What is Minimum Curvilinearity distance?

Minimum Curvilinearity explanatory example

Let’s reduce for simplicity our feature space to two variables V1 and V2, where two different sample groups are distributed in two clusters (blue and yellow) according to an unknown nonlinear relation. The Euclidean Distance (on the left) is not suitable to define the real topological distance between points A and B: it does not respect the internal topological relation between the data. Whereas, the Minimum Curvilinear (MC) distance (on the right) exploits the MST path to navigate and compute the nonlinear (curvilinear) distance between the points A and B. All the pairwise distances between the points are stored in the MC-distance-matrix also called MC-Kernel.

References

Machine learning and computational biology

Nonlinear dimension reduction and clustering by Minimum Curvilinearity unfold neuropathic pain and tissue embryological classes

CV Cannistraci, T Ravasi, FM Montevecchi, T Ideker, M Alessio

Bioinformatics 26 (18), i531-i539, 2010

Minimum curvilinearity to enhance topological prediction of protein interactions by network embedding

CV Cannistraci, G Alanis-Lobato, T Ravasi

Bioinformatics 29 (13), i199-i209, 2013

Machine learning and network science

Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Alessandro Muscoloni, Josephine Maria Thomas, Sara Ciucci, Ginestra Bianconi & Carlo Vittorio Cannistraci

Nature Communicationsvolume 8, Article number: 1615 (2017)

Minimum curvilinear automata with similarity attachment for network embedding and link prediction in the hyperbolic space

A Muscoloni, CV Cannistraci

arXiv preprint arXiv:1802.01183, 2018