Classification And Clustering Via Image Convolution Filters Alternative To Generative Mixture Models Vincent Granville by Vincent Granville instant download after payment.

I generate synthetic data using a superimposition of stochastic processes, comparing it to Bayesian gen- erative mixture models (Gaussian mixtures). I explain the benefits and differences. The actual classification and clustering algorithms are model-free, and performed in GPU as image filters, after transforming the raw data into an image. I then discuss the generalization to 3D or 4D, and to higher dimensions with sparse tensors. The technique is particularly suitable when the number of observations is large, and the overlap between clusters is substantial.

It can be done using few iterations and a large filter window, comparable to a neural network, with pixels in the local window being the nodes, and their distance to the local center being the weight function. Or you can implement the method with a large number of iterations – the equivalent of hundreds of layers in a deep neural network – and a tiny window. This latter case corresponds to a sparse network with zero or one connection per node. It is used to implement fractal classification, where point labeling changes at each iteration, around highly non-linear cluster boundaries. This is equivalent to putting a prior on class assignment probabilities in a Bayesian framework. Yet, classification is performed without underlying model. Finally, the clustering (unsupervised) part of the algorithm relies on the same filtering techniques, combined with a color equalizer. The latter can be used to perform hierarchical clustering.