On Clustering Images Using Compression

The need for the ability to cluster unknown data to better understand its relationship to know data is prevalent throughout science. Besides a better understanding of the data itself or learning about a new unknown object, cluster analysis can help with processing data, data standardization, and outlier detection. Most clustering algorithms are based on known features or expectations, such as the popular partition based, hierarchical, density-based, grid based, and model based algorithms. The choice of algorithm depends on many factors, including the type of data and the reason for clustering, nearly all rely on some known properties of the data being analyzed. Recently, Li et al. proposed a new universal similarity metric, this metric needs no prior knowledge about the object. Their similarity metric is based on the Kolmogorov Complexity of objects, the objects minimal description. While the Kolmogorov Complexity of an object is not computable, in "Clustering by Compression," Cilibrasi and Vitanyi use common compression algorithms to approximate the universal similarity metric and cluster objects with high success. Unfortunately, clustering using compression does not trivially extend to higher dimensions. Here we outline a method to adapt their procedure to images. We test these techniques on images of letters of the alphabet.