如何对 Pandas 系列进行分箱，将箱大小设置为每个箱的最大/最小预设值

Question

I have a pd.Series of floats and I would like to bin it into n bins where the bin size for each bin is set so that max/min is a preset value (eg 1.20)?

The requirement means that the size of the bins is not constant. For example:

data = pd.Series(np.arange(1, 11.0))
print(data)

0     1.0
1     2.0
2     3.0
3     4.0
4     5.0
5     6.0
6     7.0
7     8.0
8     9.0
9    10.0
dtype: float64

I would like the bin sizes to be:

1.00 <= bin 1 < 1.20
1.20 <= bin 2 < 1.20 x 1.20 = 1.44
1.44 <= bin 3 < 1.44 x 1.20 = 1.73
...

etc

Thanks

Answer 1

Here's one with pd.cut , where the bins can be computed taking the np.cumprod of an array filled with 1.2 :

data = pd.Series(list(range(11)))
import numpy as np

n = 20 # set accordingly
bins= np.r_[0,np.cumprod(np.full(n, 1.2))]
# array([ 0.        ,  1.2       ,  1.44      ,  1.728 ...
pd.cut(data, bins)

0                 NaN
1          (0.0, 1.2]
2      (1.728, 2.074]
3      (2.986, 3.583]
4        (3.583, 4.3]
5         (4.3, 5.16]
6       (5.16, 6.192]
7       (6.192, 7.43]
8       (7.43, 8.916]
9     (8.916, 10.699]
10    (8.916, 10.699]
dtype: category

---

Where bins in this case goes up to:

np.r_[0,np.cumprod(np.full(20, 1.2))]

array([ 0.        ,  1.2       ,  1.44      ,  1.728     ,  2.0736    ,
        2.48832   ,  2.985984  ,  3.5831808 ,  4.29981696,  5.15978035,
        6.19173642,  7.43008371,  8.91610045, 10.69932054, 12.83918465,
       15.40702157, 18.48842589, 22.18611107, 26.62333328, 31.94799994,
       38.33759992])

So you'll have to set that according to the range of values of the actual data

Answer 2

This is I believe the best way to do it because you are considering the max and min values from your array. Therefore you won't need to worry about what values are you using, only the multiplier or step_size for your bins (of course you'd need to add a column name or some additional information if you will be working with a DataFrame):

data = pd.Series(np.arange(1, 11.0))
bins = []
i = min(data)
while i < max(data):
    bins.append(i)
    i = i*1.2
    bins.append(i)
bins = list(set(bins))
bins.sort()
df = pd.cut(data,bins,include_lowest=True)
print(df)

Output:

0       (0.999, 1.2]
1     (1.728, 2.074]
2     (2.986, 3.583]
3       (3.583, 4.3]
4        (4.3, 5.16]
5      (5.16, 6.192]
6      (6.192, 7.43]
7      (7.43, 8.916]
8    (8.916, 10.699]
9    (8.916, 10.699]

Bins output:

Categories (13, interval[float64]): [(0.999, 1.2] < (1.2, 1.44] < (1.44, 1.728] < (1.728, 2.074] < ... <
                                     (5.16, 6.192] < (6.192, 7.43] < (7.43, 8.916] <
                                     (8.916, 10.699]]

Answer 3

Thanks everyone for all the suggestions. None does quite what I was after (probably because my original question wasn't clear enough) but they really helped me figure out what to do so I have decided to post my own answer (I hope this is what I am supposed to do as I am relatively new at being an active member of stackoverflow...)

I liked @yatu's vectorised suggestion best because it will scale better with large data sets but I am after the means to not only automatically calculate the bins but also figure out the minimum number of bins needed to cover the data set.

This is my proposed algorithm:

1. The bin size is defined so that bin_max_i/bin_min_i is constant:

bin_max_i / bin_min_i = bin_ratio

2. Figure out the number of bins for the required bin size (bin_ratio):

data_ratio = data_max / data_min
n_bins = math.ceil( math.log(data_ratio) / math.log(bin_ratio) )

3. Set the lower boundary for the smallest bin so that the smallest data point fits in it:

bin_min_0 = data_min

4. Create n non-overlapping bins meeting the conditions:

bin_min_i+1 = bin_max_i
bin_max_i+1 = bin_min_i+1 * bin_ratio

5. Stop creating further bins once all dataset can be split between the bins already created. In other words, stop once:

bin_max_last > data_max

Here is a code snippet:

import math
import pandas as pd

bin_ratio = 1.20

data = pd.Series(np.arange(2,12))
data_ratio = max(data) / min(data)

n_bins = math.ceil( math.log(data_ratio) / math.log(bin_ratio) )
n_bins = n_bins + 1               # bin ranges are defined as [min, max)

bins = np.full(n_bins, bin_ratio) # initialise the ratios for the bins limits
bins[0] = bin_min_0               # initialise the lower limit for the 1st bin
bins = np.cumprod(bins)           # generate bins

print(bins)
[ 2.          2.4         2.88        3.456       4.1472      4.97664
  5.971968    7.1663616   8.59963392 10.3195607  12.38347284]

I am now set to build a histogram of the data:

data.hist(bins=bins)