# Clustering: K-Means

Clustering is an unsupervised machine learning technique that aims to partition a set of data points into groups or clusters based on the similarity among the data points. One popular algorithm for clustering is the K-means algorithm, which is widely used due to its simplicity and efficiency.

##### How does K-means Algorithm work?

The K-means algorithm works by iteratively assigning data points to K clusters and then computing the centroid of each cluster. The centroids are updated in each iteration until convergence criteria are met. The steps involved in the K-means algorithm are as follows:

1. Initialization: Choose K initial centroids randomly from the data points.

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

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

4. Repeat steps 2 and 3 until convergence (i.e., no change in assignments or centroids).

##### Key Concepts in K-means Clustering:
• K: denotes the number of clusters desired, which needs to be specified beforehand.

• Centroids: represent the center point of each cluster and are continually adjusted during iterations.

• Cluster Assignment: Each data point is assigned to the cluster with the nearest centroid.

• Inertia/SSE (Sum of Squared Errors): Quantifies how compactly grouped the data points are within a cluster.

• Simple and easy to implement.

• Efficient for large datasets with a moderate number of clusters.

• Scales well with increasing dimensions/features.

Limitations:

• Requires predefined value forΒ `K`.

• Sensitive to initial centroid selection, affecting final results.

• Prone to getting stuck in local optima due to random initialization.

In conclusion, K-means clustering is a fundamental method for grouping unlabeled data into meaningful clusters based on feature similarities. Despite its simplicity, understanding key concepts like initialization strategies, centroids updates, and evaluation metrics can help optimize its performance for various applications.

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