Partitional clustering

Partitional clustering using Euclidean distance as a measure of dissimilarity between pattern classes has been selected for the grouping of AE hits. 

The simulated annealing algorithm (37) for the partitional clustering as we required in this work was designed based on the following problem formation. 

Kmeans Clustering. Type of partitioning cluster analysis in which an object, such as a chemical structure, is placed into one of K clusters, based on how similar the structure is to the average value (or centroid) of each cluster. The average of the cluster may be an actual structure itself, in which case the technique is referred to as K-medoids clustering. 

The perturbation operator for partitional clustering switches a randomly-chosen object i in Q from one cluster to another randomly chosen cluster. Algorithm 2 shows the basic procedure. The set L contains the cluster labels used in p. Similarly, L° contains the labels not used in p. The switching procedure first selects an integer m in the range [0, L ]. If m equals 0 and there exists an unused cluster label (i.e., L < ), then object i is placed in its own singleton cluster. Otherwise, i switches to another, existing cluster. 

We emphasize that the choice of the internal criterion for use in a partitional clustering problem is critical to the interpretability and usefulness of the resulting output. However, for computational reasons, it is desired that the criterion be simple. One of the simplest of the internal clustering criteria is total within-cluster distance ... 

To compare the two criteria we examined 32 data sets where each data set has between 150 and 600 objects, split into 20 true clusters on the average. We applied simulated annealing partitional clustering 5 times to each set with both B(p) and W(p). We then compared the best test results for W(p) and B(p) over the 32 data sets. Table 1 shows for each data set the best Jaccard score for each of the criteria. In addition, for W(p) it shows the best number of clusters parameter k in 18, 19, 20, 21, 22. Similarly, for B(p) the table shows the best median distance parameter v in the set 2.0, 2.5, 3.0, 3.5, 4.0 and the associated number of clusters in the final partitioning. At the bottom of the table is the minimum, maximum, and mean of each column. 

We applied three hierarchical clustering methods to the same 32 data sets used in the previous section for partitional clustering (1) simulated annealing with the criterion in equation (11) (2) simulated annealing with the criterion in equation (12) and (3) Ward s algorithm. Each method generated a separate dendrogram for each data set. 

These results show clearly the importance of the optimization criterion to clustering. The computationally simple Ward s method performs better than the simulated annealing approach with a simplistic criterion. However, a criterion that more correctly accounts for the hierarchy, by minimizing the sum of squared error at each level, performs much better. As with partitional clustering the application of simulated annealing to hierarchical clustering requires careful selection of the internal clustering criterion. 

Lastly we demonstrated the use of simulated annealing on examples from multi-sensor data fusion. These examples showed the effectiveness of simulated annealing in performing both hierarchical and partitional clustering. They also showed the importance of the internal criterion to the results obtained. 

It is useful to categorize the various classes of dimers and clusters before discussing the theoretical approaches and models for understanding the cluster dissociation rates and energy partitioning. Clusters fall into three broad classes ... 

Euclidean distance has been widely used in the partitional clustering algorithms (Xu and Wunsch, 2005). 

K-Means X-means is a very straightforward, commonly used partitional clustering method. In atypical implementation of the X-means algorithm, the first step is to randomly select K objects, each representing the initial cluster centroid. After the initialization step, each object in the dataset is assigned to the closest centroid, and a cluster... 

We have defined a design step partitioning-clustering [5, 6, 7] to decompose the regularized DG in a network of similar reduced-size DGs, called tiles. We call this network the tile graph. An alternative approach, based on the same principles but tuned towards latency-driven applications, is discussed in chapter 3. 

Step 3 Next we apply both hierarchical and partitional clustering methods to supplier data. We choose the method which has the highest value pooled over all the 14 attributes. A summary table showing the pooled values is shown in Table 6.28. 

After scheduling and allocation, a greedy global partitioning / clustering algorithm is used to optimize the interconnect. 

Partitional clustering methods attempt to directly decompose a data set into a fixed number of disjoint clusters. The methods attempt to minimize a criterion function, typically based on minimizing the dissimilarity inside classes, while maximizing the dissimilarity between different classes. 

Nonhierarchical or partitional clustering uses algorithms, which determine all clusters at once. 

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