K-Means Clustering Algorithm

Clustering: K-means

Definition

• K-means is a type of unsupervised machine learning algorithm used for clustering data.
• It groups similar data points into clusters based on their features.

How it Works

1. Initialization:
   • Choose a value for K (number of clusters).
   • Randomly assign centroids (cluster centers) for each cluster.
2. Assignment:
   • Calculate the distance between each data point and the centroid of each cluster.
   • Assign each data point to the cluster with the closest centroid.
3. Update:
   • Calculate the new centroid of each cluster as the mean of all data points assigned to that cluster.
   • Repeat steps 2-3 until convergence or a stopping criterion is reached.

Key Concepts

• Centroids: The mean vector of each cluster.
• Cluster assignment: The process of assigning each data point to a cluster.
• Distance metric: Typically, Euclidean distance is used to calculate the distance between data points and centroids.

Advantages

• Easy to implement and computationally efficient.
• Scalable to large datasets.
• Interpretable results, with clear cluster assignments.

Disadvantages

• Sensitive to initial placement of centroids.
• Sensitive to outliers, which can affect centroid calculations.
• Assumes spherical clusters, which may not always be the case.

Applications

• Customer segmentation: Clustering customers based on demographics and behavior.
• Image segmentation: Clustering pixels in an image to identify objects or features.
• Gene expression analysis: Clustering genes based on their expression levels.

Clustering: K-means

• A type of unsupervised machine learning algorithm used for clustering data.

How it Works

• Initialization involves choosing a value for K (number of clusters) and randomly assigning centroids (cluster centers) for each cluster.
• Assignment involves calculating the distance between each data point and the centroid of each cluster and assigning each data point to the cluster with the closest centroid.
• Update involves calculating the new centroid of each cluster as the mean of all data points assigned to that cluster, and repeating steps 2-3 until convergence or a stopping criterion is reached.

Key Concepts

• Centroids are the mean vector of each cluster.
• Cluster assignment is the process of assigning each data point to a cluster.
• Distance metric is typically Euclidean distance used to calculate the distance between data points and centroids.

Advantages

• Easy to implement and computationally efficient.
• Scalable to large datasets.
• Interpretable results, with clear cluster assignments.

Disadvantages

• Sensitive to initial placement of centroids.
• Sensitive to outliers, which can affect centroid calculations.
• Assumes spherical clusters, which may not always be the case.

Applications

• Customer segmentation: Clustering customers based on demographics and behavior.
• Image segmentation: Clustering pixels in an image to identify objects or features.
• Gene expression analysis: Clustering genes based on their expression levels.