Authors: Benoît Colange, Laurent Vuillon, Sylvain Lespinats, Denys Dutykh
Abstract: To perform visual data exploration, many dimensionality reduction
methods have been developed. These tools allow data analysts to represent
multidimensional data in a 2D or 3D space, while preserving
as much relevant information as possible. Yet, they cannot preserve
all structures simultaneously and they induce some unavoidable distortions.
Hence, many criteria have been introduced to evaluate a
map’s overall quality, mostly based on the preservation of neighbourhoods.
Such global indicators are currently used to compare several
maps, which helps to choose the most appropriate mapping method
and its hyperparameters. However, those aggregated indicators tend
to hide the local repartition of distortions. Thereby, they need to be
supplemented by local evaluation to ensure correct interpretation of
In this paper, we describe a new method, called MING, for “Map
Interpretation using Neighbourhood Graphs”. It offers a graphical
interpretation of pairs of map quality indicators, as well as local
evaluation of the distortions. This is done by displaying on the map
the nearest neighbours graphs computed in the data space and in the
embedding. Shared and unshared edges exhibit reliable and unreliable
neighbourhood information conveyed by the mapping. By this
mean, analysts may determine whether proximity (or remoteness) of
points on the map faithfully represents similarity (or dissimilarity)
of original data, within the meaning of a chosen map quality criteria.
We apply this approach to two pairs of widespread indicators: precision/
recall and trustworthiness/continuity, chosen for their wide use
in the community, which will allow an easy handling by users.