We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

The Object Management Group's (OMG) Model Driven Architecture (MDA) strategy envisages a world where models play a more direct role in software production, being amenable to manipulation and transformation by machine. Model Driven Engineering (MDE) is wider in scope than MDA. MDE combines process and analysis with architecture. This article sets out a framework for model driven engineering, which can be used as a point of reference for activity in this area. It proposes an organisation of the modelling 'space' and how to locate models in that space. It discusses different kinds of mappings between models. It explains why process and architecture are tightly connected. It discusses the importance and nature of tools. It identifies the need for defining families of languages and transformations, and for developing techniques for generating/configuring tools from such definitions. It concludes with a call to align metamodelling with formal language engineering techniques.

Model Driven Engineering

コンピュータ・サイエンス : ACM computing surveys

Kaizen: The key to Japan‚s competitive success

Purpose – Maturity models are a prospering approach to improving a company's processes and business process management (BPM) capabilities. In fact, the number of corresponding maturity models is so high that practitioners and scholars run the risk of losing track. This paper therefore aims to provide a systematic in‐depth review of BPM maturity models.Design/methodology/approach – The paper follows the accepted research process for literature reviews. It analyzes a sample of ten BPM maturity models according to a framework of general design principles. The framework particularly focuses on the applicability and usefulness of maturity models.Findings – The analyzed maturity models sufficiently address basic design principles as well as principles for a descriptive purpose of use. The design principles for a prescriptive use, however, are hardly met. Thus, BPM maturity models provide limited guidance for identifying desirable maturity levels and for implementing improvement measures.Research limitations/imp...

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Maturity Models in Business Process Management

In multimedia systems we usually need to retrieve database (DB) objects based on their similarity to a query object, while the similarity assessment is provided by a measure which defines a (dis)similarity score for every pair of DB objects. In most existing applications, the similarity measure is required to be a metric, where the triangle inequality is utilized to speed up the search for relevant objects by use of metric access methods (MAMs), for example, the M-tree. A recent research has shown, however, that nonmetric measures are more appropriate for similarity modeling due to their robustness and ease to model a made-to-measure similarity. Unfortunately, due to the lack of triangle inequality, the nonmetric measures cannot be directly utilized by MAMs. From another point of view, some sophisticated similarity measures could be available in a black-box nonanalytic form (e.g., as an algorithm or even a hardware device), where no information about their topological properties is provided, so we have to consider them as nonmetric measures as well. From yet another point of view, the concept of similarity measuring itself is inherently imprecise and we often prefer fast but approximate retrieval over an exact but slower one.To date, the mentioned aspects of similarity retrieval have been solved separately, that is, exact versus approximate search or metric versus nonmetric search. In this article we introduce a similarity retrieval framework which incorporates both of the aspects into a single unified model. Based on the framework, we show that for any dissimilarity measure (either a metric or nonmetric) we are able to change the “amount” of triangle inequality, and so obtain an approximate or full metric which can be used for MAM-based retrieval. Due to the varying “amount” of triangle inequality, the measure is modified in a way suitable for either an exact but slower or an approximate but faster retrieval. Additionally, we introduce the TriGen algorithm aimed at constructing the desired modification of any black-box distance automatically, using just a small fraction of the database.

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Unified framework for fast exact and approximate search in dissimilarity spaces

The task of similarity search is widely used in various areas of computing, including multimedia databases, data mining, bioinformatics, social networks, etc. In fact, retrieval of semantically unstructured data entities requires a form of aggregated qualification that selects entities relevant to a query. A popular type of such a mechanism is similarity querying. For a long time, the database-oriented applications of similarity search employed the definition of similarity restricted to metric distances. Due to its topological properties, metric similarity can be effectively used to index a database which can then be queried efficiently by so-called metric access methods. However, together with the increasing complexity of data entities across various domains, in recent years there appeared many similarities that were not metrics—we call them nonmetric similarity functions. In this article we survey domains employing nonmetric functions for effective similarity search, and methods for efficient nonmetric similarity search. First, we show that the ongoing research in many of these domains requires complex representations of data entities. Simultaneously, such complex representations allow us to model also complex and computationally expensive similarity functions (often represented by various matching algorithms). However, the more complex similarity function one develops, the more likely it will be a nonmetric. Second, we review state-of-the-art techniques for efficient (fast) nonmetric similarity search, concerning both exact and approximate search. Finally, we discuss some open problems and possible future research trends.

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On nonmetric similarity search problems in complex domains

In this paper we introduce the Pivoting M-tree (PM-tree), a metric access method combining M-tree with the pivot-based approach. While in M-tree a metric region is represented by a hyper-sphere, in PM-tree the shape of a metric region is determined by intersection of the hyper-sphere and a set of hyper-rings. The set of hyper-rings for each metric region is related to a fixed set of pivot objects. As a consequence, the shape of a metric region bounds the indexed objects more tightly which, in turn, significantly improves the overall efficiency of similarity search. We present basic algorithms on PM-tree and two cost models for range query processing. Finally, the PM-tree efficiency is experimentally evaluated on large synthetic as well as real-world datasets.

PM-tree: Pivoting Metric Tree for Similarity Search in Multimedia Databases.

Business process management (BPM) is a still-emerging field in the academic discipline of Information Systems (IS). This article reflects on a workshop on current and future issues in BPM research that was conducted by seventeen IS researchers from eight European countries as part of the 2010 annual meeting of the European Research Center for Information Systems (ERCIS). The results of this workshop suggest that BPM research can meaningfully contribute to investigating a broad variety of phenomena that are of interest to IS scholars, ranging from rather technical (e.g., the implementation of software architectures) to managerial (e.g., the impact of organizational culture on process performance). It further becomes noticeable that BPM researchers can make use of several research strategies, including qualitative, quantitative, and design-oriented approaches. The article offers the participants' outlook on the future of BPM research and combines their opinions with research results from the academic literature on BPM, with the goal of contributing to establishing BPM as a distinct field of research in the IS discipline.

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Current and Future Issues in BPM Research: A European Perspective from the ERCIS Meeting 2010

We introduce a method of searching the k nearest neighbours (k-NN) using PM-tree. The PM-tree is a metric access method for similarity search in large multimedia databases. As an extension of M-tree, the structure of PM-tree exploits local dynamic pivots (like M-tree does it) as well as global static pivots (used by LAESA-like methods). While in M-tree a metric region is represented by a hyper-sphere, in PM-tree the ”volume” of metric region is further reduced by a set of hyper-rings. As a consequence, the shape of PM-tree's metric region bounds the indexed objects more tightly which, in turn, improves the overall search efficiency. Besides the description of PM-tree, we propose an optimal k-NN search algorithm. Finally, the efficiency of k-NN search is experimentally evaluated on large synthetic as well as real-world datasets.

/pdf/nearest-neighbours-search-using-the-pm-tree-1j1n2pg21c.pdf

Tomáš Skopal

Papers

Unified framework for fast exact and approximate search in dissimilarity spaces

On nonmetric similarity search problems in complex domains

PM-tree: Pivoting Metric Tree for Similarity Search in Multimedia Databases.

Current and Future Issues in BPM Research: A European Perspective from the ERCIS Meeting 2010

Nearest neighbours search using the PM-Tree