Clustering of Bispectral Index Measurements Data by Using the Fuzzy Neighborhood Relations

Cluster analysis has an important role in analysis of the ElectroEnsepholoGraphy (EEG) signals of the brain activities [Escalona-Moran et al., 2007; Jin S-H. Et al., 2005; Van Hese et al., 2008]. The primary objective of clustering is to simplify statistical analysis by grouping similar objects in a cluster. Clustering methods can be divided into five main groups such as hierarchical, prototype-based, density (or neighborhood)-based, model-based, and grid-based [Han&Kamber, 2001]. From another point of view, the clustering methods can be investigated whether they are crisp or fuzzy clustering methods. Most of the proposed fuzzy clustering methods are based on the Fuzzy c-means (FCM) algorithm [MacQueen J., 1967; Han&Kamber, 2001]. These methods conceive the fuzziness of clustering as being assigned to some clusters with certain degrees of membership. Nevertheless, FJP algorithm handles the fuzziness from a different point of view [Nasibov, 2006; Nasibov&Ulutagay, 2006; Nasibov&Ulutagay, 2007]. The basic property of the FJP method is that it handles the fuzziness with respect to levels. Thus, it investigates in how much detail the elements are handled in the formation of clusters. DBSCAN is another algorithm which has a low complexity, i.e. it runs fast and it uses two parameters which determine neighborhood radius and neighborhood threshold respectively. Unfortunately, these parameters should be set properly according to the scale of the dataset and the density of clusters. So, it means that, the speed of this algorithm is meaningful with an effective setting of these parameters [Ester et al., 1996]. Another method FJP runs slower than DBSCAN algorithm principally. However, it is easier to determine correct structure of clusters in a wide change interval of these parameters regardless of the scale of dataset and the density within clusters. So, it is plausible to say that FJP algorithm is more robust than DBSCAN with respect to the parameters. Another difference of FJP algorithm from DBSCAN is that it uses fuzzy neighborhood relations instead of classical neighborhood analysis as DBSCAN does. In the paper Nasibov (2007) the Fuzzy Neighborhood-DBSCAN (FN-DBSCAN) algorithm which combines the speed of DBSCAN and robustness of FJP algorithms is proposed. In this sudy, FN-DBSCAN algorithm is compared with classical FCM method by using BIS data which were recorded in sleep time by using EEG. 1. Dataset. The Bispectral Index (BIS) is a continuous processed EEG parameter that correlates to the patient’s level of hypnosis, where 100=awake and 0=flat line EEG. BIS was designed to correlate with “hypnotic” clinical endpoints (sedation, lack of awareness, and memory) and to track changes in the effects of anesthetics on the brain. The main purpose of this study is not to show the effectiveness of any method numerically, but to show that studies on neighborhood-based cluster analysis could provide more effective results. 22 datasets each of which are registered in every five seconds during sleep for a 25-minute periods are used to compare FCM and FN-DBSCAN clustering algorithms. Thus, each dataset contains 306 BIS measurements. In order to use in learning process, experts determined the BIS stage values corresponding to each measurement moment. Another purpose of the study is to predict the stage intervals and levels to the utmost. Because of this, we present not all of the datasets, but just one of them in order to point out the difference between two methods. 2. FN-DBSCAN algorithm. The main objective of the neighborhood-based clustering algorithms is to grow the concerned cluster until its density is greater than a specified threshold. Namely, each point in the concerned cluster should contain at least minimum number points