AQOCI extends prior QOCI by adding Gauss-Seidel-style adaptive refinement to a QUBO formulation of centroid initialization, yielding up to 26% V-measure gains over k-means++ on MOTIF at small sample sizes and better results than k-means++ on heavily overlapping synthetic clusters.
k-Means Clustering Is Matrix Factorization
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abstract
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature.
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Adaptive Quantum Optimized Centroid Initialization
AQOCI extends prior QOCI by adding Gauss-Seidel-style adaptive refinement to a QUBO formulation of centroid initialization, yielding up to 26% V-measure gains over k-means++ on MOTIF at small sample sizes and better results than k-means++ on heavily overlapping synthetic clusters.