  We propose a technique to develop (and localize in) topological maps from
light detection and ranging (Lidar) data. Localizing an autonomous vehicle with
respect to a reference map in real-time is crucial for its safe operation.
Owing to the rich information provided by Lidar sensors, these are emerging as
a promising choice for this task. However, since a Lidar outputs a large amount
of data every fraction of a second, it is progressively harder to process the
information in real-time. Consequently, current systems have migrated towards
faster alternatives at the expense of accuracy. To overcome this inherent
trade-off between latency and accuracy, we propose a technique to develop
topological maps from Lidar data using the orthogonal Tucker3 tensor
decomposition. Our experimental evaluations demonstrate that in addition to
achieving a high compression ratio as compared to full data, the proposed
technique, $\textit{TensorMap}$, also accurately detects the position of the
vehicle in a graph-based representation of a map. We also analyze the
robustness of the proposed technique to Gaussian and translational noise, thus
initiating explorations into potential applications of tensor decompositions in
Lidar data analysis.
