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October 19, 2011 18:23
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Jenks natural breaks classification
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# 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 |
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