A histogram-based classifier on overlapped bins

The subclass method is a classifier based on approximation of class regions. It assumes that all classes are separable (but not necessarily linear separable). We extend the method so as to meet cases in which class-conditional probability density functions (PDFs) overlap each other. In this extension, the method becomes a histogram approach for approximating PDFs, but the method allows overlapping of bins unlike usual histogram approaches. It is shown that this method is consistent in the sense that the error rate approaches the Bayes error rate as the number of samples tends to infinity. It is also shown that the convergence rate is faster than that using a previous MDL-based histogram approach in the range of practical number of samples