1.
We now know what the concepts involving cluster analysis are, the different types of clusterings and clusters, the basic algorithms etc. That leads us to the second paper, titled: "Cluster analysis in marketing research: review and suggestions for application". Where the book chapter mainly explains the theory underlying cluster analysis, this paper actually focuses on the practical issues regarding the use and validation of cluster analytic methods. This part of the presentation is built up as follows: first, we provide you guys with a short introduction on the paper. Of course, there is quite some overlap with the book chapter and the first part of the paper so we will keep it short. Second, a major contribution of this paper is its empirical comparison of clustering methods to evaluate their performance. Therefore I will discuss the findings of this comparison with you. In the final part, my team member will guide you through the recommendations for using cluster analysis, as proposed by the authors. This part contains the major issues regarding the use of clustering methods.
2. Problems
The main problem is the large number of different clustering methods that makes it hard for a potential user to choose the right method(s) that suits his or her purpose best. As also stated in the book chapter, cluster analysis has independently developed in a multitude of different disciplines. This is the main reason for the fact that (at least at the time, the paper is from 1983) almost a jungle of different cluster analytic methods have been developed, while a number of them only have their name to differentiate themselves from other methods. It is obvious that this has created a confusing situation for the potential user of these methods. In addition, also the lack of a clear definition of what actually is a "cluster" makes this situation even more confusing. We have also seen these different ideas, on what the boundaries of a cluster are, in a previous part of the presentation. These different ideas have lead to different clustering algorithms. And as we all have read, the book chapter already discusses some of these different common algorithms in detail.
3. Clustering algorithms
In table 2 of the paper, the authors have actually grouped the different methods based on their algorithm. It shows that out of these methods, seven different methods (in terms of algorithms) can be obtained: single linkage, complete linkage, average linkage, Ward's minimum variance method, K-means, hill climbing, and joint K-means, climbing. My team members have already elaborated upon the single linkage, complete linkage and average linkage, as well as on K-means. Therefore, I will focus primarily on the Minimum variance cluster analysis, the Hill-climbing methods and the Combined K-means and hill-climbing methods.
4.
Hierarchical methods:
-Single linkage
-Complete linkage
-Average linkage
-The method of the Minimum variance cluster analysis shouldn't lead to much confusion as it is basically the same as Ward's method. Clusters are generated in a way that the variance (a function of deviations from the mean) within the cluster is minimized. Ward's method is also seen as a type of average linkage method since it aims at minimizing the average distance of the cases within the cluster.
5.
Then there are also the nonhierarchical methods. The methods that fall into this category have in common that the observations are assigned into clusters initially, either random or based on some sort of criteria. Then the observations will be reassigned continuously until a stopping criteria (minimized within-cluster variance or another optimal objective) is achieved.
- K-means
- Now we will continue with the Hill-climbing methods. We know that with K-means, cases are continuously reassigned to the cluster whose centroid is closest to the case until this has happened for all cases, thereby minimizing the variance in each individual cluster. However, with Hill-climbing methods, cases are actually transferred to another cluster if an arbitrary solution has been reached. Then the algorithm attempts to find a better solution, and if this happens changes will be made, thus cases will be moved again based on this solution. This will go on until the optimal allocation has been achieved. Think about it this way, the example may not be directly related to clustering but at least gives you an idea: If you have a product and you want to sell it, you can go to every place in the world to sell your product. However, this solution is far from optimal. With the proposed method, the algorithm makes small improvements to the initial solution, for example regarding what cities to visit and what order to visit them in. In the optimal solution, the route you have to travel to sell your product is a lot shorter and thus efficient than with the initial solution.
-Then finally there is also the option to combine K-means and the hill-climbing method together.
6. Results of empirical comparison clustering methods
First I will talk about the so-called mixture model approach. This approach is used to the evaluate the different clustering algorithms and works as follows: You have a data set of which you already know the characteristics, for example you already know the mixture of groups in this data set. Then you apply the different clustering methods of your liking to this data set and check to what extent each clustering method produces results that you would expect based on your knowledge of the data set's characteristics. In table 4, we could see the empirical results of 12 studies of the mixture model approach.