A few days ago, I put together a demo of data anomaly detection for mixed numeric and categorical data using a self-organizing map (SOM), from scratch, using the C# language. I figured I’d refactor the C# version to Python. Refactoring a non-trivial system from one language to another always gives me new insights into the algorithm being used and the programming languages involved.
A self-organizing map (SOM) is a data structure and associated algorithms that can be used to cluster data. Each cluster has a representative vector. Data items that assigned to a SOM cluster but are far (usually Euclidean distance) from the cluster representative vector are anomalous.
I made a 240-item set of synthetic data that looks like:
F short 24 arkansas 29500 liberal M tall 39 delaware 51200 moderate F short 63 colorado 75800 conservative M medium 36 illinois 44500 moderate F short 27 colorado 28600 liberal . . .
The fields are sex, height, age, State, income, political leaning.
Because SOM clustering uses Euclidean distance, the data must be normalized and encoded. I used min-max normalization on the age (min = 18, max = 68) and income (min = $20,300, max = $81,800) columns. I used one-over-n-hot encoding on the sex, State, and political leaning columns. I used equal-interval encoding for the height column, because it has a natural order.
The resulting normalized and encoded data looks like:
0.5, 0.25, 0.1200, 0.25, 0.00, 0.00, 0.00, 0.1496, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.4200, 0.00, 0.00, 0.25, 0.00, 0.5024, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.9000, 0.00, 0.25, 0.00, 0.00, 0.9024, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.3600, 0.00, 0.00, 0.00, 0.25, 0.3935, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.1800, 0.00, 0.25, 0.00, 0.00, 0.1350, 0.0000, 0.0000, 0.3333
. . .
I set up the demo SOM map as 2-by-2 for a total of 4 map nodes. Creating a SOM map is an iterative process that requires a steps_max value (I used 1,000) and a lrn_rate_max value (I used 2.00). SOM maps are very sensitive to these values, and they must be determined by trial and error. I monitored the SOM map building every 200 iterations by computing the sum of Euclidean distances (SED) between map node vectors and data items assigned to the map node / cluster:
Computing SOM clustering map build step 0 | SED = 311.4767 map build step 200 | SED = 229.7895 map build step 400 | SED = 160.0903 map build step 600 | SED = 122.9567 map build step 800 | SED = 105.7636 Done
Each of the 4 map nodes is identified by a [row][col] pair of indices. The four resulting map node vectors are:
SOM map nodes:
[0][0] : [0.00 0.67 0.81 0.10 0.02 0.11 0.02 0.78 0.04 0.09 0.20]
[0][1] : [0.50 0.31 0.23 0.08 0.06 0.09 0.01 0.23 0.04 0.07 0.23]
[1][0] : [0.00 0.45 0.31 0.09 0.07 0.08 0.02 0.43 0.16 0.18 0.00]
[1][1] : [0.50 0.34 0.72 0.06 0.06 0.04 0.09 0.68 0.19 0.12 0.02]
It’s important to look at the SOM mapping to determine if the steps_max and lrn_rate_max parameter values are good. The 240 data items were assigned to map nodes according to this distribution:
SOM mapping: [0][0] : 43 items [0][1] : 49 items [1][0] : 77 items [1][1] : 71 items
My demo has a function to display the [r][c] cluster ID for each data item. The first four cluster assignments are:
Clustering: X[0] : [0 1] X[1] : [1 0] X[2] : [1 1] X[3] : [1 0] . . .
After the SOM map was constructed, I analyzed the data, looking for the data item assigned to each cluster/node that is farthest from the map node vector:
node [0][0] :
most anomalous data idx = 208
[0.00 0.25 0.72 0.00 0.25 0.00 0.00 0.72 0.00 0.00 0.33]
M short 54 colorado 64800 liberal
distance = 0.5381
node [0][1] :
most anomalous data idx = 179
[0.50 0.75 0.40 0.00 0.00 0.25 0.00 0.37 0.00 0.33 0.00]
F tall 38 delaware 43000 moderate
distance = 0.6320
node [1][0] :
most anomalous data idx = 232
[0.00 0.50 0.04 0.25 0.00 0.00 0.00 0.14 0.00 0.00 0.33]
M medium 20 arkansas 28700 liberal
distance = 0.6067
node [1][1] :
most anomalous data idx = 99
[0.50 0.75 0.48 0.00 0.00 0.00 0.25 0.43 0.00 0.33 0.00]
F tall 42 illinois 47000 moderate
distance = 0.6335
I displayed the index of the anomalous data item, its normalized and encoded form, its raw form, and the distance from the item to its map node vector. In a non-demo scenario, these data items would be examined to determine if they are in fact anomalies, and if so, what might be the cause.
Good fun!
Eight out of 12 months are celebrated in the U.S. as Heritage Months where the idea is to acknowledge the contributions of immigrants from a particular country. The months of January, February, August, and December are anomalous in the sense that there’s no generally recognized heritage country (January), or immigrants from the labeled countries really haven’t made significant positive contributions (February).
March: Irish-American Heritage Month, Greek-American Heritage. April: Arab-American Heritage, Scottish-American Heritage. May: South Asian Heritage, Asian Pacific American Heritage, Jewish American Heritage. June: Caribbean-American Heritage, Russian Heritage. July: French-American Heritage. September: Hispanic Heritage, German-American Heritage. October: Filipino-American Heritage, Italian-American Heritage, Polish-American Heritage. November: American Indian Heritage.
I’m half French (my mother) and half Irish (my father). Left: The movie “Leprechaun 3” (1995) features the evil protagonist in Las Vegas. Very funny but not a realistic depiction of Irish culture. Right: “The Pink Panther” (2006) features bumbling Inspector Jacques Clouseau in Paris. Moderately funny but not a completely realistic depiction of French culture.
Demo code. Replace “lt” (less than), “gt”, “lte”, “gte”, “and” with Boolean operator symbols.
# som_anomaly.py
# self-organizing map anomaly detection
# from-scratch Python
import numpy as np
class ClusterSOM:
def __init__(self, data, map_rows,
map_cols, seed):
self.map_rows = map_rows
self.map_cols = map_cols
self.data = data # by ref
self.rnd = np.random.RandomState(seed)
dim = len(data[0])
self.map = np.zeros((map_rows, map_cols,dim),
dtype=np.float64)
for i in range(map_rows):
for j in range(map_cols):
for d in range(dim): # could do random vector
self.map[i][j][d] = self.rnd.rand()
self.mapping = np.zeros((map_rows, map_cols),
dtype=object)
for i in range(map_rows):
for j in range(map_cols):
self.mapping[i][j] = [] # empty list
# ---------------------------------------------------------
def cluster(self, lrn_rate_max, steps_max):
n = len(self.data)
dim = len(self.data[0])
range_max = self.map_rows + self.map_cols
# compute map
for step in range(steps_max):
if step % (steps_max // 5) == 0: # progress
# print("map build step " + str(step), end = "")
sum = 0.0
for ix in range(n):
(r,c) = self.closest_node(ix)
# print(r); print(c); input()
data_item = self.data[ix]
node_vec = self.map[r][c]
dist = np.linalg.norm(data_item - \
node_vec)
sum += dist
s1 = "map build step " + str(step).ljust(4, " ")
s2 = " | SED = %0.4f " % sum
print(s1 + s2)
# print(" | SED = %0.4f " % sum)
pct_left = 1.0 - (step / steps_max)
curr_range = pct_left * lrn_rate_max
curr_lrn_rate = pct_left * lrn_rate_max
idx = self.rnd.randint(0,n)
(r,c) = self.closest_node(idx)
for i in range(self.map_rows):
for j in range(self.map_cols):
if ClusterSOM.manhatt_dist(r, c, i, j) <= \
curr_range:
for d in range(dim):
self.map[i][j][d] = \
self.map[i][j][d] + curr_lrn_rate * \
(self.data[idx][d] - self.map[i][j][d])
# compute mapping from map
for idx in range(n):
(r,c) = self.closest_node(idx)
# print(r); print(c); input()
self.mapping[r][c].append(idx)
# ---------------------------------------------------------
def closest_node(self, idx): # helper
r = -1; c = -1
small_dist = 1000000.0
for i in range(self.map_rows):
for j in range(self.map_cols):
dist = np.linalg.norm(self.data[idx] - \
self.map[i][j])
# print(dist); input()
if dist "lt" small_dist:
small_dist = dist
anom_idx = idx
# ---- end class ------------------------------------------
def file_load(fn, comment):
result = []
fi = open(fn)
for line in fi:
line = line.strip()
if line.startswith(comment): continue
result.append(line)
fi.close()
return result
def main():
print("\nBegin self-organizing" +
" map (SOM) anomaly analysis for mixed data" +
" from scratch Python")
print("\nLoading 240-item synthetic People dataset ")
rf = ".\\Data\\people_raw.txt"
raw_file_array = file_load(rf, "#")
fn = ".\\Data\\people_240.txt"
X = np.loadtxt(fn, usecols=[0,1,2,3,4,5,6,7,8,9,10],
delimiter=",", comments="#", dtype=np.float64)
print("\nFirst three rows normalized data: ")
np.set_printoptions(precision=4, suppress=True,
floatmode='fixed', linewidth=120)
for i in range(3):
print(X[i])
map_rows = 2
map_cols = 2
lrn_rate_max = 2.00
steps_max = 1000
print("\nsetting map_rows = " + str(map_rows))
print("setting map_cols = " + str(map_cols))
print("Setting lrn_max_rate = %0.2f " % lrn_rate_max)
print("Setting steps_max = " + str(steps_max))
print("\nComputing SOM clustering ")
som = ClusterSOM(X, map_rows, map_cols, seed=3)
som.cluster(lrn_rate_max, steps_max)
print("Done ")
# np.set_printoptions(precision=2, suppress=True,
# floatmode='fixed', linewidth=120)
print("\nSOM map nodes: ")
for i in range(map_rows):
for j in range(map_cols):
print("[" + str(i) + "][" + str(j) + "] : ", end="")
print(som.map[i][j]) # a vector
print("\nSOM mapping: ")
for i in range(map_rows):
for j in range(map_cols):
# show count items assigned to each map node
print("[" + str(i) + "][" + str(j) + "] : ", end="")
print(str(len(som.mapping[i][j])) + " items ")
# show idx assigned to each node
# print("\nmap node: " + str(i) + " " + str(j))
# for k in range(len(som.mapping[i][j])):
# print(str(som.mapping[i][j][k]) + " ", end="")
# print("")
# show (r,c) cluster ID for each data item
clustering = som.get_clustering()
print("\nClustering: ")
# for i in range(len(X)): # all 240 items
for i in range(4): # first 4
print("X" + "[" + str(i).ljust(2, " ") + "] : ",\
end="")
print(clustering[i])
print(". . .")
print("\nAnalyzing for anomalies ")
som.analyze(raw_file_array)
print("\nEnd SOM anomaly ")
if __name__ == "__main__":
main()
Raw data:
# people_raw.txt # F short 24 arkansas 29500 liberal M tall 39 delaware 51200 moderate F short 63 colorado 75800 conservative M medium 36 illinois 44500 moderate F short 27 colorado 28600 liberal F short 50 colorado 56500 moderate F medium 50 illinois 55000 moderate M tall 19 delaware 32700 conservative F short 22 illinois 27700 moderate M tall 39 delaware 47100 liberal F short 34 arkansas 39400 moderate M medium 22 illinois 33500 conservative F medium 35 delaware 35200 liberal M tall 33 colorado 46400 moderate F short 45 colorado 54100 moderate F short 42 illinois 50700 moderate M tall 33 colorado 46800 moderate F tall 25 delaware 30000 moderate M medium 31 colorado 46400 conservative F short 27 arkansas 32500 liberal F short 48 illinois 54000 moderate M tall 64 illinois 71300 liberal F medium 61 colorado 72400 conservative F short 54 illinois 61000 conservative F short 29 arkansas 36300 conservative F short 50 delaware 55000 moderate F medium 55 illinois 62500 conservative F medium 40 illinois 52400 conservative F short 22 arkansas 23600 liberal F short 68 colorado 78400 conservative M tall 60 illinois 71700 liberal M tall 34 delaware 46500 moderate M medium 25 delaware 37100 conservative M short 31 illinois 48900 moderate F short 43 delaware 48000 moderate F short 58 colorado 65400 liberal M tall 55 illinois 60700 liberal M tall 43 colorado 51100 moderate M tall 43 delaware 53200 moderate M medium 21 arkansas 37200 conservative F short 55 delaware 64600 conservative F short 64 colorado 74800 conservative M tall 41 illinois 58800 moderate F medium 64 delaware 72700 conservative M medium 56 illinois 66600 liberal F short 31 delaware 36000 moderate M tall 65 delaware 70100 liberal F tall 55 illinois 64300 conservative M short 25 arkansas 40300 conservative F short 46 delaware 51000 moderate M tall 36 illinois 53500 conservative F short 52 illinois 58100 moderate F short 61 delaware 67900 conservative F short 57 delaware 65700 conservative M tall 46 colorado 52600 moderate M tall 62 arkansas 66800 liberal F short 55 illinois 62700 conservative M medium 22 delaware 27700 moderate M tall 50 illinois 62900 conservative M tall 32 illinois 41800 moderate M short 21 delaware 35600 conservative F medium 44 colorado 52000 moderate F short 46 illinois 51700 moderate F short 62 colorado 69700 conservative F short 57 illinois 66400 conservative M medium 67 illinois 75800 liberal F short 29 arkansas 34300 liberal F short 53 illinois 60100 conservative M tall 44 arkansas 54800 moderate F medium 46 colorado 52300 moderate M tall 20 illinois 30100 moderate M medium 38 illinois 53500 moderate F short 50 colorado 58600 moderate F short 33 colorado 42500 moderate M tall 33 colorado 39300 moderate F short 26 colorado 40400 conservative F short 58 arkansas 70700 conservative F tall 43 illinois 48000 moderate M medium 46 arkansas 64400 conservative F short 60 arkansas 71700 conservative M tall 42 arkansas 48900 moderate M tall 56 delaware 56400 liberal M short 62 colorado 66300 liberal M short 50 arkansas 64800 moderate F short 47 illinois 52000 moderate M tall 67 colorado 80400 liberal M tall 40 delaware 50400 moderate F short 42 colorado 48400 moderate F short 64 arkansas 72000 conservative M medium 47 arkansas 58700 liberal F medium 45 colorado 52800 moderate M tall 25 delaware 40900 conservative F short 38 arkansas 48400 conservative F short 55 delaware 60000 moderate M tall 44 arkansas 60600 moderate F medium 33 arkansas 41000 moderate F short 34 delaware 39000 moderate F short 27 colorado 33700 liberal F short 32 colorado 40700 moderate F tall 42 illinois 47000 moderate M short 24 delaware 40300 conservative F short 42 colorado 50300 moderate F short 25 delaware 28000 liberal F short 51 colorado 58000 moderate M medium 55 colorado 63500 liberal F short 44 arkansas 47800 liberal M short 18 arkansas 39800 conservative M tall 67 colorado 71600 liberal F short 45 delaware 50000 moderate F short 48 arkansas 55800 moderate M short 25 colorado 39000 moderate M tall 67 arkansas 78300 moderate F short 37 delaware 42000 moderate M short 32 arkansas 42700 moderate F short 48 arkansas 57000 moderate M tall 66 delaware 75000 liberal F tall 61 arkansas 70000 conservative M medium 58 delaware 68900 moderate F short 19 arkansas 24000 liberal F short 38 delaware 43000 moderate M medium 27 arkansas 36400 moderate F short 42 arkansas 48000 moderate F short 60 arkansas 71300 conservative M tall 27 delaware 34800 conservative F tall 29 colorado 37100 conservative M medium 43 arkansas 56700 moderate F medium 48 arkansas 56700 moderate F medium 27 delaware 29400 liberal M tall 44 arkansas 55200 conservative F short 23 colorado 26300 liberal M tall 36 colorado 53000 liberal F short 64 delaware 72500 conservative F short 29 delaware 30000 liberal M short 33 arkansas 49300 moderate M tall 66 colorado 75000 liberal M medium 21 delaware 34300 conservative F short 27 arkansas 32700 liberal F short 29 arkansas 31800 liberal M tall 31 arkansas 48600 moderate F short 36 delaware 41000 moderate F short 49 colorado 55700 moderate M short 28 arkansas 38400 conservative M medium 43 delaware 56600 moderate M medium 46 colorado 58800 moderate F short 57 arkansas 69800 conservative M short 52 delaware 59400 moderate M tall 31 delaware 43500 moderate M tall 55 arkansas 62000 liberal F short 50 arkansas 56400 moderate F short 48 colorado 55900 moderate M medium 22 delaware 34500 conservative F short 59 delaware 66700 conservative F short 34 arkansas 42800 liberal M tall 64 arkansas 77200 liberal F short 29 delaware 33500 liberal M medium 34 colorado 43200 moderate M medium 61 arkansas 75000 liberal F short 64 delaware 71100 conservative M short 29 arkansas 41300 conservative F short 63 colorado 70600 conservative M medium 29 colorado 40000 conservative M tall 51 arkansas 62700 moderate M tall 24 delaware 37700 conservative F medium 48 colorado 57500 moderate F short 18 arkansas 27400 conservative F short 18 arkansas 20300 liberal F short 33 colorado 38200 liberal M medium 20 delaware 34800 conservative F short 29 delaware 33000 liberal M short 44 delaware 63000 conservative M tall 65 delaware 81800 conservative M tall 56 arkansas 63700 liberal M medium 52 delaware 58400 moderate M medium 29 colorado 48600 conservative M tall 47 colorado 58900 moderate F medium 68 arkansas 72600 liberal F short 31 delaware 36000 moderate F short 61 colorado 62500 liberal F short 19 colorado 21500 liberal F tall 38 delaware 43000 moderate M tall 26 arkansas 42300 conservative F short 61 colorado 67400 conservative F short 40 arkansas 46500 moderate M medium 49 arkansas 65200 moderate F medium 56 arkansas 67500 conservative M short 48 colorado 66000 moderate F short 52 arkansas 56300 liberal M tall 18 arkansas 29800 conservative M tall 56 delaware 59300 liberal M medium 52 colorado 64400 moderate M medium 18 colorado 28600 moderate M tall 58 arkansas 66200 liberal M tall 39 colorado 55100 moderate M tall 46 arkansas 62900 moderate M medium 40 colorado 46200 moderate M medium 60 arkansas 72700 liberal F short 36 colorado 40700 liberal F short 44 arkansas 52300 moderate F short 28 arkansas 31300 liberal F short 54 delaware 62600 conservative M medium 51 arkansas 61200 moderate M short 32 colorado 46100 moderate F short 55 arkansas 62700 conservative F short 25 delaware 26200 liberal F medium 33 delaware 37300 liberal M medium 29 colorado 46200 conservative F short 65 arkansas 72700 conservative M tall 43 colorado 51400 moderate M short 54 colorado 64800 liberal F short 61 colorado 72700 conservative F short 52 colorado 63600 conservative F short 30 colorado 33500 liberal F short 29 arkansas 31400 liberal M tall 47 delaware 59400 moderate F short 39 colorado 47800 moderate F short 47 delaware 52000 moderate M medium 49 arkansas 58600 moderate M tall 63 delaware 67400 liberal M medium 30 arkansas 39200 conservative M tall 61 delaware 69600 liberal M medium 47 delaware 58700 moderate F short 30 delaware 34500 liberal M medium 51 delaware 58000 moderate M medium 24 arkansas 38800 moderate M short 49 arkansas 64500 moderate F medium 66 delaware 74500 conservative M tall 65 arkansas 76900 conservative M short 46 colorado 58000 conservative M tall 45 delaware 51800 moderate M short 47 arkansas 63600 conservative M tall 29 arkansas 44800 conservative M tall 57 delaware 69300 liberal M medium 20 arkansas 28700 liberal M medium 35 arkansas 43400 moderate M tall 61 delaware 67000 liberal M short 31 delaware 37300 moderate F short 18 arkansas 20800 liberal F medium 26 delaware 29200 liberal M medium 28 arkansas 36400 liberal M tall 59 delaware 69400 liberal
Normalized and encoded data:
# people_240.txt
#
# sex (M = 0.0, F = 0.5)
# height (short, medium, tall)
# age (min = 18, max = 68)
# State (Arkansas, Colorado, Delaware, Illinois)
# income (min = $20,300, max = $81,800)
# political leaning (conservative, moderate, liberal)
#
0.5, 0.25, 0.1200, 0.25, 0.00, 0.00, 0.00, 0.1496, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.4200, 0.00, 0.00, 0.25, 0.00, 0.5024, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.9000, 0.00, 0.25, 0.00, 0.00, 0.9024, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.3600, 0.00, 0.00, 0.00, 0.25, 0.3935, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.1800, 0.00, 0.25, 0.00, 0.00, 0.1350, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.6400, 0.00, 0.25, 0.00, 0.00, 0.5886, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.6400, 0.00, 0.00, 0.00, 0.25, 0.5642, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.0200, 0.00, 0.00, 0.25, 0.00, 0.2016, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.0800, 0.00, 0.00, 0.00, 0.25, 0.1203, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.4200, 0.00, 0.00, 0.25, 0.00, 0.4358, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.3200, 0.25, 0.00, 0.00, 0.00, 0.3106, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.0800, 0.00, 0.00, 0.00, 0.25, 0.2146, 0.3333, 0.0000, 0.0000
0.5, 0.50, 0.3400, 0.00, 0.00, 0.25, 0.00, 0.2423, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.3000, 0.00, 0.25, 0.00, 0.00, 0.4244, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.5400, 0.00, 0.25, 0.00, 0.00, 0.5496, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.4800, 0.00, 0.00, 0.00, 0.25, 0.4943, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.3000, 0.00, 0.25, 0.00, 0.00, 0.4309, 0.0000, 0.3333, 0.0000
0.5, 0.75, 0.1400, 0.00, 0.00, 0.25, 0.00, 0.1577, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.2600, 0.00, 0.25, 0.00, 0.00, 0.4244, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.1800, 0.25, 0.00, 0.00, 0.00, 0.1984, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.6000, 0.00, 0.00, 0.00, 0.25, 0.5480, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9200, 0.00, 0.00, 0.00, 0.25, 0.8293, 0.0000, 0.0000, 0.3333
0.5, 0.50, 0.8600, 0.00, 0.25, 0.00, 0.00, 0.8472, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.7200, 0.00, 0.00, 0.00, 0.25, 0.6618, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.2602, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.6400, 0.00, 0.00, 0.25, 0.00, 0.5642, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.7400, 0.00, 0.00, 0.00, 0.25, 0.6862, 0.3333, 0.0000, 0.0000
0.5, 0.50, 0.4400, 0.00, 0.00, 0.00, 0.25, 0.5220, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.0800, 0.25, 0.00, 0.00, 0.00, 0.0537, 0.0000, 0.0000, 0.3333
0.5, 0.25, 1.0000, 0.00, 0.25, 0.00, 0.00, 0.9447, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.8400, 0.00, 0.00, 0.00, 0.25, 0.8358, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.3200, 0.00, 0.00, 0.25, 0.00, 0.4260, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.1400, 0.00, 0.00, 0.25, 0.00, 0.2732, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.2600, 0.00, 0.00, 0.00, 0.25, 0.4650, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.5000, 0.00, 0.00, 0.25, 0.00, 0.4504, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.8000, 0.00, 0.25, 0.00, 0.00, 0.7333, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.7400, 0.00, 0.00, 0.00, 0.25, 0.6569, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.5000, 0.00, 0.25, 0.00, 0.00, 0.5008, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.5000, 0.00, 0.00, 0.25, 0.00, 0.5350, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.0600, 0.25, 0.00, 0.00, 0.00, 0.2748, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.7400, 0.00, 0.00, 0.25, 0.00, 0.7203, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.9200, 0.00, 0.25, 0.00, 0.00, 0.8862, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.4600, 0.00, 0.00, 0.00, 0.25, 0.6260, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.9200, 0.00, 0.00, 0.25, 0.00, 0.8520, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.7600, 0.00, 0.00, 0.00, 0.25, 0.7528, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2600, 0.00, 0.00, 0.25, 0.00, 0.2553, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9400, 0.00, 0.00, 0.25, 0.00, 0.8098, 0.0000, 0.0000, 0.3333
0.5, 0.75, 0.7400, 0.00, 0.00, 0.00, 0.25, 0.7154, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.1400, 0.25, 0.00, 0.00, 0.00, 0.3252, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.5600, 0.00, 0.00, 0.25, 0.00, 0.4992, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.3600, 0.00, 0.00, 0.00, 0.25, 0.5398, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.6800, 0.00, 0.00, 0.00, 0.25, 0.6146, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.8600, 0.00, 0.00, 0.25, 0.00, 0.7740, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.7800, 0.00, 0.00, 0.25, 0.00, 0.7382, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.5600, 0.00, 0.25, 0.00, 0.00, 0.5252, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.8800, 0.25, 0.00, 0.00, 0.00, 0.7561, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.7400, 0.00, 0.00, 0.00, 0.25, 0.6894, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.0800, 0.00, 0.00, 0.25, 0.00, 0.1203, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.6400, 0.00, 0.00, 0.00, 0.25, 0.6927, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.2800, 0.00, 0.00, 0.00, 0.25, 0.3496, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.0600, 0.00, 0.00, 0.25, 0.00, 0.2488, 0.3333, 0.0000, 0.0000
0.5, 0.50, 0.5200, 0.00, 0.25, 0.00, 0.00, 0.5154, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.5600, 0.00, 0.00, 0.00, 0.25, 0.5106, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.8800, 0.00, 0.25, 0.00, 0.00, 0.8033, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.7800, 0.00, 0.00, 0.00, 0.25, 0.7496, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.9800, 0.00, 0.00, 0.00, 0.25, 0.9024, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.2276, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.7000, 0.00, 0.00, 0.00, 0.25, 0.6472, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.5200, 0.25, 0.00, 0.00, 0.00, 0.5610, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.5600, 0.00, 0.25, 0.00, 0.00, 0.5203, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.0400, 0.00, 0.00, 0.00, 0.25, 0.1593, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.4000, 0.00, 0.00, 0.00, 0.25, 0.5398, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6400, 0.00, 0.25, 0.00, 0.00, 0.6228, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.3000, 0.00, 0.25, 0.00, 0.00, 0.3610, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.3000, 0.00, 0.25, 0.00, 0.00, 0.3089, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.1600, 0.00, 0.25, 0.00, 0.00, 0.3268, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.8000, 0.25, 0.00, 0.00, 0.00, 0.8195, 0.3333, 0.0000, 0.0000
0.5, 0.75, 0.5000, 0.00, 0.00, 0.00, 0.25, 0.4504, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.5600, 0.25, 0.00, 0.00, 0.00, 0.7171, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.8400, 0.25, 0.00, 0.00, 0.00, 0.8358, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.4800, 0.25, 0.00, 0.00, 0.00, 0.4650, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.7600, 0.00, 0.00, 0.25, 0.00, 0.5870, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.8800, 0.00, 0.25, 0.00, 0.00, 0.7480, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.6400, 0.25, 0.00, 0.00, 0.00, 0.7236, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.5800, 0.00, 0.00, 0.00, 0.25, 0.5154, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9800, 0.00, 0.25, 0.00, 0.00, 0.9772, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.4400, 0.00, 0.00, 0.25, 0.00, 0.4894, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.4800, 0.00, 0.25, 0.00, 0.00, 0.4569, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.9200, 0.25, 0.00, 0.00, 0.00, 0.8407, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.5800, 0.25, 0.00, 0.00, 0.00, 0.6244, 0.0000, 0.0000, 0.3333
0.5, 0.50, 0.5400, 0.00, 0.25, 0.00, 0.00, 0.5285, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.1400, 0.00, 0.00, 0.25, 0.00, 0.3350, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.4000, 0.25, 0.00, 0.00, 0.00, 0.4569, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.7400, 0.00, 0.00, 0.25, 0.00, 0.6455, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.5200, 0.25, 0.00, 0.00, 0.00, 0.6553, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.3000, 0.25, 0.00, 0.00, 0.00, 0.3366, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.3200, 0.00, 0.00, 0.25, 0.00, 0.3041, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.1800, 0.00, 0.25, 0.00, 0.00, 0.2179, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2800, 0.00, 0.25, 0.00, 0.00, 0.3317, 0.0000, 0.3333, 0.0000
0.5, 0.75, 0.4800, 0.00, 0.00, 0.00, 0.25, 0.4341, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.1200, 0.00, 0.00, 0.25, 0.00, 0.3252, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.4800, 0.00, 0.25, 0.00, 0.00, 0.4878, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.1400, 0.00, 0.00, 0.25, 0.00, 0.1252, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.6600, 0.00, 0.25, 0.00, 0.00, 0.6130, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.7400, 0.00, 0.25, 0.00, 0.00, 0.7024, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.5200, 0.25, 0.00, 0.00, 0.00, 0.4472, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.0000, 0.25, 0.00, 0.00, 0.00, 0.3171, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.9800, 0.00, 0.25, 0.00, 0.00, 0.8341, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.5400, 0.00, 0.00, 0.25, 0.00, 0.4829, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6000, 0.25, 0.00, 0.00, 0.00, 0.5772, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.1400, 0.00, 0.25, 0.00, 0.00, 0.3041, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9800, 0.25, 0.00, 0.00, 0.00, 0.9431, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.3800, 0.00, 0.00, 0.25, 0.00, 0.3528, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.2800, 0.25, 0.00, 0.00, 0.00, 0.3642, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6000, 0.25, 0.00, 0.00, 0.00, 0.5967, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9600, 0.00, 0.00, 0.25, 0.00, 0.8894, 0.0000, 0.0000, 0.3333
0.5, 0.75, 0.8600, 0.25, 0.00, 0.00, 0.00, 0.8081, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.8000, 0.00, 0.00, 0.25, 0.00, 0.7902, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.0200, 0.25, 0.00, 0.00, 0.00, 0.0602, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.4000, 0.00, 0.00, 0.25, 0.00, 0.3691, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.1800, 0.25, 0.00, 0.00, 0.00, 0.2618, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.4800, 0.25, 0.00, 0.00, 0.00, 0.4504, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.8400, 0.25, 0.00, 0.00, 0.00, 0.8293, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.1800, 0.00, 0.00, 0.25, 0.00, 0.2358, 0.3333, 0.0000, 0.0000
0.5, 0.75, 0.2200, 0.00, 0.25, 0.00, 0.00, 0.2732, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.5000, 0.25, 0.00, 0.00, 0.00, 0.5919, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.6000, 0.25, 0.00, 0.00, 0.00, 0.5919, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.1800, 0.00, 0.00, 0.25, 0.00, 0.1480, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.5200, 0.25, 0.00, 0.00, 0.00, 0.5675, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.1000, 0.00, 0.25, 0.00, 0.00, 0.0976, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.3600, 0.00, 0.25, 0.00, 0.00, 0.5317, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.9200, 0.00, 0.00, 0.25, 0.00, 0.8488, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.2200, 0.00, 0.00, 0.25, 0.00, 0.1577, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.3000, 0.25, 0.00, 0.00, 0.00, 0.4715, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9600, 0.00, 0.25, 0.00, 0.00, 0.8894, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.0600, 0.00, 0.00, 0.25, 0.00, 0.2276, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.1800, 0.25, 0.00, 0.00, 0.00, 0.2016, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.1870, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.2600, 0.25, 0.00, 0.00, 0.00, 0.4602, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.3600, 0.00, 0.00, 0.25, 0.00, 0.3366, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6200, 0.00, 0.25, 0.00, 0.00, 0.5756, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.2000, 0.25, 0.00, 0.00, 0.00, 0.2943, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.5000, 0.00, 0.00, 0.25, 0.00, 0.5902, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.5600, 0.00, 0.25, 0.00, 0.00, 0.6260, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.7800, 0.25, 0.00, 0.00, 0.00, 0.8049, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.6800, 0.00, 0.00, 0.25, 0.00, 0.6358, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.2600, 0.00, 0.00, 0.25, 0.00, 0.3772, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.7400, 0.25, 0.00, 0.00, 0.00, 0.6780, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.6400, 0.25, 0.00, 0.00, 0.00, 0.5870, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6000, 0.00, 0.25, 0.00, 0.00, 0.5789, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.0800, 0.00, 0.00, 0.25, 0.00, 0.2309, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.8200, 0.00, 0.00, 0.25, 0.00, 0.7545, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.3200, 0.25, 0.00, 0.00, 0.00, 0.3659, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.9200, 0.25, 0.00, 0.00, 0.00, 0.9252, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2200, 0.00, 0.00, 0.25, 0.00, 0.2146, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.3200, 0.00, 0.25, 0.00, 0.00, 0.3724, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.8600, 0.25, 0.00, 0.00, 0.00, 0.8894, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.9200, 0.00, 0.00, 0.25, 0.00, 0.8260, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.3415, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.9000, 0.00, 0.25, 0.00, 0.00, 0.8179, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.2200, 0.00, 0.25, 0.00, 0.00, 0.3203, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.6600, 0.25, 0.00, 0.00, 0.00, 0.6894, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.1200, 0.00, 0.00, 0.25, 0.00, 0.2829, 0.3333, 0.0000, 0.0000
0.5, 0.50, 0.6000, 0.00, 0.25, 0.00, 0.00, 0.6049, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.0000, 0.25, 0.00, 0.00, 0.00, 0.1154, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.0000, 0.25, 0.00, 0.00, 0.00, 0.0000, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.3000, 0.00, 0.25, 0.00, 0.00, 0.2911, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.0400, 0.00, 0.00, 0.25, 0.00, 0.2358, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.2200, 0.00, 0.00, 0.25, 0.00, 0.2065, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.5200, 0.00, 0.00, 0.25, 0.00, 0.6943, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.9400, 0.00, 0.00, 0.25, 0.00, 1.0000, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.7600, 0.25, 0.00, 0.00, 0.00, 0.7057, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.6800, 0.00, 0.00, 0.25, 0.00, 0.6195, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.2200, 0.00, 0.25, 0.00, 0.00, 0.4602, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.5800, 0.00, 0.25, 0.00, 0.00, 0.6276, 0.0000, 0.3333, 0.0000
0.5, 0.50, 1.0000, 0.25, 0.00, 0.00, 0.00, 0.8504, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2600, 0.00, 0.00, 0.25, 0.00, 0.2553, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.8600, 0.00, 0.25, 0.00, 0.00, 0.6862, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.0200, 0.00, 0.25, 0.00, 0.00, 0.0195, 0.0000, 0.0000, 0.3333
0.5, 0.75, 0.4000, 0.00, 0.00, 0.25, 0.00, 0.3691, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.1600, 0.25, 0.00, 0.00, 0.00, 0.3577, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.8600, 0.00, 0.25, 0.00, 0.00, 0.7659, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.4400, 0.25, 0.00, 0.00, 0.00, 0.4260, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.6200, 0.25, 0.00, 0.00, 0.00, 0.7301, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.7600, 0.25, 0.00, 0.00, 0.00, 0.7675, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.6000, 0.00, 0.25, 0.00, 0.00, 0.7431, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.6800, 0.25, 0.00, 0.00, 0.00, 0.5854, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.0000, 0.25, 0.00, 0.00, 0.00, 0.1545, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.7600, 0.00, 0.00, 0.25, 0.00, 0.6341, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.6800, 0.00, 0.25, 0.00, 0.00, 0.7171, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.0000, 0.00, 0.25, 0.00, 0.00, 0.1350, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.8000, 0.25, 0.00, 0.00, 0.00, 0.7463, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.4200, 0.00, 0.25, 0.00, 0.00, 0.5659, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.5600, 0.25, 0.00, 0.00, 0.00, 0.6927, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.4400, 0.00, 0.25, 0.00, 0.00, 0.4211, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.8400, 0.25, 0.00, 0.00, 0.00, 0.8520, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.3600, 0.00, 0.25, 0.00, 0.00, 0.3317, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.5200, 0.25, 0.00, 0.00, 0.00, 0.5203, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.2000, 0.25, 0.00, 0.00, 0.00, 0.1789, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.7200, 0.00, 0.00, 0.25, 0.00, 0.6878, 0.3333, 0.0000, 0.0000
0.0, 0.50, 0.6600, 0.25, 0.00, 0.00, 0.00, 0.6650, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.2800, 0.00, 0.25, 0.00, 0.00, 0.4195, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.7400, 0.25, 0.00, 0.00, 0.00, 0.6894, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.1400, 0.00, 0.00, 0.25, 0.00, 0.0959, 0.0000, 0.0000, 0.3333
0.5, 0.50, 0.3000, 0.00, 0.00, 0.25, 0.00, 0.2764, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.2200, 0.00, 0.25, 0.00, 0.00, 0.4211, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.9400, 0.25, 0.00, 0.00, 0.00, 0.8520, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.5000, 0.00, 0.25, 0.00, 0.00, 0.5057, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.7200, 0.00, 0.25, 0.00, 0.00, 0.7236, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.8600, 0.00, 0.25, 0.00, 0.00, 0.8520, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.6800, 0.00, 0.25, 0.00, 0.00, 0.7041, 0.3333, 0.0000, 0.0000
0.5, 0.25, 0.2400, 0.00, 0.25, 0.00, 0.00, 0.2146, 0.0000, 0.0000, 0.3333
0.5, 0.25, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.1805, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.5800, 0.00, 0.00, 0.25, 0.00, 0.6358, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.4200, 0.00, 0.25, 0.00, 0.00, 0.4472, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.5800, 0.00, 0.00, 0.25, 0.00, 0.5154, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.6200, 0.25, 0.00, 0.00, 0.00, 0.6228, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.9000, 0.00, 0.00, 0.25, 0.00, 0.7659, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.2400, 0.25, 0.00, 0.00, 0.00, 0.3073, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.8600, 0.00, 0.00, 0.25, 0.00, 0.8016, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.5800, 0.00, 0.00, 0.25, 0.00, 0.6244, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.2400, 0.00, 0.00, 0.25, 0.00, 0.2309, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.6600, 0.00, 0.00, 0.25, 0.00, 0.6130, 0.0000, 0.3333, 0.0000
0.0, 0.50, 0.1200, 0.25, 0.00, 0.00, 0.00, 0.3008, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.6200, 0.25, 0.00, 0.00, 0.00, 0.7187, 0.0000, 0.3333, 0.0000
0.5, 0.50, 0.9600, 0.00, 0.00, 0.25, 0.00, 0.8813, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.9400, 0.25, 0.00, 0.00, 0.00, 0.9203, 0.3333, 0.0000, 0.0000
0.0, 0.25, 0.5600, 0.00, 0.25, 0.00, 0.00, 0.6130, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.5400, 0.00, 0.00, 0.25, 0.00, 0.5122, 0.0000, 0.3333, 0.0000
0.0, 0.25, 0.5800, 0.25, 0.00, 0.00, 0.00, 0.7041, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.2200, 0.25, 0.00, 0.00, 0.00, 0.3984, 0.3333, 0.0000, 0.0000
0.0, 0.75, 0.7800, 0.00, 0.00, 0.25, 0.00, 0.7967, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.0400, 0.25, 0.00, 0.00, 0.00, 0.1366, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.3400, 0.25, 0.00, 0.00, 0.00, 0.3756, 0.0000, 0.3333, 0.0000
0.0, 0.75, 0.8600, 0.00, 0.00, 0.25, 0.00, 0.7593, 0.0000, 0.0000, 0.3333
0.0, 0.25, 0.2600, 0.00, 0.00, 0.25, 0.00, 0.2764, 0.0000, 0.3333, 0.0000
0.5, 0.25, 0.0000, 0.25, 0.00, 0.00, 0.00, 0.0081, 0.0000, 0.0000, 0.3333
0.5, 0.50, 0.1600, 0.00, 0.00, 0.25, 0.00, 0.1447, 0.0000, 0.0000, 0.3333
0.0, 0.50, 0.2000, 0.25, 0.00, 0.00, 0.00, 0.2618, 0.0000, 0.0000, 0.3333
0.0, 0.75, 0.8200, 0.00, 0.00, 0.25, 0.00, 0.7984, 0.0000, 0.0000, 0.3333
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James D. McCaffrey 
Greatings M. James,I wish you to be fine,
Thank you for sharing,
Please M. James, could you give me your opinion about a problem that I try to solve which is declined like this:
I want to implement SOM to my time series data for detecting suspicious transactions and analyze the profile of the customers who made them, but there are some categorical variables which have many categories to encode, can I still use SOM with this high cardinality while considering that I apply one hot encoding ?
Thank you Sir,
Kind regards.
Yes, you can use a SOM with categorical data, but I recommend using one-over-n-hot encoding instead of standard one-hot encoding. With standard one-hot encoding, the difference between any two categorical variables, regardless of how many possible values the variable has, is sqrt(2) = 1.41. With one-over-n-hot encoding, the distance between variables with many possible values is less than the distance between variables with fewer possible values. This makes sense from an entropy point of view.