Subspace clustering has established itself as a state-of-the-art approach to clustering high-dimensional data. In particular, methods relying on the self-expressiveness property have recently proved especially successful. However, they suffer from two major shortcomings: First, a quadratic-size coefficient matrix is learned directly, preventing these methods from scaling beyond small datasets. Secondly, the trained models are transductive and thus cannot be used to cluster out-of-sample data unseen during training. Instead of learning self-expression coefficients directly, we propose a novel metric learning approach to learn instead a subspace affinity function using a siamese neural network architecture. Consequently, our model benefits from a constant number of parameters and a constant-size memory footprint, allowing it to scale to considerably larger datasets. In addition, we can formally show that out model is still able to exactly recover subspace clusters given an independence assumption. The siamese architecture in combination with a novel geometric classifier further makes our model inductive, allowing it to cluster out-of-sample data. Additionally, non-linear clusters can be detected by simply adding an auto-encoder module to the architecture. The whole model can then be trained end-to-end in a self-supervised manner. This work in progress reports promising preliminary results on the MNIST dataset. In the spirit of reproducible research, me make all code publicly available. In future work we plan to investigate several extensions of our model and to expand experimental evaluation.

Multiplayer Online Battle Arena (MOBA) games are among the most played digital games in the world. In these games, teams of players fight against each other in arena environments, and the gameplay is focused on tactical combat. Mastering MOBAs requires extensive practice, as is exemplified in the popular MOBA Defence of the Ancients 2 (DotA 2). In this paper, we present three data-driven measures of spatio-temporal behavior in DotA 2: 1) Zone changes; 2) Distribution of team members and: 3) Time series clustering via a fuzzy approach. We present a method for obtaining accurate positional data from DotA 2. We investigate how behavior varies across these measures as a function of the skill level of teams, using four tiers from novice to professional players. Results indicate that spatio-temporal behavior of MOBA teams is related to team skill, with professional teams having smaller within-team distances and conducting more zone changes than amateur teams. The temporal distribution of the within-team distances of professional and high-skilled teams also generally follows patterns distinct from lower skill ranks.