{'fraction_non_alphanumeric': 0.02009273570324575, 'fraction_numerical': 0.0015455950540958269, 'mean_word_length': 5.230769230769231, '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}}
A Randomized Rounding Algorithm for Sparse PCA

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. In the proposed approach, we first solve an ℓ1-penalized version of the NP-hard sparse PCA optimization problem and then we use a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Extensive experimental evaluation indicates that the proposed approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.