I posted this question over on Esri's GeoNet, but have not yet gotten an answer.
Using ArcGIS v10.2.1, I have been using the Grouping Analysis tool to generate a range of clusters from my data. I wrote a Python script to run Grouping Analysis a large number of times (with different clustering algorithms and spatial constraints and with the number of clusters (k) ranging from 3 to 250) and report the 'grouping effectiveness' statistic (the Calinski-Harabasz pseudo-F statistic: see ArcGIS Help (http://resources.arcgis.com/en/help/main/10.2/#/How_Grouping_Analysis_works/005p0000004w000000/), or CH Index for short ) so I can try to identify the 'best' number(s) of clusters for my data. This has all been working fine.
To compare these results with some from additional clustering methods, I have also used another application (REDCAP: http://www.spatialdatamining.org/software/redcap) on my data as well. Fantastic though the software is, REDCAP does not report the CH Index to help evaluate the 'best' number of clusters in the data. I would like to be able to compare/evaluate my results from ArcGIS's Grouping Analysis with those from REDCAP using the same 'grouping effectiveness' statistic, so I have written another Python script to try to calculate the CH Index 'by hand', as it were, and this is where I've run into a problem.
I wrote my script to try to replicate the approach set out in the Help file for 'How Grouping Analysis works' (see the link to Esri's online Help above) and in the Python script the tool calls (Partition.py). I tried out my script on some of my output feature classes from Grouping Analysis, to check that my script was producing the same results. Here (finally) is the problem: when the Grouping Analysis was based on a single variable, I get exactly the same CH Index result from my script as from Esri's own tool; when the Grouping Analysis was based on more than one variable, I get a different (higher) CH Index result from my script. I am stumped as to why this is happening.
Here are some examples of the different CH Index values I get: For the data referenced in my code below, where the grouping is based on 3 variables and 9 groups:
CH Index from Esri tool: 1911.75679228486
CH Index from my script: 2448.47996865
For a similar dataset, using the same 3 variables but with 31 groups:
CH Index from Esri tool: 1069.1115254454
CH Index from my script: 1114.27024452
Compare this with the results from a dataset where the grouping is based on 1 variable, with 4 groups:
CH Index from Esri tool: 6349.09734505356
CH Index from my script: 6349.09734505
This is my Python 2.7 code:
# Get and print the starting time for running the script import datetime start_time = datetime.datetime.now() print("Script started at " +str(start_time)) import arcpy import numpy as np arcpy.env.workspace = r"E:\Pr6653_GIS_Data_Maps\SKATER_ClusterOutputs_1021FGDB.gdb" # The input feature class inFC = "Clstrs_DstNcl_All_DSHC_RC_K9" # The fields used to generate the clusters using Grouping Analysis inFields = ["DstNcl_All_SCL01INV", "DSInterp_SCL01INV", "HCInterp_SCL01INV"] # The field holding the values identifying the clusters clstField = "SS_GROUP" # Create a new list from inFields and add the cluster field, to be used when # creating the structured Numpy array from the input FC table arrFields = list(inFields) arrFields.append(clstField) # Convert the attribute table of the input FC to a Numpy array baseArr = arcpy.da.TableToNumPyArray(inFC, arrFields) n = len(baseArr) * 1.0 # This is the number of features in the input FC # Get values based on the clustering field clstArr = np.unique(baseArr[clstField]) nc = len(clstArr) * 1.0 # This is the number of groups nc_min = clstArr.min() # This is the minimum value for cluster ID nc_max = clstArr.max() # This is the maximum value for cluster ID SST = 0.0 # This is the total sum of squared differences for fld in inFields: # For each field/variable... varMean = baseArr[fld].mean() # Get the overall mean for the variable varSS = ((baseArr[fld] - varMean)**2.0).sum() # Calculate the sum of squared differences from the variable mean for each value SST += varSS # Add that sum to the total sum of squared differences SSE = 0.0 # This is the sum of squared differences within each group for group in range(nc_min, nc_max + 1): # For each group... grpArr = baseArr[baseArr[clstField] == group] # Create a new array just for that group for fld in inFields: # For each field/variable... grpMean = grpArr[fld].mean() # Get the mean for the variable in that group grpSS = ((grpArr[fld] - grpMean)**2.0).sum() # Calculate the sum of squared differences from the group mean for each value in the group SSE += grpSS # Add that sum to the within-group sum of squared differences # Calculate the pseudo-F statistic R2 = (SST - SSE) / SST fStat = float((R2 / (nc - 1.0)) / ((1.0 - R2) / (n - nc))) # Print the results print("For input " + inFC + ":") print("Number of features = " + str(n)) print("Number of clusters = " + str(nc)) print("SST = " + str(SST)) print("SSE = " + str(SSE)) print("R2 = " + str(R2)) print("CH Index = " + str(fStat)) # Clean up del baseArr, grpArr, clstArr del n, nc, nc_max, nc_min del SST, SSE, R2, fStat del inFields, arrFields print("Script complete. Elapsed time: " + str(datetime.datetime.now() - start_time)) # End of script
If it would help, I'd be happy to post some example data as well.
This code seems to work fine in a univariate situation, but not in a multivariate situation. I should also point out that I don't have a strong background in either statistics or programming.