TAILIEUCHUNG - Data Mining and Knowledge Discovery Handbook, 2 Edition part 31

Data Mining and Knowledge Discovery Handbook, 2 Edition part 31. Knowledge Discovery demonstrates intelligent computing at its best, and is the most desirable and interesting end-product of Information Technology. To be able to discover and to extract knowledge from data is a task that many researchers and practitioners are endeavoring to accomplish. There is a lot of hidden knowledge waiting to be discovered – this is the challenge created by today’s abundance of data. Data Mining and Knowledge Discovery Handbook, 2nd Edition organizes the most current concepts, theories, standards, methodologies, trends, challenges and applications of data mining (DM) and knowledge discovery. | 280 Lior Rokach Partitioning Methods Partitioning methods relocate instances by moving them from one cluster to another starting from an initial partitioning. Such methods typically require that the number of clusters will be pre-set by the user. To achieve global optimality in partitioned-based clustering an exhaustive enumeration process of all possible partitions is required. Because this is not feasible certain greedy heuristics are used in the form of iterative optimization. Namely a relocation method iteratively relocates points between the k clusters. The following subsections present various types of partitioning methods. Error Minimization Algorithms These algorithms which tend to work well with isolated and compact clusters are the most intuitive and frequently used methods. The basic idea is to find a clustering structure that minimizes a certain error criterion which measures the distance of each instance to its representative value. The most well-known criterion is the Sum of Squared Error SSE which measures the total squared Euclidian distance of instances to their representative values. SSE may be globally optimized by exhaustively enumerating all partitions which is very time-consuming or by giving an approximate solution not necessarily leading to a global minimum using heuristics. The latter option is the most common alternative. The simplest and most commonly used algorithm employing a squared error criterion is the K-means algorithm. This algorithm partitions the data into K clusters Ci C2 . CK represented by their centers or means. The center of each cluster is calculated as the mean of all the instances belonging to that cluster. Figure presents the pseudo-code of the K-means algorithm. The algorithm starts with an initial set of cluster centers chosen at random or according to some heuristic procedure. In each iteration each instance is assigned to its nearest cluster center according to the Euclidean distance between the two. .

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