Non Hierarchical Clustering

Cluster analysis or clustering is a commonly used statistical method in data analysis and data mining. Clustering is a process of grouping variables or cases in so-called clusters according to some similar characteristics. The main idea is that cases or variables in one cluster are the most similar to each other meanwhile cases or variables from different clusters are the least similar. Cluster analysis provides a different perspective to analyzed data and enables to see relations between selected variables. Flexibility of the method is based on the fact that it is not needed to define amount of clusters, as this method is not predictive, but descriptive. Its application has been adopted by scientists with various background such as marketing,

Non-hierarchical methods

When running non-hierarchical method there is need to predefine a number of clusters and this decision is upon user. The are only two requirements which need to be fulfilled.

Each cluster consists of minimum one object

One object can be a representative of only one group

In practice, these two assumptions lead to fact that there cannot be more clusters than objects and intersection coefficient of two different clusters is equal to zero. Due to limitations and of this thesis, the following descriptions of partioning methods are really brief.

K-means

The centre of gravity is being changed every time a new representative enters a cluster. Recalculation helps to see the process how cluster are being optimized .

Partitioning around medoids

The basic idea of medoids partitioning is obtain predefined k clusters. Alghorithm finds exactly k objects which takes name representative objects. Other objects are matched with representative objects and create clusters. Representative objects are also called medoids and therefore this method is often called k-medoids

One of the difference a between non-hierarchical and hierarchical methods is there is no need to enter number of clusters. Second significant difference is that the process of gathering and separating is done on the way, meaning what have been done in previous steps cannot be fixed back, while in case of partitioning method it is the aim to select the best option of objects in k clusters during the whole process. One might claim they are similar, but they can lead to absolutely different results. The results of hierarchical methods are graphs with a certain gradualism. The only difference between k and k+1 clusters is that one of the clusters splits up (shown in Figure 8 – Example of dendrogram). It is up to user to decide whether to use k clusters or k+1. Graphical result of hierarchical method is called