Intro to k-Means

 K-Means clustering is a popular unsupervised learning algorithm used for customer segmentation and various other applications. It falls under the category of partitioning clustering algorithms, which divide the data into K non-overlapping subsets or clusters without any internal structure or labels.

To apply K-Means clustering, we first need to determine the number of clusters, denoted as K. This can be a challenging task and is often based on domain knowledge or trial and error. Once the number of clusters is decided, K-Means initializes K centroids, which are representative points for each cluster.

There are two common approaches to choose these centroids:

Random Initialization: Selecting K random observations from the dataset and using them as initial centroids.

Random Point Creation: Generating K random points as centroids within the range of the feature space.

After initializing the centroids, the algorithm proceeds iteratively through the following steps:

Assigning Data Points to Clusters: Calculate the distance of each data point from each centroid. Common distance metrics include Euclidean distance, Manhattan distance, or cosine similarity. Data points are then assigned to the cluster whose centroid is closest.

Updating Centroids: Once all data points are assigned to clusters, the centroids are updated to the mean of the data points within each cluster. This step aims to minimize the within-cluster sum of squares error, indicating the total distance of data points from their respective centroids.

Iterative Refinement: Steps 1 and 2 are repeated iteratively until convergence, meaning centroids no longer change significantly between iterations or a predefined stopping criterion is met. It's important to note that in each iteration, the distances of all data points from the centroids need to be recalculated.

Due to its heuristic nature, K-Means may converge to a local optimum rather than the global optimum, and results can vary depending on the initial centroids. To mitigate this, it's common practice to run the algorithm multiple times with different initializations.

In summary, K-Means clustering is an iterative algorithm that partitions data into K clusters by minimizing the distance of data points from their centroids. It is widely used for customer segmentation, pattern recognition, and other data analysis tasks. However, it's essential to understand its limitations and consider the impact of initialization on the clustering results.