Comprehensive K-Means Clustering

The k-means algorithm is a popular data clustering technique due to its speed and simplicity. However, it is susceptible to issues such as sensitivity to the chosen seeds, and inaccurate clusters due to poor initial seeds, particularly in complex datasets or datasets with non-spherical clusters. In this paper, a Comprehensive K-Means Clustering algorithm is presented, in which multiple trials of k-means are performed on a given dataset. The clustering results from each trial are transformed into a five-dimensional data point, containing the scope values of the x and y coordinates of the clusters along with the number of points within that cluster. A graph is then generated displaying the configuration of these points using Principal Component Analysis (PCA), from which we can observe and determine the common clustering patterns in the dataset. The robustness and strength of these patterns are then examined by observing the variance of the results of each trial, wherein a different subset of the data keeping a certain percentage of original data points is clustered. By aggregating information from multiple trials, we can distinguish clusters that consistently emerge across different runs from those that are more sensitive or unlikely, hence deriving more reliable conclusions about the underlying structure of complex datasets. Our experiments show that our algorithm is able to find the most common associations between different dimensions of data over multiple trials, often more accurately than other algorithms, as well as measure stability of these clusters, an ability that other k-means algorithms lack.