Abstract
As data is becoming more and more prolific and complex, the ability to process it and extract valuable information has become a critical requirement. However, performing such signal processing tasks requires to solve multiple challenges. Indeed, information must frequently be extracted (a) from many distinct data streams, (b) using limited resources, and (c) in real time to be of value. The aim of this chapter is to describe and optimize the specifications of signal processing systems, aimed at extracting in real time valuable information out of large-scale decentralized datasets. A first section will explain the motivations and stakes which have made stream mining a new and emerging field of research and describe key characteristics and challenges of stream mining applications. We then formalize an analytical framework which will be used to describe and optimize distributed stream mining knowledge extraction from large scale streams. In stream mining applications, classifiers are organized into a connected topology mapped onto a distributed infrastructure. We will study linear chains of classifiers and determine how the ordering of the classifiers in the chain impacts accuracy of classification and delay and determine how to choose the most suitable order of classifiers. Finally, we present a decentralized decision framework upon which distributed algorithms for joint topology construction and local classifier configuration can be constructed. Stream mining is an active field of research, at the crossing of various disciplines, including multimedia signal processing, distributed systems, machine learning etc. As such, we will indicate several areas for future research and development.
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- 1.
As we will discuss later, there are two types of configuration choices we must make: the topological ordering of classifiers and the local operating points at each classifier
- 2.
For example, since the operating point p F = 0 corresponds to a saddle point of the utility function, it would achieve steepest utility slope. Furthermore, the slope of the DET curve is maximal at p F = 0 (due to concavity of the DET curve), such that high detection probabilities can be obtained under low false alarm probabilities near the origin.
- 3.
Furthermore, when classifiers are independent, the transition matrices \(T_{i}^{}\) are diagonal and therefore commute. As a consequence the end throughput t N (x) and goodput g N (x) are independent of the order. However, intermediate throughputs do depend on the ordering—leading to varying expected delays for the overall processing.
- 4.
Observe that for a perfect classifier (\(p_{\sigma (h)}^{D} = 1\) and \(p_{\sigma (h)}^{F} = 0\)), the a-priori conditional probability \(\phi _{h}^{\sigma }\) and the ex-post conditional probabilities \(\psi _{h}^{\sigma }\) are equal.
- 5.
t i − 1 and g i − 1 are not required since: \(\mathop{\mathrm{argmax}}\limits_{\ }\ \ U_{i} =\mathop{\mathrm{ argmax}}\limits_{\ }\ \frac{U_{i}} {g_{i-1}} =\) \(\left (-\left [\begin{array}{cccc} \rho _{i}&0\end{array} \right ]+\right.\) \(\left.\left [\begin{array}{cccc} v_{i+1} & w_{i+1} \end{array} \right ]T_{i}^{}\right )\left [\begin{array}{cccc} \theta _{i} \\ 1 \end{array} \right ]\).
- 6.
This can take τ > 5 min for seven classifiers.
- 7.
The utility parameters \(\left [\begin{array}{cccc} v_{j}&w_{j} \end{array} \right ]\) fed back from classifier C j to classifier C i are independent of any classifiers’ operating points.
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Acknowledgements
This work is based upon work supported by the National Science Foundation under Grant No. 1016081. We would like to thank Dr. Deepak Turaga (IBM Research) for introducing us to the topic of stream mining and for many productive conversation associated with the material of this chapter as well as providing us with Figs. 1 and 3 of this chapter. We also would like to thank Dr. Fangwen Fu and Dr. Brian Foo, who have been PhD students in Prof. van der Schaar group and have made contributions to the area of stream mining from which this chapter benefited. Finally, we thank Mr. Siming Song for kindly helping us with formatting and polishing the final version of the chapter.
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Ducasse, R., van der Schaar, M. (2013). Finding It Now: Construction and Configuration of Networked Classifiers in Real-Time Stream Mining Systems. In: Bhattacharyya, S., Deprettere, E., Leupers, R., Takala, J. (eds) Handbook of Signal Processing Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6859-2_4
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