Cluster Analysis for Applications by Michael R. Anderberg download in ePub, pdf, iPad
Grid-based Method In this, the objects together form a grid. Eventually, objects converge to local maxima of density. This method also provides a way to automatically determine the number of clusters based on standard statistics, taking outlier or noise into account.
All we do now is move onto the next variable and do the same. In the simple linkage method, we begin with the two most similar cases.
Bungle, however, has a very different set of responses. For these data, we saw three clear clusters and so we could re-run the analysis asking for cluster group codings for three clusters in fact, I told you to do this as part of the original analysis. As such, we can use this variable to tell us which cases fall into the same clusters. Once this third case has been added, the average similarity within the cluster is re-calculated. Basically, this means that at each stage the average similarity of the cluster is measured.
First, imagine the similarity coefficient as a vertical scale ranging from low similarity to high. However, this measure is heavily affected by variables with large size or dispersion differences. Clusters are then merged based on a criterion specific to the method chosen. In theory, we could apply the correlation coefficient to two people rather than two variables to see whether the pattern of responses for one person is the same as the other.
In addition, in situations in which we have hundreds of people and lots of variables, the graphs of responses that we plot would become very cumbersome and almost impossible to interpret. This is the simplest method and so is a good starting point for understanding the basic principles of how clusters are formed and the hierarchical nature of the process. At this stage the average similarity within the cluster is calculated.
One prominent method is known as Gaussian mixture models using the expectation-maximization algorithm. They did however provide inspiration for many later methods such as density based clustering. Density-based Method This method is based on the notion of density. The rationale behind this analysis is that people with the same disorder should report a similar pattern of scores across the measures so the profiles of their responses should be similar. By inspecting the progression of cluster merging it is possible to isolate clusters of cases with high similarity.
Divisive Approach This approach is also known as the top-down approach. As explained earlier, cluster analysis works upwards to place every case into a single cluster. The next case to be added to the cluster is the one with the highest similarity to the average similarity value for the cluster.
To avoid this problem, we simply square each difference before adding them up. In this, we start with each object forming a separate group. Dropping one case can drastically affect the course in which the analysis progresses.
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