Data Partitioning and Image Segmentation by Use of Information Compression and Graph Structures

In this paper we propose a multistage computational procedure for partitioning of large data sets and for segmentation of images. In the first step the original ldquorawrdquo data set (or the set of pixels from a given image) is compressed by use of the neural-gas unsupervised learning algorithm into compressed information model (CIM) that contains small predefined number of neurons. In the second step a graph structure is generated by using all the neurons as nodes of the graph and a number of consistent arcs. Two kinds of consistent arcs are defined here, namely crisp and fuzzy arcs that lead to the respective crisp and fuzzy graph structures. The crisp graphs use the Euclidean distance between the nodes as ldquoarc lengthsrdquo. The fuzzy graphs use weighted arcs with different ldquoarc strengthsrdquo, computed by using the weights of the respective adjacent neurons. The third step identifies the number of the strongly connected elements (called also ldquoconnected areasrdquo) in the generated graph structure from the previous step. This is done by using the well known depth-first graph algorithm. Then each connected area corresponds to a respective segment of the given data or image. The proposed computational scheme and its application are demonstrated and explained by two test examples consisting of process data and an image.