Abstract: In this paper we explore the relationship between multivariate data analysis and techniques for graph drawing or graph layout. Although both classes of techniques were created for quite different purposes, we find many common principles and implementations. We start with a discussion of the data analysis techniques, in particular multiple correspondence analysis, multidimensional scaling, parallel coordinate plotting, and seriation. We then discuss parallels in the graph layout literature.

Abstract: Data warehouses, which are the core elements of On-Line Analytical Processing (OLAP) systems, are passive since all tasks related to analyzing and making decisions must be carried out manually. This paper introduces a novel architecture, the active data warehouse, which applies the idea of event-condition-action rules (ECA rules) from active database systems to automize repetitive analysis and decision tasks in data warehouses. The work of an analyst is mimicked by analysis rules, which extend the capabilities of conventional ECA rules in order to support multidimensional analysis and decision making.

Abstract: Data warehouses, which are the core elements of On-Line Analytical Processing (OLAP) systems, are passive since all tasks related to analyzing and making decisions must be carried out manually. This paper introduces a novel architecture, the active data warehouse, which applies the idea of event-condition-action rules (ECA rules) from active database systems to automize repetitive analysis and decision tasks in data warehouses. The work of an analyst is mimicked by analysis rules which extend the capabilities of conventional ECA rules in order to support multidimensional analysis and decision making.

Abstract: Some significant progress related to multidimensional data analysis has been achieved in the past few years, including the design of fast algorithms for computing datacubes, selecting some precomputed group-bys to materialize, and designing efficient storage structures for multidimensional data. However, little work has been carried out on multidimensional query optimization issues. Particularly the response time (or evaluation cost) for answering several related dimensional queries simultaneously is crucial to the OLAP applications. Recently, Zhao et al. first exploited this problem by presenting three heuristic algorithms. In this paper we first consider in detail two cases of the problem in which all the queries are either hash-based star joins or index-based star joins only. In the case of the hash-based star join, we devise a polynomial approximation algorithm which delivers a plan whose evaluation cost is $ O(n^{\epsilon }$) times the optimal, where n is the number of queries and $ \epsilon $ is a fixed constant with $0<\epsilon \leq 1$. We also present an exponential algorithm which delivers a plan with the optimal evaluation cost. In the case of the index-based star join, we present a heuristic algorithm which delivers a plan whose evaluation cost is n times the optimal, and an exponential algorithm which delivers a plan with the optimal evaluation cost. We then consider a general case in which both hash-based star-join and index-based star-join queries are included. For this case, we give a possible improvement on the work of Zhao et al., based on an analysis of their solutions. We also develop another heuristic and an exact algorithm for the problem. We finally conduct a performance study by implementing our algorithms. The experimental results demonstrate that the solutions delivered for the restricted cases are always within two times of the optimal, which confirms our theoretical upper bounds. Actually these experiments produce much better results than our theoretical estimates. To the best of our knowledge, this is the only development of polynomial algorithms for the first two cases which are able to deliver plans with deterministic performance guarantees in terms of the qualities of the plans generated. The previous approaches including that of [ZDNS98] may generate a feasible plan for the problem in these two cases, but they do not provide any performance guarantee, i.e., the plans generated by their algorithms can be arbitrarily far from the optimal one.

Abstract: PROBLEM TO BE SOLVED: To provide a device and a system for multidimensional analysis which can perform data analysis among multiple multidimensional databases and data analysis among multiple databases having different systems and a recording medium. SOLUTION: This multidimensional data analyzing device 2 which is equipped with a multidimensional database 21 storing multiple pieces of multidimensional cube data and analyzes the data in the multidimensional database 21 is equipped with a data acquiring means (e.g. a data processing part 23, etc.), which acquires designated data over plural multidimensional cubes, a data processing means (e.g. a data processing part 23, etc.), which processes the data acquired by the data acquiring means into prescribed data format, and a data analyzing means (e.g. an application server 22, etc.), which analyzes the data processed by the data processing means.

Abstract: On-line analytical processing provides multidimensional data analysis, through extensive computation based on aggregation, along many dimensions and hierarchies. To accelerate query-response time, pre-computed results are often stored for later retrieval. This adds a prohibitive storage overhead when applied to the whole set of aggregates. In this paper we describe a novel approach which provides the means for the efficient selection, computation and storage of multidimensional aggregates. The approach identifies redundant aggregates, by inspection, thus allowing only distinct aggregates to be computed and stored. We propose extensions to relational theory and also present new algorithms for implementing the approach, providing a solution which is both scalable and low in complexity. The experiments were conducted using real and synthetic datasets and demonstrate that significant savings in computation time and storage space can be achieved when redundant aggregates are eliminated. Savings have also been shown to increase as dimensionality increases. Finally, the implications of this work affect the indexing and maintenance of views and the user interface.

Abstract: The history of statistical data analysis is old, it goes back to the 1920's. Many fundamental concepts of multivariate statistical data analysis, especially pure theoretical notions, have been accomplished by the 1950's. After the 1960's, the practical applications of multivariate statistical data analysis have been available, coupled with the progress of computers, and these have also been an affect on theoretical considerations. The basic process of data analysis is given as follows; p1). An objective of data analysis is given. p2). The data which seems to be closely connected with the objective is observed, (sampling data) p3). Constructing a model (or a set of models) for explaining the variation of the data. p4). Preprocessing (or transforming) the original data in order to make consistency between input data and the model. p5). Identification of the model based on observed (input) data. p6). Evaluate a goodness of fit. If the goodness of fit is insufficient, then return to P2) or P3), else go to next process. p7). Interpretation of the result and investigate the validity. The most different point on "data mining" and statistical data analysis seems to be the concept of "Data". In data mining, the data is given as a database in advance. But, in statistical data analysis, the data is observed according to the objective of the analysis. On the other hand, the object of "data mining" is to find the effective (or valuable) information in the data. From the framework of statistical data analysis above, the main processes of data mining are p3), p4) and p5). However, the concept of "efficient information" in data mining is different from the main part of the data variation in statistical data analysis. For instance, in principal component analysis, the main part of the data variation is obtained as the first principal component, which has the largest proportion. But in data mining, the major variation of the data is of no interest, because the knowledge obtained from it is trivial. Then, data mining seems to be interested in the principal components with small proportion in order to get unusual but valuable information. Hence, statistical data analysis for residual data which is removing the main part of the data variation from the original data, will be useful for data mining.

Abstract: On-line analytical processing provides multidimensional data analysis, through extensive computation based on aggregation, along many dimensions and hierarchies. To accelerate query-response time, pre-computed results are often stored for later retrieval. This adds a prohibitive storage overhead when applied to the whole set of aggregates. In this paper we describe a novel approach which provides the means for the efficient selection, computation and storage of multidimensional aggregates. The approach identifies redundant aggregates, by inspection, thus allowing only distinct aggregates to be computed and stored. We propose extensions to relational theory and also present new algorithms for implementing the approach, providing a solution which is both scalable and low in complexity. The experiments were conducted using real and synthetic datasets and demonstrate that significant savings in computation time and storage space can be achieved when redundant aggregates are eliminated. Savings have also been shown to increase as dimensionality increases. Finally, the implications of this work affect the indexing and maintenance of views and the user interface.

Abstract: A data warehouse is a global information repository, which stores facts originating from multiple, heterogeneous data sources in materialised views. Up to now, a data warehouse has always been used for application data and never for control data. As efficiency, accuracy, transparency and flexibility of enterprise’s business processes have become fundamental for process reengineering programmes, paying attention to accurate and comprehensive business process analysis will become an important issue in the near future. We have chosen a data warehouse approach, called process warehouse (PWH) for multidimensional process controlling, which enables process owners, process managers or other authorised staff members, to receive comprehensive information on business processes very quickly, at different aggregation levels, from different and multidimensional points of view, over a long period of time, using a huge historic data basis prepared for analysing purposes to effectively support the management of business processes. In this paper, we give an overview of requirements and data sources of an analytical database for process decision support, addressing users at strategic, tactical and operational levels. The database design provides information at various granularity levels with navigation capabilities, gathered from heterogeneous data sources, which leads to a very balanced and comprehensive analysis. This approach is the basis for analysing and assessing business processes quickly, efficiently and accurately due to fast extraction of information, multidimensional analysis, foundation for all kinds of analysis tools and systems, navigation and exploration as well as trend and pattern recognition.

Abstract: Considers the use of online analytical processing (OLAP) tools to provide fast, interactive analysis of Web-site traffic. For the purpose of analysing our own hierarchically organized Web site, the Directory of Croatian WWW Servers, an OLAP application (OLAWEB) has been developed. We describe data extraction from existing server access log files, the data transformation necessary to prepare data for multidimensional analysis, and the storage of the Web-site traffic data. The basic characteristics of the OLAWEB application are explained. Using this application, the Web-site administrator and other users are able to get fast answers to many unpredictable and complex questions that could not be answered by available statistical tools.

Abstract: PROBLEM TO BE SOLVED: To provide a system which supports the actualization of a one-to-one marketing by effectively using rich customer information obtained by running an FSP. SOLUTION: This customer service management analysis system is equipped with the FSP system which obtains data regarding points given to a customer according to sales through a network and stores and manages the data in a database and a multidimensional data analysis system which can take multidimensional data analysis according to the data stored by the FSP system. Further, this is provided in the form of package software through a web site on the Internet. COPYRIGHT: (C)2001,JPO

Abstract: We develop multicomponent AM-FM models for multidimensional signals. The analysis is cast in a general n-dimensional framework where the component modulating functions are assumed to lie in certain Sobolev spaces. For both continuous and discrete linear shift invariant (LSI) systems with AM-FM inputs, powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations. The approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by Sobolev norms quantifying the smoothness of the modulations. The approximations are then used to develop novel spatially localized demodulation algorithms that estimate the AM and FM functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components. Two discrete computational paradigms are presented. Dominant component analysis estimates the locally dominant modulations in a signal, which are useful in a variety of machine vision applications, while channelized components analysis delivers a true multidimensional multicomponent signal representation. We demonstrate the techniques on several images of general interest in practical applications, and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components.