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【正文】 ments. Elements from different clusters are not alike. ? The distance between points in a cluster is less than the distance between a point in the cluster and any point outside it. A term similar to clustering is database segmentation, where like tuple (record) in a database are grouped together. This is done to partition or segment the database into ponents that then give the user a more general view of the data. In this case text, we do not differentiate between segmentation and clustering. A simple example of clustering is found in Example . This example illustrates the fact that that determining how to do the clustering is not straightforward. As illustrated in Figure , a given set of data may be clustered on different attributes. Here a group of homes in a geographic area is shown. The first floor type of clustering is based on the location of the home. Homes that are geographically close to each other are clustered together. In the second clustering, homes are grouped based on the size of the house. Clustering has been used in many application domains, including biology, medicine, anthropology, marketing, and economics. Clustering applications include plant and animal classification, disease classification, image processing, pattern recognition, and document retrieval. One of the first domains in which clustering was used was biological taxonomy. Recent uses include examining Web log data to detect usage patterns. When clustering is applied to a realworld database, many interesting problems occur: ? Outlier handling is difficult. Here the elements do not naturally fall into any cluster. They can be viewed as solitary clusters. However, if a clustering algorithm attempts to find larger clusters, these outliers will be forced to be placed in some cluster. This process may result in the creation of poor clusters by bining two existing clusters and leaving the outlier in its own cluster. ? Dynamic data in the database implies that cluster membership may change over time. ? Interpreting the semantic meaning of each cluster may be difficult. With classification, the labeling of the classes is known ahead of time. However, with clustering, this may not be the case. Thus, when the clustering process finishes creating a set of clusters, the exact meaning of each cluster may not be obvious. Here is where a domain expert is needed to assign a label or interpretation for each cluster. ? There is no one correct answer to a clustering problem. In fact, many answers may be found. The exact number of clusters required is not easy to determine. Again, a domain expert may be required. For example, suppose we have a set of data about plants that have been collected during a field trip. Without any prior knowledge of plant classification, if we attempt to divide this set of data into similar groupings, it would not be clear how many groups should be created. ? Another related issue is what data should be used of clustering. Unlike learning during a classification process, where there is some a priori knowledge concerning what the attributes of each classification should be, in clustering we have no supervised learning to aid the process. Indeed, clustering can be viewed as similar to unsupervised learning. We can then summarize some basic features of clustering (as opposed to classification): ? The (best) number of clusters is not known. ? There may not be any a priori knowledge concerning the clusters. ? Cluster results are dynamic. The clustering problem is stated as shown in Definition . Here we assume that the number of clusters to be created is an input value, k. The actual content (and interpretation) of each cluster, jk ,1 jk?? , is determined as a result of the function definition. Without loss of generality, we will view that the result of sol
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