An important component of a spatial clustering algorithm is the distance

An important component of a spatial clustering algorithm is the distance measure between sample points in object space. clustering algorithms. Our clustering model based on artificial immune system is also applied to the case of public facility location problem in order to establish the practical applicability of our approach. By using the clone selection principle and updating the cluster centers based on the elite antibodies the AICOE algorithm is able to achieve the global optimum and better clustering effect. 1 Introduction Spatial clustering analysis is an important research problem in data mining and knowledge discovery the aim Cenicriviroc of which is to group spatial data points into clusters. Based on the similarity or spatial proximity of spatial entities the spatial dataset is divided into a series of meaningful clusters [1]. Due to the spatial data cluster rule clustering algorithms can be divided into spatial clustering algorithm based on partition [2 3 spatial clustering algorithm based on hierarchy [4 Cenicriviroc 5 spatial clustering algorithm based on Cenicriviroc density [6] and spatial clustering algorithm based on grid [7]. The distance measure between sample points in object space is an important component of a spatial clustering algorithm. The AKAP12 above traditional clustering algorithms assume that two spatial entities are directly reachable and use a variety of straight-line distance metrics to measure the degree of similarity between spatial entities. Cenicriviroc However physical barriers often exist in the realistic region. If these obstacles and facilitators are not considered during the clustering process the clustering results are often not realistic. Taking the simulated dataset in Figure 1(a) as an example where the points represent the location of consumers the clustering Cenicriviroc result shown in Figure 1(b) can be obtained when the rivers and hill as obstacles are not considered. If the obstacles are taken into account and bridges as facilitators are not considered the clustering result in Figure 1(c) can be gained. Considering both the obstacles and facilitators Figure 1(d) demonstrates the more efficient clustering patterns. Figure 1 Spatial clustering with obstacle and facilitator constraints: (a) spatial dataset with obstacles; (b) spatial clustering result ignoring obstacles; (c) spatial clustering result considering obstacles; (d) spatial clustering result considering both obstacles … At present only a few clustering algorithms consider obstacles and/or facilitators in the spatial clustering process. COE-CLARANS algorithm [8] is the first spatial clustering algorithm with obstacles constraints in a spatial database which is an extension of classic partitional clustering algorithm. It has similar limitations to the CLARANS algorithm [9] which has sensitive density variation and poor efficiency. DBCluC [10] extends the concepts of DBSCAN algorithm [11] utilizing obstruction lines to fill the visible space of obstacles. However it cannot discover clusters of different densities. DBRS+ is the extension of DBRS algorithm [12] considering the continuity in a neighborhood. Global parameters used by DBRS+ algorithm make it suffer from the problem of uneven density. AUTOCLUST+ is a graph-based clustering algorithm which is based on AUTOCLUST clustering algorithm [13]. For the statistical indicators used by AUTOCLUST+ algorithm it could not deal with planar obstacles. Liu et al. presented an adaptive spatial clustering algorithm [14] in the presence of obstacles and facilitators which has the same defect as AUTOCLUST+ algorithm. Recently the artificial immune system (AIS) inspired by biological evolution provides a new idea for clustering analysis. Due to the adaptability and self-organising behaviour of the artificial immune system it has gradually become a research hotspot in the domain of smart computing [15–20]. Bereta and Burczyński performed the clustering analysis by means of an effective and stable immune = {= (∈ is the adjacent vertex of = 1 … ? 1 is the number of = {= (∈ ∈ is the adjacent vertex of = 1 … is the number of = {in a two-dimensional space is called directly reachable from does not intersect with any obstacle; otherwise is called indirectly reachable from ∈ ∪ be an obstacle and is the vertex subset of on your left hand when you walk along vector from point to is the vertex subset of on the.