SDR -- Medium Rare with Fast Computations

Abstract: We revisit the widely used bss eval metrics for source separation with an eye out for performance. We propose a fast algorithm fixing shortcomings of publicly available implementations. First, we show that the metrics are fully specified by the squared cosine of just two angles between estimate and reference subspaces. Second, large linear systems are involved. However, they are structured, and we apply a fast iterative method based on conjugate gradient descent. The complexity of this step is thus reduced by a factor quadratic in the distortion filter size used in bss eval, usually 512. In experiments, we assess speed and numerical accuracy. Not only is the loss of accuracy due to the approximate solver acceptable for most applications, but the speed-up is up to two orders of magnitude in some, not so extreme, cases. We confirm that our implementation can train neural networks, and find that longer distortion filters may be beneficial.