Matrix recovery from quantized and corrupted measurements

This paper deals with the recovery of an unknown, low-rank matrix from quantized and (possibly) corrupted measurements of a subset of its entries. We develop statistical models and corresponding (multi-)convex optimization algorithms for quantized matrix completion (Q-MC) and quantized robust principal component analysis (Q-RPCA). In order to take into account the quantized nature of the available data, we jointly learn the underlying quantization bin boundaries and recover the low-rank matrix, while removing potential (sparse) corruptions. Experimental results on synthetic and two real-world collaborative filtering datasets demonstrate that directly operating with the quantized measurements - rather than treating them as real values - results in (often significantly) lower recovery error if the number of quantization bins is less than about 10.