# Cluster-Centered Visualization Techniques for Fuzzy Clustering Results to Judge Single Clusters
## 3 Cluster Validity and Visualization Techniques
### Visualization Techniques Literature Review
The aim is to determine topological data structures. In this area, the mapper algorithm is considered a solid representative approach. The aim is to find concise and meaningful global topological data structures that are neither accessible nor clusterable and are identifiable by many other clustering methods. For this purpose, a new method called the Shape Fuzzy C-Means (SFCM) algorithm was developed in [25], which is based on the Fuzzy C-Means algorithm with special features of the mapper algorithm. The SFCM algorithm has the same clustering capability as the Fuzzy C-Means algorithm and reveals relationships by visualizing the global shape of the data provided by the mapper. In [26], multi-dimensional visualizations to understand fuzzy clusters are evaluated. It is well known that the use of visualization techniques for multidimensional data is beneficial for understanding fuzzy clusters. The capability of fuzzy cluster analysis is evaluated in an experiment in which four multidimensional visualization techniques are used and compared. The visualization techniques are a parallel coordinate diagram, a scatterplot matrix, principal component analysis, and Radviz. Subsequently, a guideline for the selection of suitable and efficient visualization techniques for the analysis of fuzzy clusters is presented. For the analysis of biclustering results, Furby is presented as an interactive visualization technique in [27]. On the one hand, the technique provides an overview of a biclustering result and shows the actual data; on the other hand, in the case of fuzzy clustering results, it also enables the interactive definition of threshold values in order to convert the fuzzy clustering into hard clusters. Changes to the membership thresholds are immediately visible in the visualization. The new technique is demonstrated using a corresponding data set. In [28], a cluster-oriented development of fuzzy models is proposed. The focus is on the efficient use of fuzzy clusters, in particular fuzzy C-means (FCM), for the formation of clusters for the creation of the fuzzy model. The development of the models is considered from the perspective of the creation and efficient use of clusters. In this study, fuzzy clustering is directly linked to fuzzy modeling. The augmented FCM method is mainly used for modeling purposes to achieve a balance between the structural contents in the input and output spaces. This optimizes the performance of the resulting fuzzy model. This is demonstrated by some experiments. Visualizing the cluster structure of high-dimensional data is a challenging task, as it must be able to handle the high dimensionality of the input data. The visualization of fuzzy clusters is also challenging, as soft clustering algorithms result in more complex cluster structures. By introducing a membership network in [29], which is based on the fuzzy partition matrix and represents fuzzy clustering, the visual understanding should be improved. It is shown how the elements involved in this type of complex data clustering structure interact with each other without relying on a visualization of the input data itself. The results of the experiment demonstrate the usefulness of the proposed method using the iris flower data set and two other data sets. Within the context of this paper, some ideas and approaches from the given literature are also used. In general, the newly developed CCV techniques are used for clustering results based on fuzzy \(k\)-means but can be applied in principle to any fuzzy clustering algorithm because of the duality between distances and membership degrees. From [19; 22; 25] only the ideas for clustering are used. The basics are also the membership degree, which refers to [20; 21; 29]. Since the CCV techniques also use a circular display, refs. [23; 24; 26] are very important. Especially the idea of RadViz is useful to provide maximum information from the visualization to the user.