K-Means Clustering
A simple yet powerful unsupervised learning algorithm for partitioning data into clusters
K-Means is one of the simplest and most popular unsupervised machine learning algorithms used for clustering analysis. The algorithm works by partitioning n observations into k clusters where each observation belongs to the cluster with the nearest mean (cluster centroid), serving as a prototype of the cluster.
The K-Means Algorithm
The standard K-Means algorithm follows an iterative refinement approach:
- Initialization: Randomly select k points as initial centroids
- Assignment: Assign each data point to the nearest centroid, forming k clusters
- Update: Recalculate the centroids as the mean of all points in each cluster
- Repeat: Repeat steps 2 and 3 until convergence (centroids no longer change significantly or a maximum number of iterations is reached)
Key Concepts
Centroids
The mean point of all samples in a cluster, representing the cluster's center. The goal of K-Means is to find centroids that minimize the distance to points in their respective clusters.
Number of Clusters (k)
A user-defined parameter that specifies how many clusters to partition the data into. Selecting the optimal k is crucial and often determined using techniques like the elbow method.
Inertia
The sum of squared distances of samples to their closest centroid, measuring how internally coherent clusters are. Lower inertia indicates better-defined clusters.
Distance Metric
Typically Euclidean distance is used, but other metrics like Manhattan or cosine distance can be employed depending on the problem domain and data characteristics.
Advantages and Limitations
Advantages
- Simple to understand and implement
- Scales well to large datasets
- Guarantees convergence
- Easily adapts to new examples
- Generalizes to clusters of different shapes and sizes
Limitations
- Requires number of clusters (k) to be specified
- Sensitive to initial placement of centroids
- May converge to local optima
- Assumes clusters are spherical and equally sized
- Sensitive to outliers