An Alternating Optimization Scheme for Binary Sketches

Searching for similar objects in intrinsically high-dimensional data sets is a challenging task. The use of compact sketches has been proposed for faster similarity search using linear scans. Binary sketches are one such approach to find a good mapping from the original data space to bit strings of a fixed length. These bit strings can be compared efficiently using only few XOR and bit count operations, replacing costly similarity computations with an inexpensive approximation. We propose a new scheme to initialize and improve binary sketches for similarity search in Euclidean spaces. Our optimization iteratively improves the quality of the sketches with a form of orthogonalization. We provide empirical evidence that the quality of the sketches has a peak beyond which it is not correlated to neither bit independence nor bit balance, which contradicts a previous hypothesis in the literature. Regularization in the form of noise added to the training data can turn the peak into a plateau and applying the optimization in a stochastic fashion, i.e., training on smaller subsets of the data, allows for rapid initialization. We provide a loss function that allows to approximate the same objective using neural network frameworks such as PyTorch, elevating the approach to GPU-based training.