Arbitrary-shaped cluster extraction using one-dimensional data mapping and K-means

Abstract

The K-means algorithm is well known as the most popular clustering method because of its good performance. However, we cannot extract meaningful clusters by applying Kmeans to data that are not linearly separable. For overcoming this difficulty, some researchers have adopted high-dimensional data mappings such as kernel mappings to clustering methods including K-means. We may extract meaningful clusters by using such mapping but requires high-computational costs and a large amount of memory. We present a simple algorithm including Kmeans for extracting arbitrary-shaped clusters by mapping data into a one-dimensional space. This 1D data mapping is achieved by minimizing the square error of the average 1D coordinates of the neighbors of data in input space. After this mapping, Kmeans is applied to the histogram of the distribution of the data in 1D space. The performance of our method is verified with the experiments on synthetic 2D data, image and video segmentation.