Last week, I was asked to implement the K-Means clustering algorithm from scratch in python as part of my MSc Data Science Degree Apprenticeship from the University of Exeter.

In this article, I present briefly the K-Means clustering algorithm and my Python implementation without using SkLearn.⠀

• Clustering
• K-Means
• Pseudo-code
• Python Implementation
• Conclusion

## 🪓 Clustering

Clustering is an unsupervised machine learning method that is used when you do not have labels for your data. The goal of clustering algorithms is to segment similar data points into groups; to extract meaning from the data.

One of the most common applications of clustering in industry is customer segmentation. A company can benefit by targeting each group with different marketing emails/ strategies (i.e relevant offers).

A definition that I found online is:

Clustering is the process of dividing the entire data into groups (also known as clusters) based on the patterns in the data.

## ⚙️ K-Means

K-Means is a very simple unsupervised clustering algorithm which clusters the data into K groups based on similar attributes. It is one of the 'must-haves' algorithms in a Data Scientist's tool box.

## 💻 Pseudo-code

Let's see in the picture below a pseudo-code implementation of K-Mean:

Just to clarify the following:

• X is our n-dimension data matrix
• P is an array of len(P)==len(X) holding the class in which each data point belongs to.
• Representative is the centroid of the cluster; the average point
• The stopping criteria is defined when P doesn't change between two consecutive iterations or we reach the maximum number of iterations

## 🐍 Python Implementation

Let's implement the above pseudo-code in Python:

def kmeans(X,k=3,max_iterations=100):
'''
X: multidimensional data
k: number of clusters
max_iterations: number of repetitions before clusters are established

Steps:
1. Convert data to numpy aray
2. Pick indices of k random point without replacement
3. Find class (P) of each data point using euclidean distance
4. Stop when max_iteration are reached of P matrix doesn't change

Return:
np.array: containg class of each data point
'''
if isinstance(X, pd.DataFrame):X = X.values
idx = np.random.choice(len(X), k, replace=False)
centroids = X[idx, :]
P = np.argmin(distance.cdist(X, centroids, 'euclidean'),axis=1)
for _ in range(max_iterations):
centroids = np.vstack([X[P==i,:].mean(axis=0) for i in range(k)])
tmp = np.argmin(distance.cdist(X, centroids, 'euclidean'),axis=1)
if np.array_equal(P,tmp):break
P = tmp
return P

Below you can screenshots of a working example. The notebook is also available on my GitHub page.

Note that we normalize the data before using the K-Means.

Standardizing data is recommended because otherwise the range of values in each feature will act as a weight when determining how to cluster data, which is typically undesired.

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## 🤖 Conclusion

This brings us to the end of this article. Hope you learn how to implement the K-Means clustering algorithm from scratch in Python .

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