The Search for Irregularly Shaped Clusters in Data Mining
Ángel Kuri-Morales, Edwyn Aldana-Bobadill · InTech eBooks · 2011
ClusteringOur problem will be focused under the assumption that the data under consideration correspond to numerical variables.This will not be always the case and several other methodologies have been devised to allow clustering with non-numerical (or categorical) variables.Research on analyzing categorical data has received significant attention see (Agresti,2002), (Chandola et al.,2009), (Chang & Ding,2005) and (Gibson,2000).However, many traditional techniques associated to the exploration of data sets assume the attributes have continuous data (covariance, density functions, Principal Component's Analysis, etc.).In order to use these techniques, the categorical attributes have to be discarded, although they are loaded with valuable information.Investigation under way (Kuri & Garcia,2010) will allow us to apply the methods to be discussed in what follows even in the presence of categorical variables.Suffice it to say, however, that we shall not consider these special cases and, rather,focus on numerically expressible attributes of the data sets. DefinitionClustering, as stated, is an unsupervised process that allows the partition of a data set X in k groups or clusters in accordance with a similarity criterion.Generally all elements of data set X belong to a metric space D, where there exist relationships between them that are expressible in terms of a distance.In the great majority of clustering methods, the similarity between two or more elements is defined as a measure of its proximity whose value is a consequence of such distance.The elements are rendered similar if its proximity is less than a certain threshold.This threshold represents the radius that defines the bound of a cluster as a n-dimensional spherical hull. MetricsFormally a metric is a function that defines the distance between elements of a set.The set with a metric is called a metric space.Definition 1 A metric on a set X is a function d : X × X → R where R is the set of the real numbers.For all x, y, z in X this function must satisfy the following conditions How to referenceIn order to correctly reference this scholarly work, feel free to copy and paste the following: Angel Kuri-Morales and Edwyn Aldana-Bobadilla (2011).