k-Means Clustering

k-Means Clustering is a clustering algorithm that divides a training set into $k$ different clusters of examples that are near each other. It works by initializing $k$ different centroids {$\mu\left(1\right),\ldots,\mu\left(k\right)$} to different values, then alternating between two steps until convergence:

(i) each training example is assigned to cluster $i$ where $i$ is the index of the nearest centroid $\mu^{(i)}$

(ii) each centroid $\mu^{(i)}$ is updated to the mean of all training examples $x^{(j)}$ assigned to cluster $i$.

Text Source: Deep Learning, Goodfellow et al

Image Source: scikit-learn


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