{'fraction_non_alphanumeric': 0.014666666666666666, 'fraction_numerical': 0.0, 'mean_word_length': 5.206611570247934, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Exploiting random matrix theory to improve noisy low-rank matrix approximation

We consider an estimation and denoising problem where the measurement matrix is modeled as a low-rank signal matrix corrupted by a Gaussian white noise matrix. We exploit recent results from random matrix theory to develop an algorithm for improving the quality of the estimated low-rank signal matrix that explicitly accounts for the noisiness of the estimated signal singular vectors. We explain why we are able to obtain this improvement relative to the Eckart-Young-Mirsky theorem motivated “optimal” approximation that employs the rank-k SVD of the measurement matrix and discuss extensions of the result to settings where the Gaussianity assumption can be dropped.