For many KDD applications finding the outliers, i.e. the rare events, is more interesting and useful than finding the common cases, e.g. detecting criminal activities in E-commerce. Being an outlier, however, is not just a binary property. Instead, it is a property that applies to a certain degree to each object in a data set, depending on how 'isolated' this object is, with respect to the surrounding clustering structure. In this paper, we formally introduce a new notion of outliers which bases outlier detection on the same theoretical foundation as density-based cluster analysis. Our notion of an outlier is 'local' in the sense that the outlier-degree of an object is determined by taking into account the clustering structure in a bounded neighborhood of the object. We demonstrate that this notion of an outlier is more appropriate for detecting different types of outliers than previous approaches, and we also present an algorithm for finding them. Furthermore, we show that by combining the outlier detection with a density-based method to analyze the clustering structure, we can get the outliers almost for free if we already want to perform a cluster analysis on a data set.
The R-tree, one of the most popular access methods for rectangles, IS based on the heurlstlc optlmlzatlon of the area of the enclosmg rectangle m each mner node By running numerous experiments m a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which mcorporates a combined optlmlzatlon of area, margin and overlap of each enclosmg rectangle m the directory Using our standardized testbed m an exhaustive performance comparison, It turned out that the R*-tree clearly outperforms the exlstmg R-tree varmnts Guttman's linear and quadratic R-tree and Greene's variant of the R-tree This superlorlty of the R*-tree holds for different types of queries and operations, such as map overlay. for both rectangles and multldlmenslonal points m all experiments From a practical pomt of view the R*-tree 1s very attractive because of the followmg two reasons 1 It effrclently supports pomt and spattal data at the same time and 2 Its lmplementatlon cost 1s only slightly higher than that of other R-trees l.Introduction In this paper we will consider spatial access methods (SAMs) which are based on the approxlmatlon of a complex spatial object by the mmlmum boundmg rectangle with the sides of the rectangle parallel to the axes of the data space yIp---+ This work was supported by grant no Kr 670/4-3 from the Deutsche Forschun&iememschaft (German Research Society) and by the Mmlstry of Environmental and Urban Planning of Bremen Pemxss~on to copy wthout fee all or part of this maternal IS granted prowded that the copses are not made or dlstnbuted for dwzct commeraal advantage, the ACM copy&t notice and the title of the pubbcatlon and its date appear, and notw IS gwn that cqymg II by pemuwon of the Assoaatlon for Computmg Machmq To copy othemw, or to repubbsh requ,res a fee and/or speoflc pemllsslon 0 1990 ACM 089791365 5/!90/0@35/0322 $150The most important property of this simple approxlmatlon 1s that a complex object 1s represented by a limited number of bytes Although a lot of mformatlon 1s lost, mnumum bounding rectangles of spatial oblects preserve the most essential geometric properties of the object, 1 e the location of the oblect and the extension of the object in each axisIn [SK 881 we showed that known SAMs organlzmg (mmlmum bounding) rectangles are based on an underlymg point access method (PAM) using one of the followmg three techniques cllpplng, transformation and overlapping regionsThe most popular SAM for storing rectangles 1s the Rtree [Gut 841 Followmg our classlflcatlon, the R-tree 1s based on the PAM B+-tree [Knu 731 usmg the technique over-lapping regions Thus the R-tree can be easily implemented which considerably contributes to Its popularity The R-tree 1s based on a heurlstlc optlmlzatlon The optlmlzatton crlterlon which It persues, 1s to mmlmlze the area of each enclosing rectangle m the mner nodes This crlterlon IS taken for granted and not shown to be the best possible Questions arise such as Why not mnumlze the margin or the overlap of such mlnlmum...
Abstract. Both, the number and the size of spatial databases, such as geographic or medical databases, are rapidly growing because of the large amount of data obtained from satellite images, computer tomography or other scientific equipment. Knowledge discovery in databases (KDD) is the process of discovering valid, novel and potentially useful patterns from large databases. Typical tasks for knowledge discovery in spatial databases include clustering, characterization and trend detection. The major difference between knowledge discovery in relational databases and in spatial databases is that attributes of the neighbors of some object of interest may have an influence on the object itself. Therefore, spatial knowledge discovery algorithms heavily depend on the efficient processing of neighborhood relations since the neighbors of many objects have to be investigated in a single run of a typical algorithm. Thus, providing general concepts for neighborhood relations as well as an efficient implementation of these concepts will allow a tight integeration of spatial knowledge discovery algorithms with a spatial database management system. This will speed-up both, the development and the execution of spatial KDD algorithms. For this purpose, we define a small set of database primitives, and we demonstrate that typical spatial KDD algorithms are well supported by the proposed database primitives. By implementing the database primitives on top of a commercial database management system, we show the effectiveness and efficiency of our approach, experimentally as well as analytically. The paper concludes by outlining some interesting issues for future research in the emerging field of knowledge discovery in spatial databases.
http://www.dbs.ifi.lmu.de/~borgward/MMD.
Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NP-hard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortest-path kernels show significantly higher classification accuracy than walk-based kernels.
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