K-Means Clustering Algorithm
K-Means Clustering Algorithm
K-Means is one of the most popular unsupervised machine learning algorithms used for clustering. It is used to group similar data points into clusters based on their features. The algorithm attempts to minimize the variance within each cluster, ensuring that data points within the same cluster are as close as possible while maximizing the difference between clusters.
How K-Means Clustering Works?
The K-Means algorithm follows these steps:
- Choose the number of clusters (K).
- Randomly initialize K cluster centroids.
- Assign each data point to the nearest centroid, forming clusters.
- Recalculate the centroids by taking the mean of all data points in each cluster.
- Repeat the process until the centroids do not change significantly.
Formula for K-Means Clustering
The K-Means algorithm aims to minimize the sum of squared distances (SSD) between each data point and its corresponding cluster centroid. The objective function is:
J = Σ Σ || xi – μj ||²
Where:
- J is the total within-cluster variance.
- xi represents each data point.
- μj is the centroid of cluster j.
- The summation runs over all clusters and all data points.
Choosing the Value of K
Choosing the right number of clusters (K) is crucial for accurate clustering. A common method to determine the optimal K is the Elbow Method, which involves:
- Plotting the sum of squared distances (SSD) for different values of K.
- Looking for an “elbow point” where the decrease in SSD slows down.
Applications of K-Means Clustering
K-Means clustering is widely used in various domains, including:
- Customer segmentation in marketing.
- Anomaly detection in cybersecurity.
- Image compression and segmentation.
- Recommendation systems.
