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The distribution of optimal α is focused in range [1,2], allowing
us to easily limit the range of α
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Variable neighborhood Prediction of temporal collective profiles by Keun-Woo Lim, Telecom ParisTech
- 1. VARIABLE NEIGHBORHOOD PREDICTION OF TEMPORAL COLLECTIVE PROFILES Presentation for EuroIoTA ’16 Speaker: Keun-Woo Lim Telecom Paristech 24-11-2016
- 2. Brief Overview What do we do in this work? Analysis of temporal collective profiles (time-series) Use of mobile datasets (cellular, Wi-Fi) Real–time & Lightweight prediction (online prediction) What do we try to achieve? Better prediction accuracy Lower computational complexity Better application & use case
- 3. Contents Contents Introduction Methodology Prediction Outlier Detection Future Work
- 4. Introduction
- 5. Temporal collective profiles Representation of data that aggregate behavior of group of individuals – over time Can be categorized in various ways “Daily Profiles”
- 6. What are collected? Basic telephone calls and SMS? However, we want to focus on more specific matters Specific application data Usage of Internet service
- 7. Why do we analyze these data? For “online network analysis” Real-time prediction of the near-future Recognition of sudden changes/outliers Timely adaptation Use cases Resource allocation Traffic handling Social behavior
- 8. Requirements Low computational complexity Lightweight prediction methods Accuracy Still have to be accurate
- 9. Dataset Cellular mobile dataset 1-week data from 90 lacs in Paris More than 500 daily profiles Wi-Fi cloud dataset 122 days (March 1st to June 30th, 2014) 60 million URL connection logs (Top 20 mobile applications)
- 10. Methodology
- 11. What should we do with daily profiles? Daily profiles can be: Very similar to each other (same day, location, etc.) Very different too (outlier, events) We use methods to calculate similarity Cluster similar profiles Distinguish different profiles
- 12. Previous work (Offline analysis)1 Utilization of clustering methods (UPGMA) With similarity comparison techniques (DTW, quantiles) Not ideal in online data analysis Clustering may take long time (𝑂(𝑀2 𝑁3)with DTW) 1K. Lim, S. Secci, L. Tabourier, B. Tebbani, “Characterizing and predicting mobile application usage,” https://hal.archives-ouvertes.fr/hal-01345824/document
- 13. Profile similarity We use two examples of similarity measures (M values in a time-series) Euclidean distance (ED) = Θ(M) Dynamic time warping (DTW) = Θ(M2) For specific dataset containing N profiles, ED = Θ(N2M) DTW = Θ(N2M2) to compare all with each other
- 14. Weighted graph representation Using similarity measures, we acquire a graph structure of neighbors E.g., if ED is used, lower value = more similar
- 15. Filtering paths Filter neighbors with high distance Depending on the value of α, the number of neighbors change for all profiles
- 16. Visualization of graph structure Example graph structure for ED – cellular dataset
- 18. Principle of VNP For a new day 𝑥 𝑛(𝑡), we configure 𝑡0 = 0, 𝑡1 = 0~24, 𝑡2 = 24 (hour) Objective Observation period = 𝑥 𝑛 𝑡0, 𝑡1 Create a temporal profile to predict 𝑥 𝑛 𝑡1, 𝑡2 Find 𝑥 from the observation period The closest profile 𝑥, in 𝑥 𝑡0, 𝑡1 and 𝑥 𝑛 𝑡0, 𝑡1
- 19. Find the neighbors Using closest neighbor 𝑥, we find the group of neighbors 𝑁 𝑛 to be used for prediction For any other profile y of the training set, 𝑦 ∈ 𝑁𝑛 𝑖𝑖𝑓 𝑠 𝑥 𝑛 𝑡0, 𝑡1 , 𝑦 𝑡0, 𝑡1 ≤ 𝑎 ∙ 𝑠 𝑥 𝑛 𝑡0, 𝑡1 , 𝑥 𝑡0, 𝑡1
- 20. Creating the prediction profile Using 𝑁 𝑛, formulate the prediction 𝑥 𝑛 𝑡 = σ 𝑦∈𝑁 𝑛 𝑠(𝑥 𝑛,𝑦)∙𝑦(𝑡) σ 𝑦∈𝑁 𝑛 𝑠(𝑥 𝑛,𝑦) Simply put, it is the weighted average over the profiles of its neighborhood
- 21. Training Parameter 𝑎 𝑎 can be tuned to select the optimal number of neighbors Variable neighborhood search to find the 𝑎 that yields the highest accuracy over time E.g. 1.0 < 𝑎 < 10.0 Drawbacks Increase in complexity (recalculate for each 𝑎)
- 22. Calculating multiple 𝑡1 For a more fine-grained prediction, multiple 𝑡1 can be used in one day Repetition of the VNP (e.g. per-hour analysis)
- 23. Handling Complexity - VNP Computation of calculating neighborhood of target day per 𝑎 : ED = Θ(NM) DTW = Θ(NM2) Depending on N, this can be large in practice Also, in case of multiple 𝑡1 analysis, large M can also impact
- 24. Handling Complexity - Graph Can be heavy ED = Θ(N2M) DTW = Θ(N2M2) Luckily, graph representation is only updated once per day Although, needed for various M in case of multiple 𝑡1 analysis Also, space partitioning can be used to reduce time Via Kd-tree This can reduce complexity of ED to Θ(log(N)M)
- 26. Prediction accuracy analysis Prediction through relative error, defined as 𝜀 = σ 𝑡=𝑡1 𝑡2 𝑥 𝑛 𝑡 − 𝑥 𝑛 𝑡 2 σ 𝑡=𝑡1 𝑡2 𝑥 𝑛 𝑡 2 Comparison with closest neighbor ( 𝑎 =1), UPGMA 𝑡1 = 12 cellular data - ED cellular data - DTW
- 27. Effect of changing 𝑡1 Per-hour analysis The length of observation period may also effect the performance of prediction cellular data - ED cellular data - DTW
- 28. Time consumption The required time can be acceptable for both methods in a per-hour analysis. However, need caution for DTW when many profiles are used cellular data - ED cellular data - DTW
- 29. Distribution of α The distribution of optimal α is focused in range [1,2], allowing us to easily limit the range of α Distribution of neighbors is heterogeneous, but most are < 20
- 30. Conclusion & Future work
- 31. Conclusion & Future work We have proposed a methodology for online prediction of mobile time-series datasets Acceptable time for our current dataset Can be used for other time-series datasets in various IoT environment Further studies include Testing in a bigger scale dataset
- 32. Any Questions?
- 33. Appendix – Wi-Fi data prediction Wifi data - ED Wifi data - DTW