  Efficient tracking algorithms are a crucial part of particle tracking
detectors. While a lot of work has been done in designing a plethora of
algorithms, these usually require tedious tuning for each use case. (Weakly)
supervised Machine Learning-based approaches can leverage the actual raw data
for maximal performance. Yet in realistic scenarios, sufficient high-quality
labeled data is not available. While training might be performed on simulated
data, the reproduction of realistic signal and noise in the detector requires
substantial effort, compromising this approach.
  Here we propose a novel, fully unsupervised, approach to track
reconstruction. The introduced model for learning to disentangle the factors of
variation in a geometrically meaningful way employs geometrical space
invariances. We train it through constraints on the equivariance between the
image space and the latent representation in a Deep Convolutional Autoencoder.
Using experimental results on synthetic data we show that a combination of
different space transformations is required for meaningful disentanglement of
factors of variation. We also demonstrate the performance of our model on real
data from tracking detectors.
