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For example, the SVM or ANN methods perform search of a surface which would separate the data points in a best way. This surface is returned in the vector or parametric form. Are there methods returning a spatial bitmap each voxel of which contains a numeric value defining a class for all points lying within a given voxel?
I would like to share some of the results of my attempts in this direction. Since I'm relatively new in machine learning I can't be quite sure that this was not done before. Perhaps there are some reasons that are obscure to me which make this approach meaningless for a real data.
The below images were obtained by representing each data point by RBF and calculating influence of all such RBFs for each voxel. The adaptive grid was used to optimize calculations. Taking the first step in this direction, I received encouraging performance results with the dummy data and with the one real dataset. Obviously, more tests are required to draw conclusions about the effectiveness of this method. Perhaps, this approach will be useful for noise reduction and datasets with complicated clusters, also it is capable of processing data points in batch mode having no significant impact to a final result.

Dummy dataset.

Zip Code dataset:
voxel view f10 voxel view f20 voxel view f30 voxel view f50 voxel view f100 rbf view f225

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  • $\begingroup$ Radial basis functions are already a thing. Sums of voxels or RBFs do not scale well in terms of capacity. What does is composition; building increasingly complex units out of simpler ones, and this is what multilayer neural networks do. This is why they are everywhere. $\endgroup$
    – Emre
    Jun 26, 2018 at 23:01
  • $\begingroup$ @Emre Suggested method doesn't imply summing of voxels. Instead it returns a spatial bitmap, each voxel of which stores summed influence of RBFs of all processed points. As regards the capacity scaling (as I understand): perhaps, there is rather simple rule allowing to define optimal values of the initial grid density and RBF's parameters given the number of points in a batch and supposed complexity of clusters (something like the Nyquist–Shannon sampling theorem). $\endgroup$
    – Zubetto
    Jun 27, 2018 at 14:01

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There are many ways to create a bitmap output. One option is with neural networks. The output layer could be a tensor where the dimensions are: x coordinate, y coordinate, and RGB color value. The goal of the model is to predict the RGB color value for each x coordinate and y coordinate. This frames the problem as multivariate regression.

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