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K-means clustering is a widely used unsupervised machine learning algorithm designed to partition a dataset into K distinct, non-overlapping clusters. The objective is to minimize the variance within each cluster while maximizing the variance between clusters. The algorithm works through the following steps:

1. Initialization: Randomly choose K initial centroids (cluster centers).

2. Assignment: Assign each data point to the nearest centroid based on a distance metric (usually Euclidean distance).

3. Update: Recalculate the centroids by computing the mean of all points assigned to each cluster.

4. Repeat: Repeat the assignment and update steps until convergence, i.e., when the centroids no longer change significantly.

Limitations of K-means:

1. Sensitive to Initialization: The algorithm’s performance can vary based on the initial selection of centroids, which may lead to suboptimal clustering.

2. Fixed Number of Clusters (K): The number of clusters (K) must be specified in advance, and determining the optimal K can be difficult.

3. Non-Spherical Clusters: K-means assumes spherical clusters with roughly equal sizes, making it ineffective for clusters with irregular shapes or differing densities.

4. Sensitive to Outliers: Outliers can significantly affect the placement of centroids and lead to poor clustering results.

5. Scalability: While efficient, K-means may struggle with very large datasets, especially in high-dimensional spaces.