Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails

Junglen, Stefan

doi:10.1214/ecp.v16-1629

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A Priori Bounds For Optimal Quantizers1

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2016

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“…More precise results can be found in [14] and [8] for various families of distributions with exponential or polynomial tails at infinity. Under certain condition on X, the asymptotic behaviour of R = R(N ) can be analyzed sharply as N goes to infinity.…”

Section: A Priori Bounds For Optimal Quantizersmentioning

confidence: 98%

Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension

Pagès

2016

SIAM J. Control Optim.

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We establish the pointwise convergence of the iterative Lloyd algorithm, also known as kmeans algorithm, when the quadratic quantization error of the starting grid (with size N ≥ 2) is lower than the minimal quantization error with respect to the input distribution is lower at level N − 1. Such a protocol is known as the splitting method and allows for convergence even when the input distribution has an unbounded support. We also show under very light assumption that the resulting limiting grid still has full size N . These results are obtained without continuity assumption on the input distribution. A variant of the procedure taking advantage of the asymptotic of the optimal quantizer radius is proposed which always guarantees the boundedness of the iterated grids.

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Section: A Priori Bounds For Optimal Quantizersmentioning

confidence: 98%

Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension

Pagès

2016

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

Quantization Balls and Asymptotics of Quantization Radii for Probability Distributions with Radial Exponential Tails

Cited by 1 publication

References 4 publications

Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension

Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension

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