There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and more succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.

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Anomaly detection: A survey

A data model, called the entity-relationship model, is proposed. This model incorporates some of the important semantic information in the real world. A special diagramatic technique is introduced as a tool for data base design. An example of data base design and description using the model and the diagramatic technique is given. Some implications on data integrity, information retrieval, and data manipulation are discussed.The entity-relationship model can be used as a basis for unification of different views of data: the network model, the relational model, and the entity set model. Semantic ambiguities in these models are analyzed. Possible ways to derive their views of data from the entity-relationship model are presented.

/pdf/the-entity-relationship-model-toward-a-unified-view-of-data-i5q0wnv07u.pdf

The entity-relationship model: toward a unified view of data

The R-tree, one of the most popular access methods for rectangles, is based on the heuristic optimization of the area of the enclosing rectangle in each inner node. By running numerous experiments in a standardized testbed under highly varying data, queries and operations, we were able to design the R*-tree which incorporates a combined optimization of area, margin and overlap of each enclosing rectangle in the directory. Using our standardized testbed in an exhaustive performance comparison, it turned out that the R*-tree clearly outperforms the existing R-tree variants. Guttman's linear and quadratic R-tree and Greene's variant of the R-tree. This superiority of the R*-tree holds for different types of queries and operations, such as map overlay, for both rectangles and multidimensional points in all experiments. From a practical point of view the R*-tree is very attractive because of the following two reasons 1 it efficiently supports point and spatial data at the same time and 2 its implementation cost is only slightly higher than that of other R-trees.

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The R*-tree: an efficient and robust access method for points and rectangles

We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

A frequently encountered type of query in Geographic Information Systems is to find the k nearest neighbor objects to a given point in space. Processing such queries requires substantially different search algorithms than those for location or range queries. In this paper we present an efficient branch-and-bound R-tree traversal algorithm to find the nearest neighbor object to a point, and then generalize it to finding the k nearest neighbors. We also discuss metrics for an optimistic and a pessimistic search ordering strategy as well as for pruning. Finally, we present the results of several experiments obtained using the implementation of our algorithm and examine the behavior of the metrics and the scalability of the algorithm.

https://infolab.usc.edu/csci599/Fall2007/papers/a-1.pdf

Nearest neighbor queries

The problem of indexing multidimensional objects is considered. First, a classification of existing methods is given along with a discussion of the major issues involved in multidimensional data indexing. Second, a variation to Guttman’s Rtrees (R+-trees) that avoids overlapping rectangles in intermediate nodes of the tree is introduced. Algorithms for searching, updating, initial packing and reorganization of the structure are discussed in detail. Finally, we provide analytical results indicating that R+-trees achieve up to 50% savings in disk accesses compared to an R-tree when searching files of thousands of rectangles.

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The R+-Tree: A Dynamic Index for Multi-Dimensional Objects

Database systems were a solution to the problem of shared access to heterogeneous files created by multiple autonomous applications in a centralized environment. To make data usage easier, the files were replaced by a globally integrated database. To a large extent, the idea was successful, and many databases are now accessible through local and long-haul networks. Unavoidably, users now need shared access to multiple autonomous databases. The question is what the corresponding methodology should be. Should one reapply the database approach to create globally integrated distributed database systems or should a new approach be introduced?We argue for a new approach to solving such data management system problems, called multidatabase or federated systems. These systems make databases interoperable, that is, usable without a globally integrated schema. They preserve the autonomy of each database yet support shared access.Systems of this type will be of major importance in the future. This paper first discusses why this is the case. Then, it presents methodologies for their design. It further shows that major commerical relational database systems are evolving toward multidatabase systems. The paper discusses their capabilities and limitations, presents and discusses a set of prototypes, and, finally, presents some current research issues.

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Interoperability of multiple autonomous databases

Pictorial databases require efficient and duect spatml search based on the analog form of spatial obJects and relatlonshlps instead of search based on some cumbersome alphanumeric encodings of the pmtures R-trees (two-dimensional B-trees) are excellent devices for indexing spatial ObJects and relationships found on pictures Their most important feature 1s that they provide high level ObJect onented search rather than search based on the low level elements of spatial ObJects This paper presents an efficient initial packing technique for creatmg R-trees to index spatial ObJects Since pictorial databases are not update mtensive but rather static, the beneflts of this technique are very significant

Direct spatial search on pictorial databases using packed R-trees

This paper addresses the problem of finding k nearest neighbors for moving query point (we call it k-NNMP). It is an important issue in both mobile computing research and real-life applications. The problem assumes that the query point is not static, as in k-nearest neighbor problem, but varies its position over time. In this paper, four different methods are proposed for solving the problem. Discussion about the parameters affecting the performance of the algorithms is also presented. A sequence of experiments with both synthetic and real point data sets are studied. In the experiments, our algorithms always outperform the existing ones by fetching 70% less disk pages. In some settings, the saving can be as much as one order of magnitude.

/pdf/k-nearest-neighbor-search-for-moving-query-point-3ntnllgm7b.pdf

Nick Roussopoulos

Papers

Nearest neighbor queries

The R+-Tree: A Dynamic Index for Multi-Dimensional Objects

Interoperability of multiple autonomous databases

Direct spatial search on pictorial databases using packed R-trees

K-Nearest Neighbor Search for Moving Query Point