Equal Weight Bins

Another method of converting the measured data y₁, y₂, ..., y_N into a symbol string i₁, i₂, ..., i_N is to select the bin boundaries B₁, B₂, and B₃ so

one quarter of the yk satisfy yk <= B1,

one quarter of the yk satisfy B1 < yk <= B2,

one quarter of the yk satisfy B2 < yk <= B3, and

one quarter of the yk satisfy B3 < yk.

For example,

Because each bin contains the same number of points, this is called an equal-weight binning.

One way to produce an equal-weight binning is to sort the list of y_k in increasing order. Then take

B₃ the element one-quarters of the way from the top of the sorted list,

B₂ the element of one-half of the way from the top of the sorted list, and

B₁ to be the element three-quarter of the way from the top of the sorted list.

Equal-weight bins can be called a maximum entropy partition.

Here is a time series generated by the logistic map, and the driven IFS produced using equal-weight bins.

Return to Coarse-Graining