Processing count queries over event streams at multiple time granularities

Management and analysis of streaming data has become crucial with its applications in web, sensor data, network tra c data, and stock market. Data streams consist of mostly numeric data but what is more interesting is the events derived from the numerical data that need to be monitored. The events obtained from streaming data form event streams. Event streams have similar properties to data streams, i.e., they are seen only once in a fixed order as a continuous stream. Events appearing in the event stream have time stamps associated with them in a certain time granularity, such as second, minute, or hour. One type of frequently asked queries over event streams is count queries, i.e., the frequency of an event occurrence over time. Count queries can be answered over event streams easily, however, users may ask queries over di erent time granularities as well. For example, a broker may ask how many times a stock increased in the same time frame, where the time frames specified could be hour, day, or both. This is crucial especially in the case of event streams where only a window of an event stream is available at a certain time instead of the whole stream. In this paper, we propose a technique for predicting the frequencies of event occurrences in event streams at multiple time granularities. The proposed approximation method e ciently estimates the count of events with a high accuracy in an event stream at any time granularity by examining the distance distributions of event occurrences. The proposed method has been implemented and tested on di erent real data sets and the results obtained are presented to show its e ectiveness

Processing count queries over event streams at multiple time granularities

Cataloged from PDF version of article.Management and analysis of streaming data has become crucial with its applications to web, sensor data, network traffic data, and stock market. Data streams consist of mostly numeric data but what is more interesting are the events derived from the numerical data that need to be monitored. The events obtained from streaming data form event streams. Event streams have similar properties to data streams, i.e., they are seen only once in a fixed order as a continuous stream. Events appearing in the event stream have time stamps associated with them at a certain time granularity, such as second, minute, or hour. One type of frequently asked queries over event streams are count queries, i.e., the frequency of an event occurrence over time. Count queries can be answered over event streams easily, however, users may ask queries over different time granularities as well. For example, a broker may ask how many times a stock increased in the same time frame, where the time frames specified could be an hour, day, or both. Such types of queries are challenging especially in the case of event streams where only a window of an event stream is available at a certain time instead of the whole stream. In this paper, we propose a technique for predicting the frequencies of event occurrences in event streams at multiple time granularities. The proposed approximation method efficiently estimates the count of events with a high accuracy in an event stream at any time granularity by examining the distance distributions of event occurrences. The proposed method has been implemented and tested on different real data sets including daily price changes in two different stock exchange markets. The obtained results show its effectiveness. (C) 2005 Elsevier Inc. All rights reserved

A survey of temporal knowledge discovery paradigms and methods

With the increase in the size of data sets, data mining has recently become an important research topic and is receiving substantial interest from both academia and industry. At the same time, interest in temporal databases has been increasing and a growing number of both prototype and implemented systems are using an enhanced temporal understanding to explain aspects of behavior associated with the implicit time-varying nature of the universe. This paper investigates the confluence of these two areas, surveys the work to date, and explores the issues involved and the outstanding problems in temporal data mining

Mining Sequential Relations from Multidimensional Data Sequence for Prediction

By analyzing historical data sequences and identifying relations between the occurring of data items and certain types of business events we have opportunities to gain insights into future status and thereby take action proactively. This paper proposes a new approach to cope with the problem of prediction on data sequence characterized by multiple dimensions. The proposed relation mining approach improves the existing sequential pattern mining algorithm by considering multidimensional data sequences and incorporating time constraints. We demonstrate that multidimensional relations extracted by our approach are an enhancement of single dimensional relations by showing significantly stronger prediction capability, despite of the substantial work done in the latter area. In addition, matching algorithm based on the obtained relations is proposed to make prediction. The effectiveness of the proposed methods is validated by experiments conducted on a mobile user context dataset

Mining Temporal Sequential Patterns Based on Multi-granularities

Sequential pattern mining is an important data mining problem that can extract frequent subsequences from sequences. However, the times between successive items in a sequence is typically used as user-specified constraints to pre-process the input data or to prune the pattern search space. In either cases, the times cannot be used to identify item intervals of sequential patterns. In this paper, we introduce a form of multi-granularity sequence patterns, which is a sequential pattern where each transition time is annotated with multi-granularity boundary interval and average time derived from the source data rather than the user-predetermined time interval or only a typical time. Then we present a novel algorithm, MG-PrefixSpan, of multiple granularity sequential patterns based on PrefixSpan[, which discovers all such patterns. Empirical evaluation shows that MG-PrefixSpan scales up linearly as the size of database, and has a good scalability with respect to the length of sequence and the size of transaction

Temporalized logics and automata for time granularity

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered structures, which are infinitely refinable structures consisting of a coarsest domain and an infinite number of finer and finer domains, and of upward unbounded layered structures, which consist of a finest domain and an infinite number of coarser and coarser domains, with expressively complete and elementarily decidable temporal logic counterparts. We obtain such a result in two steps. First, we define a new class of combined automata, called temporalized automata, which can be proved to be the automata-theoretic counterpart of temporalized logics, and show that relevant properties, such as closure under Boolean operations, decidability, and expressive equivalence with respect to temporal logics, transfer from component automata to temporalized ones. Then, we exploit the correspondence between temporalized logics and automata to reduce the task of finding the temporal logic counterparts of the given theories of time granularity to the easier one of finding temporalized automata counterparts of them.Comment: Journal: Theory and Practice of Logic Programming Journal Acronym: TPLP Category: Paper for Special Issue (Verification and Computational Logic) Submitted: 18 March 2002, revised: 14 Januari 2003, accepted: 5 September 200