Stochastic Numerical Methods for Optimal Voronoï Quantization
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In this post, I remind what is quadratic optimal quantizations. Then, I explain the two algorithms that were first devised in order to build an optimal quantization of a random vector $X$, namely: the fixed-point search called Lloyd method and the stochastic gradient descent known as Competitive Learning Vector Quantization (CLVQ).
All explanations are accompanied by some code examples in Python and is available in the following Github repository: montest/stochastic-methods-optimal-quantization.
In my previous blog post, I detailed the methods used to build an optimal Voronoï quantizer of random vectors \(X\) whatever the dimension \(d\). In this post, I will focus on real valued random variables and present faster methods for dimension $1$.
In this post, I present a PyTorch implementation of the stochastic version of the Lloyd algorithm, aka K-means, in order to build Optimal Quantizers of $X$, a random variable of dimension one. The use of PyTorch allows me perform all the numerical computations on GPU and drastically increase the speed of the algorithm.
In this post, I present several PyTorch implementations of the Competitive Learning Vector Quantization algorithm (CLVQ) in order to build Optimal Quantizers of $X$, a random variable of dimension one. In my previous blog post, the use of PyTorch for Lloyd allowed me to perform all the numerical computations on GPU and drastically increase the speed of the algorithm. However, in this article, we do not observe the same behavior, this pytorch implementation is slower than the numpy one. Moreover, I also take advantage of the autograd implementation in PyTorch allowing me to make use of all the optimizers in