I would like to ask for references to algorithms that can project shape information about an object to 1 dimension. Specifically I am training a neural network to be able to identify objects with similar shape as the ones in the training set. The objects in my case are molecules for which the positions, masses and radii of the atoms are known. So far I have used information about the interatomic distances. The shape of the molecule is characterized by the distributions of atomic distances to four strategic reference locations. In turn, each of these distributions is described through its first three moments. In this way, each molecule has associated a vector of 12 shape descriptors. E.g.
shape = [5.263145206201491, 2.374050283937628, 0.5667128412399703, -0.9294169868091768, 5.248610806623028, 2.540858433874688, 0.6060854720036649, -0.8149532304046945, 10.186033275946016, 5.224912272773887, -0.5637327938909833, -1.1097296046204561]
However, a 12-element feature vector is too small to describe accurately the molecular shape. I tried to add more reference location and consequently more atomic distances but I noticed no gains in accuracy. Is anyone aware of any other algorithm that can express the molecular shape in a feature vector form? Please point me to references if you know.