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Jenks natural breaks classification
# code from http://danieljlewis.org/files/2010/06/Jenks.pdf
# described at http://danieljlewis.org/2010/06/07/jenks-natural-breaks-algorithm-in-python/
def getJenksBreaks( dataList, numClass ):
dataList.sort()
mat1 = []
for i in range(0,len(dataList)+1):
temp = []
for j in range(0,numClass+1):
temp.append(0)
mat1.append(temp)
mat2 = []
for i in range(0,len(dataList)+1):
temp = []
for j in range(0,numClass+1):
temp.append(0)
mat2.append(temp)
for i in range(1,numClass+1):
mat1[1][i] = 1
mat2[1][i] = 0
for j in range(2,len(dataList)+1):
mat2[j][i] = float('inf')
v = 0.0
for l in range(2,len(dataList)+1):
s1 = 0.0
s2 = 0.0
w = 0.0
for m in range(1,l+1):
i3 = l - m + 1
val = float(dataList[i3-1])
s2 += val * val
s1 += val
w += 1
v = s2 - (s1 * s1) / w
i4 = i3 - 1
if i4 != 0:
for j in range(2,numClass+1):
if mat2[l][j] >= (v + mat2[i4][j - 1]):
mat1[l][j] = i3
mat2[l][j] = v + mat2[i4][j - 1]
mat1[l][1] = 1
mat2[l][1] = v
k = len(dataList)
kclass = []
for i in range(0,numClass+1):
kclass.append(0)
kclass[numClass] = float(dataList[len(dataList) - 1])
countNum = numClass
while countNum >= 2:#print "rank = " + str(mat1[k][countNum])
id = int((mat1[k][countNum]) - 2)
#print "val = " + str(dataList[id])
kclass[countNum - 1] = dataList[id]
k = int((mat1[k][countNum] - 1))
countNum -= 1
return kclass
def getGVF( dataList, numClass ):
"""
The Goodness of Variance Fit (GVF) is found by taking the
difference between the squared deviations
from the array mean (SDAM) and the squared deviations from the
class means (SDCM), and dividing by the SDAM
"""
breaks = getJenksBreaks(dataList, numClass)
dataList.sort()
listMean = sum(dataList)/len(dataList)
print listMean
SDAM = 0.0
for i in range(0,len(dataList)):
sqDev = (dataList[i] - listMean)**2
SDAM += sqDev
SDCM = 0.0
for i in range(0,numClass):
if breaks[i] == 0:
classStart = 0
else:
classStart = dataList.index(breaks[i])
classStart += 1
classEnd = dataList.index(breaks[i+1])
classList = dataList[classStart:classEnd+1]
classMean = sum(classList)/len(classList)
print classMean
preSDCM = 0.0
for j in range(0,len(classList)):
sqDev2 = (classList[j] - classMean)**2
preSDCM += sqDev2
SDCM += preSDCM
return (SDAM - SDCM)/SDAM
# written by Drew
# used after running getJenksBreaks()
def classify(value, breaks):
for i in range(1, len(breaks)):
if value < breaks[i]:
return i
return len(breaks) - 1

HaozheW commented Jul 23, 2014

Did you test this?

ratnanil commented Jun 5, 2015

The site (http://danieljlewis.org/2010/06/07/jenks-natural-breaks-algorithm-in-python/) seems to be down! Is there another description anywhere?

121onto commented Sep 24, 2016 edited

The Jenks technique is discussed here. The blog post points to this repo for a JavaSript implementation. That repo removed their implementation of Jenks in favor of a Ckmeans.

There is an R implementation of Ckmeans in the package Ckmeans.1d.dp. See this SO question for a discussion of porting that code to Python.

Does anyone know the arguments and return values for these functions? I have the code running, but I'm not sure what the output means. For example if I run
x = [1, 1, 3, 4, 5, 5, 8, 9, 7]
getJenksBreaks(x, 3)
The output value is [0, 1, 5, 9.0]
I'm not sure how that tells me what the breaks are. The danieljlewis site forwards to http://blogs.splintdev.geog.ucl.ac.uk/, which seems to be a blank page.
Thanks!

rubemd commented Mar 20, 2017

VeloSteve, this is great that you have the code running. I still have to learn Python to do these calculations, however, I did the example you cited in RealStatistics in Excel.

The values 0, 1 and 5 that you got seems to be the lower value of the classes and 9 is the last upper value. Check the image below. Note that RealStatistics express the classes with the values existent in the table and that's why the values are not exactly the same as yours.

captura de tela 2017-03-20 00 07 09

Best regards!

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