  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.
