Equal-Size Bins

One method of converting the measured data y₁, y₂, ..., y_N into a symbol string i₁, i₂, ..., i_N is first to find the range of the values, that is, the interval between the maximum (max) and the minimun (min) of the y_i.

Next, divide the range (min, max) into four equal-size bins:

yk lies in bin1 if min <= yk < min + .25*(max - min)

yk lies in bin2 if min + .25*(max - min) <= yk < min + .50*(max - min)

yk lies in bin3 if min + .50*(max - min) <= yk < min + .75*(max - min)

yk lies in bin4 if min + .75*(max - min) <= yk < max

The numbers separating the bins are called bin boundaries, B₁, B₂, and B₃:

B1 = min + .25*(max - min)

B2 = min + .50*(max - min)

B3 = min + .75*(max - min)

Each y_k lies in one of these bins, so we can convert the sequence y₁, y₂, y₃ ... into the symbol string i₁, i₂, i₃ ... of 1s, 2s, 3s, and 4s associated with the data. Here is an example.

ik = 4 if yk lies in bin4 ik = 3 if yk lies in bin3 ik = 2 if yk lies in bin2 ik = 1 if yk lies in bin1

Click on the small picture to see how the symbol string generated by equal-size bins drives the IFS.

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

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