K-Means is a popular algorithm used for clustering data points into a specified number of groups. It works by iteratively assigning data points to clusters based on their proximity to the cluster centers, called centroids, and then updating the centroid positions.
Here's a breakdown of the process based on common implementations and the provided reference:
The K-Means Clustering Algorithm Steps
The K-Means algorithm follows an iterative process to partition data points into k clusters. The core steps are:
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Choose the number of clusters, k:
- This is a crucial first step. You must decide how many clusters you want the algorithm to find in your data.
- Choosing the right k often requires domain knowledge or techniques like the Elbow method or Silhouette analysis.
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Initialize the centroids:
- Select k initial points to be the centers (centroids) of your clusters.
- As mentioned in the reference, a common way is to select k points at random from your dataset. These points initially serve as clusters of size 1.
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Assign data points to the closest cluster:
- For each data point in your dataset, calculate its distance to every centroid.
- The data point is then assigned to the cluster whose centroid is the closest. Common distance metrics include Euclidean distance.
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Update the centroids:
- Once all data points have been assigned to a cluster, recalculate the position of the centroid for each cluster.
- The new centroid is the mean position (average) of all data points assigned to that cluster.
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Repeat steps 3 and 4:
- The algorithm iterates between assigning points to clusters and updating centroids.
- This process continues until the centroid positions no longer change significantly or a maximum number of iterations is reached. This point is called convergence.
Visualizing the Process
Imagine you have data points scattered on a graph.
- First, you pick k random points (initial centroids).
- Then, you draw boundaries based on which centroid is closest to each data point, creating initial clusters.
- Next, you move each centroid to the average location of the points in its cluster.
- You repeat this: re-draw boundaries, move centroids, until the centroids settle down and don't move much anymore.
Key Terms in K-Means
- k: The predetermined number of clusters.
- Centroid: The center point of a cluster, calculated as the mean of all data points belonging to that cluster.
- Distance Metric: The method used to calculate how far apart two points (e.g., a data point and a centroid) are. Euclidean distance is typical.
- Convergence: The state where the K-Means algorithm stops because the cluster assignments or centroid positions stabilize.
Practical Considerations
- Choosing k: The selection of k is critical and not directly determined by the algorithm itself.
- Initialization Sensitivity: The initial random selection of centroids can influence the final clustering result. Running the algorithm multiple times with different initializations and choosing the best result (e.g., based on the sum of squared distances within clusters) is a common practice.
For further details on K-Means clustering, including implementation in various tools, you can refer to resources like K-Means Clustering in R.
