This repo is my own attempt at re-creating the KMeans Clustering algorithm from scratch, in a simple way, using python solely.
By no means does this module attempt to improve or implement a better or more efficient version of the algorithm than the ones already out there.
This is my rather lame attempt at re-creating it with as little help as possible from external libraries (e.g.., we create our own squared euclidean distance function, rather than using numpy - definitely a faster way).
There is no why. This is a product of my boredoom.
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You can try this using a corresponding Python image:
docker-compose down && docker-compose up --build -dYou can execute jupyter lab using a Makefile. Run:
make jupyterlabGo to localhost:8000. The token (playground) is defined in the Dockerfile.
After spinning up the container, or your preferred environment, go to /notebooks and you can run examples there.
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Following the algorithm defined in The Elements of Statistical Learning:
-
For a given cluster assignment
$C$ , the total cluster variance is minimized with respect to$m_{1}, ..., m_{K}$ yielding the means of the currently assigned clusters. -
Given a current seat of means
$m_{1}, ..., m_{K}$ , the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is,
$$ C(i) = argmin_{1 \leq k \leq K} ||x_{i} - m_{k}||^2$$
- Repeat steps 1 and 2 until the assignments do not change
Where the Total Cluster Variance is defined as follows:
$$ \min_{C, {m_k} ^K_1 } \sum_{k=1}^{K} N_{k} ~ \sum_{C(i) = k} ||x_{i} - m_{k}||^2 $$
where
$$ N_k = \sum_{i = 1}^N I(C(i) = k) $$