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K-Means Clustering

K-means clustering is a type of unsupervised machine learning algorithm used to group similar data points together in a dataset. The algorithm works by finding k clusters, where k is a user-defined number, and assigning each data point to the cluster with the closest mean or centroid.

To perform K-means clustering, the user needs to provide the following inputs:

- The number of clusters k
- The dataset to be clustered

The K-means algorithm works as follows:

- Randomly select k data points to be the initial centroids of the k clusters
- For each data point in the dataset, calculate the distance between the data point and each of the k centroids
- Assign each data point to the closest centroid and form k clusters
- Calculate the mean of each cluster and update the centroid
- Repeat steps 2-4 until convergence, where convergence is achieved when the centroids no longer change significantly.

The goal of K-means clustering is to minimize the sum of squared distances between data points and their assigned centroids. This is known as the “within-cluster sum of squares” or “inertia” and can be used as a measure of the quality of the clustering.

K-means clustering has several advantages:

- It is simple and easy to implement
- It can handle large datasets efficiently
- It can be used for a wide range of applications, such as image segmentation, customer segmentation, and anomaly detection

However, K-means clustering also has some limitations:

- It requires the user to specify the number of clusters k, which may not always be known or easy to determine
- It is sensitive to the initial placement of centroids, which can lead to different results for different initializations
- It assumes that clusters are spherical and have equal variances, which may not always be true in real-world datasets.

Overall, K-means clustering is a powerful tool for exploratory data analysis and can be used to gain insights into complex data

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