# Cluster-Centered Visualization Techniques for Fuzzy Clustering Results to Judge Single Clusters
## 3 Cluster Validity and Visualization Techniques
### Visualization Techniques Literature Review  
For visualization techniques for clustering, there are several publications available. In the following, an overview of the current state of the existing literature is given. Automatic interpretation of evolving large data sets is of particular importance. In [19], two methods are presented that use cluster heat maps to visualize structures in static data sets. Subsequently, visual anomaly detection can also be performed to eliminate them from the data set. The methods are verified on real data sets. The algorithms can isolate anomalies and visualize changing cluster structures within the data set. Fuzzy clustering methods such as fuzzy \(k\)-means can be used to assign individual objects to multiple clusters with different degrees of membership. However, these memberships are difficult to visualize and analyze. Therefore, they are converted to 0-1 values and visualized by parallel coordinates or different shades of color. In [20], a new approach is used to visualize fuzzy cluster data. The idea is based on a geometric visualization and groups objects with similar cluster memberships. This allows relationships between individual clusters to be viewed spatially. The membership degrees are the basis in [21] to visualize fuzzy clustering results. Most fuzzy clustering techniques minimize an objective function with this parameter. But it leads to bad results if the cluster shape or the number of clusters are not chosen properly. For the evaluation of clustering results, cluster validity measures are available, but they reduce the information in a large data set to a single value. A new method was developed to avoid simplification to a single value and to visualize the clustering results. The visualization of fuzzy clusters plots the maximum membership degrees as a function of the distance from the cluster centers. Therefore, it can contain more information for the user to identify inconsistencies within the individual clusters. In [22], the problem of visualization of clusters in very large rectangular dissimilarity data is addressed. First, four clustering problems are defined, which should be answered for the assessment of cluster tendency. Two artificially generated very large rectangular data sets were generated, and the clustering of the data was performed. The developed method is a scalable approach to the four different cluster assessment problems. Another visualization technique for fuzzy clustering is radial visualization (RadViz) from [23] for visually analyzing multidimensional data sets. The results of fuzzy clustering are displayed by using RadViz, where each dimensional anchor is a representation of the clusters. The stability of one data point is based on its distance from the circumference. Other visualization techniques display only the maximum association for each data point, but RadViz considers all associations for each data point. This leads to more information about the relationship between the data points. Furthermore, the algorithm was applied for explanation to the Iris data set. For fuzzy cluster analysis, multidimensional visualization techniques are beneficial. But no single existing visualization technique can support the wide range of analytical tasks based on fuzzy clustering. In [24], a new visualization called FuzzyRadar for a better understanding of fuzzy clusters is developed. The idea is based on the combination of radial coordinate visualization (RadViz) and parallel coordinate plotting (PCP). RadViz is specialized in data-oriented analytical tasks and PCP in the performance of cluster-oriented analytical tasks. First, both approaches are integrated into one new visualization. Subsequently, two methods are introduced to reduce the visual clusters and to recognize the distribution of the degrees of membership. In a case study, the usability of FuzzyRadar is demonstrated, and the results for seven analytical tasks are shown. Topological techniques for evaluating data are used in the field of topological data analysis.