Image blurring and sharpening inspired three-way clustering approach

Three-way clustering is a new type of clustering algorithm that divides the clustering results into three different parts or regions. This division allows a clear distinction between the central core and the outer sparse or fringe regions of a cluster. This algorithm is useful in situations when clusters have an unclear and unsharp boundary. In existing studies, a pair of thresholds are typically used to define the three regions of three-way clustering which demands the determination of suitable threshold values. In this paper, we propose an approach called blurring and sharpening based three-way clustering (BS3WC) which constructs the three-way clusters without the need for determining the thresholds. The BS3WC is motivated by observing that the blurring and sharpening operations can produce a three-way representation for a typical object in an image consisting of a core inner, outer blurry, and part not belonging to the object. The BS3WC works in two steps. In step one, it converts a hard cluster into an image. It next defines cluster blur and cluster sharp operations, which are used to create three-way representation for clusters. The BS3WC is validated with 31 datasets including both synthetic and real-life datasets using typical benchmarks of ACC, ARI, NMI and compared with the existing three-way as well as other notable approaches. We also consider the performance of the BS3WC approach in the application area of open-world classification for identifying unknown instances. Experimental results suggest that BS3WC may effectively cluster the data and provide results that are comparable to well-known approaches in the considered application area.