Data-stream processing has continuously risen in importance as the amount of available data has been steadily increas- ing over the last decade. Besides traditional domains such as data-center monitoring and click analytics, there is an increasing number of network-enabled production machines that generate continuous streams of data. Due to their continuous nature, queries on data-streams can be more complex, and distinctly harder to understand then database queries. As users have to consider operational details, maintenance and debugging become challenging. Current approaches model data-streams as sequences, be- cause this is the way they are physically received. These models result in an implementation-focused perspective. We explore an alternate way of modeling data-streams by focusing on time-slicing semantics. This focus results in a model based on functions, which is better suited for reasoning about query semantics. By adapting the definitions of relevant concepts in stream processing to our model, we illustrate the practical useful- ness of our approach. Thereby, we link data-streams and query primitives to concepts in functional programming and mathematics. Most noteworthy, we prove that data-streams are monads, and show how to derive monad definitions for current data-stream models. We provide an abstract, yet practical perspective on data- stream related subjects based on a sound, consistent query model. Our work can serve as solid foundation for future data-stream query-languages.
The fundamental difference to data-streams is, that streams in type theory are not required to contain time stamps. However, we can gain the same perspective as @cite_26 (cf. Sec. ) by adding time stamps to the elimination function, :
@cite_26
2130416896 2106010611 2052464302 2119163494
Most existing data stream classification techniques ignore one important aspect of stream data: arrival of a novel class. We address this issue and propose a data stream classification technique that integrates a novel class detection mechanism into traditional classifiers, enabling automatic detection of novel classes before the true labels of the novel class instances arrive. Novel class detection problem becomes more challenging in the presence of concept-drift, when the underlying data distributions evolve in streams. In order to determine whether an instance belongs to a novel class, the classification model sometimes needs to wait for more test instances to discover similarities among those instances. A maximum allowable wait time Tc is imposed as a time constraint to classify a test instance. Furthermore, most existing stream classification approaches assume that the true label of a data point can be accessed immediately after the data point is classified. In reality, a time delay Tl is involved in obtaining the true label of a data point since manual labeling is time consuming. We show how to make fast and correct classification decisions under these constraints and apply them to real benchmark data. Comparison with state-of-the-art stream classification techniques prove the superiority of our approach. Similarity-based time-series retrieval has been a subject of long-term study due to its wide usage in many applications, such as financial data analysis, weather data forecasting, and multimedia data retrieval. Its original task was to find those time series similar to a pattern (query) time-series data, where both the pattern and data time series are static. Recently, with an increasing demand on stream data management, similarity-based stream time-series retrieval has raised new research issues due to its unique requirements during the stream processing, such as one-pass search and fast response. In this paper, we address the problem of matching both static and dynamic patterns over stream time-series data. We will develop a novel multiscale representation, called multiscale segment mean, for stream time-series data, which can be incrementally computed and thus perfectly adapted to the stream characteristics. Most importantly, we propose a novel multistep filtering mechanism, step by step, over the multiscale representation. Analysis indicates that the mechanism can greatly prune the search space and thus offer fast response. Furthermore, batch processing optimization and the dynamic case where patterns are also from stream time series are discussed. Extensive experiments show the multiscale representation together with the multistep filtering scheme can efficiently filter out false candidates and detect patterns, compared to the multiscale wavelet. Continuous queries in a Data Stream Management System (DSMS) rely on time as a basis for windows on streams and for defining a consistent semantics for multiple streams and updatable relations. The system clock in a centralized DSMS provides a convenient and well-behaved notion of time, but often it is more appropriate for a DSMS application to define its own notion of time---its own clock(s), sequence numbers, or other forms of ordering and times-tamping. Flexible application-defined time poses challenges to the DSMS, since streams may be out of order and uncoordinated with each other, they may incur latency reaching the DSMS, and they may pause or stop. We formalize these challenges and specify how to generate heartbeats so that queries can be evaluated correctly and continuously in an application-defined time domain. Our heartbeat generation algorithm is based on parameters capturing skew between streams, unordering within streams, and latency in streams reaching the DSMS. We also describe how to estimate these parameters at run-time, and we discuss how heartbeats can be used for processing continuous queries. We study the problem of maintaining a sketch of recent elements of a data stream. Motivated by applications involving network data, we consider streams that are asynchronous, in which the observed order of data is not the same as the time order in which the data was generated. The notion of recent elements of a stream is modeled by the sliding timestamp window, which is the set of elements with timestamps that are close to the current time. We design algorithms for maintaining sketches of all elements within the sliding timestamp window that can give provably accurate estimates of two basic aggregates, the sum and the median, of a stream of numbers. The space taken by the sketches, the time needed for querying the sketch, and the time for inserting new elements into the sketch are all polylogarithmic with respect to the maximum window size. Our sketches can be easily combined in a lossless and compact way, making them useful for distributed computations over data streams. Previous works on sketching recent elements of a data stream have all considered the more restrictive scenario of synchronous streams, where the observed order of data is the same as the time order in which the data was generated. Our notion of recency of elements is more general than that studied in previous work, and thus our sketches are more robust to network delays and asynchrony.