Implement overlapping clustering using K means where the points can belong to zero, one or more clusters

Clustering is a fundamental technique in data analysis and pattern recognition, aiming to group similar data points into distinct clusters. Traditional clustering algorithms assign each data point to a single cluster, assuming that the underlying structure of the data is non-overlapping. However, real-world datasets often exhibit complex relationships, where data points may belong to multiple clusters simultaneously. This work explores the concept of overlapped clustering, wherein data points are allowed to participate in more than one cluster, accommodating the inherent flexibility and diversity present in various datasets. In this work, we modify k-means to handle such situations where a point ‘A’ can belong to zero, one or more than one group. We propose a new way to use k-means that lets things be part of different groups. This helps show complex relationships in data. By leveraging the well-established foundation of the k-means algorithm, this work contributes a pragmatic solution to the challenge of overlapped clustering. We test our modified method on different data, showing it can find overlapping groups better than regular k-means. This gives a simpler way to tackle overlapping clusters in data analysis, making it easier to uncover hidden patterns in today's complex datasets.