Quantum-inspired classical algorithms for principal component analysis and supervised clustering

We describe classical analogues to quantum algorithms for principal component analysis and nearest-centroid clustering. Given sampling assumptions, our classical algorithms run in time polylogarithmic in input, matching the runtime of the quantum algorithms with only polynomial slowdown. These algorithms are evidence that their corresponding problems do not yield exponential quantum speedups. To build our classical algorithms, we use the same techniques as applied in our previous work dequantizing a quantum recommendation systems algorithm. Thus, we provide further evidence for the strength of classical $\ell^2$-norm sampling assumptions when replacing quantum state preparation assumptions, in the machine learning domain.