Skip to content

K-Means

1. Basic Concepts of K-Means

  • Cluster:

    • A group of similar data points. K-Means divides the dataset into K distinct clusters.

  • Centroid:

    • The central point of a cluster, representing the average position of all points in the cluster.

  • K Value:

    • Specifies the number of clusters. K-Means requires a predefined K, which indicates how many clusters the dataset will be divided into.

2. How K-Means Algorithm Works

K-Means algorithm iteratively proceeds through the following steps:

  1. Initialize Centroids:

    • Randomly select K initial centroids.

  2. Assign Data Points to Clusters:

    • Assign each data point to the nearest centroid, forming K clusters.

  3. Update Centroids:

    • Calculate the new centroid for each cluster by averaging all the points in the cluster.

  4. Repeat Iterations:

    • Repeat steps 2 and 3 until the centroids no longer change significantly, or until a predefined maximum number of iterations is reached.

  5. Stopping Criteria:

    • The algorithm converges and stops when the centroids no longer move.

3. Advantages of K-Means

  • Simple and Easy to Implement:

    • K-Means is straightforward and easy to understand and implement.

  • Fast and Efficient:

    • K-Means is fast and efficient, especially on large datasets, due to its low time complexity.

  • Easy to Interpret and Visualize:

    • The clusters generated by K-Means are easy to interpret, and the results can be visualized in 2D or 3D plots.

4. Disadvantages of K-Means

  • Need to Predefine K:

    • The number of clusters K must be predefined, which can be difficult to determine in advance.

  • Sensitive to Initial Centroids:

    • K-Means is sensitive to the initial placement of centroids, which can lead to different clustering results.

  • Only Detects Spherical Clusters:

    • K-Means assumes clusters are spherical, so it performs poorly on clusters with complex shapes.

  • Sensitive to Outliers:

    • Outliers can significantly affect the centroid positions, leading to poor clustering results.

5. Methods to Select K Value

  • Elbow Method:

    • Plot the SSE (Sum of Squared Errors) for each possible K value and choose the K at the "elbow" point, where the SSE starts to decrease more slowly.

  • Silhouette Coefficient:

    • Use the silhouette coefficient to evaluate the quality of clustering, and select the K with the highest silhouette score.

6. Applications of K-Means

  • Image Compression:

    • K-Means can be used for image compression by clustering pixels into different color clusters, reducing the number of colors.

  • Customer Segmentation:

    • K-Means is used in marketing to segment customers into different groups based on their behavior.

  • Document Classification:

    • K-Means can be applied to cluster documents into different topics or categories.