In this thesis, we have successfully implemented a series of our proposed approaches that offers detection of anomalies in networked distributed sensing systems. However, we believe there are further potential to our study. Here we summarise the perspective extensions of our work which could offer insights to future research.
Indexable MFDR and MFDR-N
As we have presented in Chapter 5, MFDR and MFDR-N provides improved approximations to original time series compared to other state-of-the-art approaches. Nevertheless, it is worth-while noting that our current solution has limitation in providing lower-bound guarantee. The distance between MFDR (and MFDR-N) representations in two given time series cannot guar-antee lower bounding the distance between them (i.e. the original time series). This guarguar-antee is a desirable property for a DR representation as it allows DR representations to be directly
8.2. Future Work 127
exploited by classic indexing schemes such as R-tree [Gut84] without giving false negative re-sults. Therefore, we aim to provide MFDR and MFDR-N with this guarantee while remain their small representation error. There are three directions to achieve this:
1. Establish a new scheme to compute the distance between MFDR (and MFDR-N) repre-sentations with lower-bound guarantee.
2. Provide elastic distance (a range of distance) measures between MFDR (and MFDR-N) representations. With elastic distance, lower bound distances can be provided during indexing and search to prevent false negative outcomes, whereas smallest-error distances can be used in the post-data analytics to minimise error.
3. Analyse the property of MFDR and MFDR-N and establish models to describe the lower-bound probability.
Algorithm Improvement in MFDR and MFDR-N
Although MFDR and MFDR-N are lightweight to compute, there are still further possibilities in reducing their computational complexity. Firstly, MFDR and MFDR-N need to compute the optimal combination of number of coefficients for the two components. Currently, this optimisation problem is resolved with a brute-force approach, which may be further reduced with smarter algorithms. Secondly, MFDR-N has to be better enhanced with more accurate de-noise algorithm. Our current approach is dependent on Gaussian approximated statistic test despite the fact that the energy density of white noise is actually Chi-square distributed.
We would thereby like to replace our current approach with Chi-square-based test to provide more accurate results.
Improving FGAD
Current version of FGAD is effective against general anomalies; however, we have also noticed that some malicious attacks can avoid being detected by further retarding the amount of false
128 Chapter 8. Conclusion
deviations. Since the size of pairwise window (where sensor measurements are summarised with MFDR or MFDR-N) is static in FGAD, it may be too small to reveal such slow deviations. A possible solution to this is to exploit a hierarchical design where FGAD are applied at multiple time scales. Another limitation of FGAD is that it does not detect seasonal pattern changes. To overcome this limitation, we would like to exploit the seasonal-similarity discussed in Chapter 2.2.2 and integrate the motifs techniques [KLF05, BK14] into our current framework.
Applying Our Approaches on Real-World Applications
Last but not least, we would like to see how our anomaly-detection approaches can collaborate with other research in real-world applications, such as leakage detection in underground water systems [KYM14], viral surveillance and disease tracking [SKS12, MWCH14, CM09], and IoT security[XWP14]. We are also keen to see more applications of MFDR and MFDR-N since they can be exploited in many other data processing and mining procedures such as our current research on energy-aware in-network processing mentioned in Chapter 1.5, and other graph-based similarity search techniques [YM15].
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