K-means

The K-means algorithm is used to find the centers of k clusters within a set of vectors.

The K-means algorithm is widely used in clustering tasks such as customer segmentation, image compression, and pattern recognition. It works iteratively to partition the data into k clusters, where each data point belongs to the cluster with the nearest mean.

Initially, k points are distributed randomly within the vector space to form the initial cluster centers. Then, the algorithm follows these steps:

1. Each input item is assigned to the cluster to whose center it has the lowest mean distance.
2. The cluster centers are moved so they have the lowest mean distance to the points within their respective clusters (i.e., into the geometric centers).
3. Steps 1 and 2 are repeated until the algorithm converges and the cluster centers stop moving.

For example, in customer segmentation, K-means can group customers based on their purchasing behavior, allowing businesses to target specific customer segments with tailored marketing strategies.

The main drawbacks with K-means are:

• Because the distance is minimized over all dimensions, K-means only works well where the clusters are close to spherical. It performs poorly with elongated clusters where the variance is much higher in some dimensions than in others. If the space cannot be warped to give a relatively constant variance over all dimensions before the algorithm starts, Expectation Maximization is likely to give better results provided that the other constraints it places on the data are met.
• You have to get the value of k (a hyperparameter) right before you start. If you use the algorithm with k = 3 on data that is actually arranged in 4 clearly defined, dense clusters, one of the centers will end up halfway between two of the clusters. One answer to this problem lies with the G-means algorithm, which tries out progressively larger values of k until one is found where the items around each center are arranged in a Gaussian distribution. Like Expectation Maximization but unlike standard K-means, G-means assumes a Gaussian distribution around the cluster centers.
• It is not guaranteed that K-means will always converge to the optimal solution. Different solutions can emerge with different random initial values.

In summary, the K-means algorithm is a fundamental clustering technique that is easy to implement and computationally efficient. It is widely used in various applications, but it has limitations that can be addressed by alternative algorithms such as G-means, K-medoids, and K-medians.