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I'm using sklearn and agglomerative clustering function. I have a mixed data which includes both numeric and nominal data columns. My nominal columns have values such that "Morning", "Afternoon", "Evening", "Night". If I convert my nominal data to numeric by assigning integer values like 0,1,2,3; euclidean distance will be calculated as 3 between "Night" and "Morning", but, 1 should be return value as a distance.

X = pd.read_csv("mydata.csv", sep=",", header=0, encoding="utf-8")
X = StandardScaler().fit_transform(X)
print("n_samples: %d, n_features: %d" % X.shape)

km = AgglomerativeClustering(n_clusters=5, affinity='euclidean', linkage='average')
km.fit(X)

print("k = %d, Silhouette Coefficient: %0.3f" % (x,
 metrics.silhouette_score(X, km.labels_, sample_size=None)))

Here is my code.

How can I customize the distance function in sklearn or convert my nominal data to numeric?

I think you have 3 options how to convert categorical features to numerical:

1. Use OneHotEncoder. You will transform categorical feature to four new columns, where will be just one 1 and other 0. The problem here is that difference between "morning" and "afternoon" is the same as the same as "morning" and "evening".


2. Use OrdinalEncoder. You transform categorical feature to just one column. "morning" to 1, "afternoon" to 2 etc. The difference between "morning" and "afternoon" will be smaller than "morning" and "evening" which is good, but the difference between "morning" and "night" will be greatest which might not be what you want.


3. Use transformation that I call two_hot_encoder. It is similar to OneHotEncoder, there are just two 1 in the row. The difference between The difference between "morning" and "afternoon" will be the same as the difference between "morning" and "night" and it will be smaller than difference between "morning" and "evening". I think this is the best solution. Check the code.

Code:

def two_hot(x):
 return np.concatenate([
 (x == "morning") | (x == "afternoon"),
 (x == "afternoon") | (x == "evening"),
 (x == "evening") | (x == "night"),
 (x == "night") | (x == "morning"),
 ], axis=1).astype(int)

x = np.array([["morning", "afternoon", "evening", "night"]]).T
print(x)
x = two_hot(x)
print(x)

Output:

[['morning']
 ['afternoon']
 ['evening']
 ['night']]
[[1 0 0 1]
 [1 1 0 0]
 [0 1 1 0]
 [0 0 1 1]]

Then we can measure the distances:

from sklearn.metrics.pairwise import euclidean_distances
euclidean_distances(x)

Output:

array([[0. , 1.41421356, 2. , 1.41421356],
 [1.41421356, 0. , 1.41421356, 2. ],
 [2. , 1.41421356, 0. , 1.41421356],
 [1.41421356, 2. , 1.41421356, 0. ]])

This problem is common to machine learning applications. You need to define one category as the base category (it doesn't matter which) then define indicator variables (0 or 1) for each of the other categories. In other words, create 3 new variables called "Morning", "Afternoon", and "Evening", and assign a one to whichever category each observation has. If it's a night observation, leave each of these new variables as 0.