Hands-On Unsupervised Learning with Python

Histograms

The simplest way to find out an approximation of the probability density function is based on a frequency count. If we have a dataset X containing m samples x_i ∈ ℜ (for simplicity, we are considering only univariate distributions, but the process is exactly equivalent for multidimensional samples), we can define m and M as follows:

The interval (m, M) can be split into a fixed number b of bins (which can have either the same or different widths denoted as w(b_j) so that n_p(b_j) corresponds to the number of samples included into the bin b_j. At this point, given a test sample x_t, it's easy to understand that the approximation of the ...