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Explore advanced clustering algorithms through this 27-minute conference talk that presents groundbreaking improvements to the k-means clustering problem in both classical and quantum computing contexts. Learn about a new classical epsilon-k-means algorithm that achieves exponential improvements in time complexity compared to previous approaches, matching the runtime of existing quantum algorithms while processing n vectors in d-dimensional space to output k centroid vectors. Discover an enhanced quantum q-means algorithm that surpasses previous quantum methods by utilizing QRAM to prepare quantum states based on cluster assignments and applying multivariate quantum amplitude estimation, rather than relying on traditional quantum linear algebra primitives. Examine the first quantum and classical lower bounds for single k-means iterations, demonstrating the optimality of these new algorithms across most relevant parameters. Gain insights into how these advances bridge the gap between classical and quantum approaches to one of machine learning's most fundamental clustering techniques, with implications for analyzing large datasets more efficiently.
