{"id":362,"date":"2013-12-06T15:09:21","date_gmt":"2013-12-06T20:09:21","guid":{"rendered":"http:\/\/homepages.uc.edu\/~yaozo\/wordpress\/?p=362"},"modified":"2013-12-06T15:09:21","modified_gmt":"2013-12-06T20:09:21","slug":"clustering-an-introduction","status":"publish","type":"post","link":"https:\/\/zhuoyao.net\/index.php\/2013\/12\/06\/clustering-an-introduction\/","title":{"rendered":"Clustering: An Introduction"},"content":{"rendered":"
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What is Clustering?<\/em><\/span>
\nClustering can be considered the most important\u00a0unsupervised learning<\/em>\u00a0problem; so, as every other problem of this kind, it deals with finding a\u00a0structure<\/em>\u00a0in a collection of unlabeled data.
\nA loose definition of clustering could be \u201cthe process of organizing objects into groups whose members are similar in some way\u201d.
\nA\u00a0cluster<\/em>\u00a0is therefore a collection of objects which are \u201csimilar\u201d between them and are \u201cdissimilar\u201d to the objects belonging to other clusters.
\nWe can show this with a simple graphical example:<\/span><\/p>\n

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In this case we easily identify the 4 clusters into which the data can be divided; the similarity criterion is\u00a0distance<\/em>: two or more objects belong to the same cluster if they are \u201cclose\u201d according to a given distance (in this case geometrical distance). This is called\u00a0distance-based clustering<\/em>.
\nAnother kind of clustering is\u00a0conceptual clustering<\/em>: two or more objects belong to the same cluster if this one defines a concept\u00a0common<\/em>\u00a0to all that objects. In other words, objects are grouped according to their fit to descriptive concepts, not according to simple similarity measures.<\/span><\/p>\n

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The Goals of Clustering<\/em><\/span>
\nSo, the goal of clustering is to determine the intrinsic grouping in a set of unlabeled data. But how to decide what constitutes a good clustering? It can be shown that there is no absolute \u201cbest\u201d criterion which would be independent of the final aim of the clustering. Consequently, it is the user which must supply this criterion, in such a way that the result of the clustering will suit their needs.
\nFor instance, we could be interested in finding representatives for homogeneous groups (data reduction<\/em>), in finding \u201cnatural clusters\u201d and describe their unknown properties (\u201cnatural\u201d data types<\/em>), in finding useful and suitable groupings (\u201cuseful\u201d data classes<\/em>) or in finding unusual data objects (outlier detection<\/em>).<\/span><\/p>\n

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Possible Applications<\/em><\/span>
\nClustering algorithms can be applied in many fields, for instance:<\/span><\/p>\n<\/div>\n