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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"><!--NewPage--><HTML><HEAD><!-- Generated by javadoc (build 1.5.0_13) on Mon Jul 14 01:36:44 CEST 2008 --><TITLE>LOFOutlierOperator (RapidMiner Class Documentation)</TITLE><META NAME="keywords" CONTENT="com.rapidminer.operator.preprocessing.outlier.LOFOutlierOperator class"><LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../stylesheet.css" TITLE="Style"><SCRIPT type="text/javascript">function windowTitle(){    parent.document.title="LOFOutlierOperator (RapidMiner Class Documentation)";}</SCRIPT><NOSCRIPT></NOSCRIPT></HEAD><BODY BGCOLOR="white" onload="windowTitle();"><!-- ========= START OF TOP NAVBAR ======= --><A NAME="navbar_top"><!-- --></A><A HREF="#skip-navbar_top" title="Skip navigation links"></A><TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY=""><TR><TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1"><A NAME="navbar_top_firstrow"><!-- --></A><TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY="">  <TR ALIGN="center" VALIGN="top">  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> &nbsp;<FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="class-use/LOFOutlierOperator.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A>&nbsp;</TD>  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A>&nbsp;</TD>  </TR></TABLE></TD><TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM></EM></TD></TR><TR><TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">&nbsp;<A HREF="../../../../../com/rapidminer/operator/preprocessing/outlier/KdistanceContainer.html" title="class in com.rapidminer.operator.preprocessing.outlier"><B>PREV CLASS</B></A>&nbsp;&nbsp;<A HREF="../../../../../com/rapidminer/operator/preprocessing/outlier/SearchObject.html" title="class in com.rapidminer.operator.preprocessing.outlier"><B>NEXT CLASS</B></A></FONT></TD><TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">  <A HREF="../../../../../index.html?com/rapidminer/operator/preprocessing/outlier/LOFOutlierOperator.html" target="_top"><B>FRAMES</B></A>  &nbsp;&nbsp;<A HREF="LOFOutlierOperator.html" target="_top"><B>NO FRAMES</B></A>  &nbsp;&nbsp;<SCRIPT type="text/javascript">  <!--  if(window==top) {    document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>'); 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LOF outliers or outliers with a local  outlier factor per object are density based outliers according to Breuning,  Kriegel, et al.</p>  <p>The approach to find those outliers is based on measuring the density of objects  and its relation to each other (referred to as local reachability density).  Based on the average ratio of the local reachability density of an object and its k-nearest neighbours (e.g. the objects in its k-distance neighbourhood), a local  outlier factor (LOF) is computed. The approach takes a parameter MinPts  (actually specifying the "k") and it uses the maximum LOFs for objects in a MinPts range (lower bound and upper bound to MinPts).</p>  <p>Currently, the operator supports cosine, sine or squared distances in addition to the usual euclidian distance which can be specified by the corresponding parameter. In the first step, the objects are grouped into containers. For each object, using a  radius screening of all other objects, all the available distances between that object  and another object (or group of objects) on the (same) radius given by the distance are associated with a container. That container than has the distance  information as well as the list of objects within that distance (usually only a few)  and the information, how many objects are in the container.</p>  <p>In the second step, three things are done: (1) The containers for each object are counted  in acending order according to the cardinality of the object list within the container  (= that distance) to find the k-distances for each object and the objects in that k-distance (all objects in all the subsequent containers with a smaller  distance). (2) Using this information, the local reachability densities are computed by  using the maximum of the actual distance and the k-distance for each object pair (object and objects in k-distance) and averaging it by the cardinality of  the k-neighbourhood and than taking the reciprocal value. (3) The LOF is computed for  each MinPts value in the range (actually for all up to upper bound) by averaging the ratio between the MinPts-local reachability-density of all objects in  the k-neighbourhood and the object itself. The maximum LOF in the MinPts range is  passed as final LOF to each object.</p>  <p>Afterwards LOFs are added as values for a special real-valued outlier attribute  in the example set which the operator will return.</p><P><P><DL><DT><B>Version:</B></DT>  <DD>$Id: LOFOutlierOperator.java,v 1.5 2008/07/07 07:06:46 ingomierswa Exp $</DD><DT><B>Author:</B></DT>  <DD>Stephan Deutsch, Ingo Mierswa</DD></DL><HR><P><!-- =========== FIELD SUMMARY =========== --><A NAME="field_summary"><!-- --></A><TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY=""><TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor"><TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2"><B>Field Summary</B></FONT></TH></TR>

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