting algorithm is based on the
Concave-Convex Procedure (CCCP) and provides a simple and efficient way of
visualizing changes and invariances in distance patterns as a hyperparameter is
varied. A variant to analyze the dependence on multiple hyperparameters is also
presented. A cMDS algorithm that is straightforward to implement, use and
extend is provided. To illustrate the possibilities of cMDS, cMDS is applied to
several real-world data sets.

Machine Learning