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Python implementations of the k-modes and k-prototypes clustering algorithms for clustering categorical data.

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Python implementations of the k-modes and k-prototypes clustering algorithms. Relies on numpy for a lot of the heavy lifting.

k-modes is used for clustering categorical variables. It defines clusters based on the number of matching categories between data points. (This is in contrast to the more well-known k-means algorithm, which clusters numerical data based on Euclidean distance.) The k-prototypes algorithm combines k-modes and k-means and is able to cluster mixed numerical / categorical data.

Implemented are:

The code is modeled after the clustering algorithms in scikit-learn and has the same familiar interface.

I would love to have more people play around with this and give me feedback on my implementation. If you come across any issues in running or installing kmodes, please submit a bug report.



kmodes can be installed using pip:

pip install kmodes

To upgrade to the latest version (recommended), run it like this:

pip install --upgrade kmodes

Alternatively, you can build the latest development version from source:

git clone
cd kmodes
python install


import numpy as np
from kmodes.kmodes import KModes

# random categorical data
data = np.random.choice(20, (100, 10))

km = KModes(n_clusters=4, init='Huang', n_init=5, verbose=1)

clusters = km.fit_predict(data)

# Print the cluster centroids

The examples directory showcases simple use cases of both k-modes (‘’) and k-prototypes (‘’).

Missing / unseen data

The k-modes algorithm accepts np.NaN values as missing values in the X matrix. However, users are strongly suggested to consider filling in the missing data themselves in a way that makes sense for the problem at hand. This is especially important in case of many missing values.

The k-modes algorithm currently handles missing data as follows. When fitting the model, np.NaN values are encoded into their own category (let’s call it “unknown values”). When predicting, the model treats any values in X that (1) it has not seen before during training, or (2) are missing, as being a member of the “unknown values” category. Simply put, the algorithm treats any missing / unseen data as matching with each other but mismatching with non-missing / seen data when determining similarity between points.

The k-prototypes also accepts np.NaN values as missing values for the categorical variables, but does not accept missing values for the numerical values. It is up to the user to come up with a way of handling these missing data that is appropriate for the problem at hand.

Parallel execution

The k-modes and k-prototypes implementations both offer support for multiprocessing via the joblib library, similar to e.g. scikit-learn’s implementation of k-means, using the n_jobs parameter. It generally does not make sense to set more jobs than there are processor cores available on your system.

This potentially speeds up any execution with more than one initialization try, n_init > 1, which may be helpful to reduce the execution time for larger problems. Note that it depends on your problem whether multiprocessing actually helps, so be sure to try that out first. You can check out the examples for some benchmarks.


Q: I’m seeing errors such as TypeError: '<' not supported between instances of 'str' and 'float' when using the kprototypes algorithm.

A: One or more of your numerical feature columns have string values in them. Make sure that all columns have consistent data types.


[HUANG97] (1,2)

Huang, Z.: Clustering large data sets with mixed numeric and categorical values, Proceedings of the First Pacific Asia Knowledge Discovery and Data Mining Conference, Singapore, pp. 21-34, 1997.


Huang, Z.: Extensions to the k-modes algorithm for clustering large data sets with categorical values, Data Mining and Knowledge Discovery 2(3), pp. 283-304, 1998.


Cao, F., Liang, J, Bai, L.: A new initialization method for categorical data clustering, Expert Systems with Applications 36(7), pp. 10223-10228., 2009.

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