Efficient k-nn Search for Static Queries over High Speed Time-Series Streams

Transcription

1 2014 Efficient k-nn Search for Static Queries over High Speed Time-Series Streams Bui Cong Giao, Duong Tuan Anh Presenter: Bui Cong Giao

2 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/2014 2

3 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/2014 3

4 Streaming time series A time-series stream brings about a sequence of real values, where new values are continuously appended as time progresses. At present, a significant number of real-world applications deal with time-series streams. Difficulties to handle streaming time series: o Time-series streams might transfer huge amount of data at steady high-speed rates. o Process techniques of static time series data are difficult to adapt in streaming context. 25/11/2014 4

5 Problems Improve the performance of the multi-step k-nn search for static queries in streaming time-series Deal with an important scenario in streaming applications where incoming data are from concurrent time-series streams at high speed rates 25/11/2014 5

6 Main contributions Using a tolerance reduction-based approach in k- NN search for static queries over high speed time-series streams; Adjusting range search in an R * -tree for many queries at a time. 25/11/2014 6

7 Related work 1. Lian et al., "Similarity match over high speed timeseries streams," M. Kontaki et al., "Adaptive similarity search in streaming time series with sliding windows, Bulut and Singh, "A unified framework for monitoring data streams in real time," They did not pay due attention to data normalization before conducting k-nn search less valuable 25/11/2014 7

8 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/2014 8

9 Dimensionality reduction transforms DFT, Haar DWT, and PAA They all satisfy the lower bounding condition and have multi-resolution property. Storing coefficients at resolutions Each predefined query is segmented into nonoverlapped segments These segments are normalized and transformed into coefficients by the above transforms. 25/11/2014 9

10 Data Structures A round-robin buffer is used to contain data points from a time-series stream. A priority queue organized as a max-heap to keep k candidates of a query. Multi-resolution index structure An array of R * -trees is used to store coefficients extracted from query segments. The index of the array corresponds to the resolution level that filters out the data. 25/11/

11 Improved range search in R * -tree if dt +h min < tl, then the time-series sequence is likely to be a candidate item of the k-nn set of the query. Fig. 2. The improved range search for a query point to a time-series point in the 2-dimensional space 25/11/

12 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/

13 Proposed method Phase 1: Preprocessing k-nn sets of all queries are initialized with k false items whose distances are. Queries are segmented and normalized and then their coefficients are calculated and stored in the array of R * -trees. 25/11/

14 Proposed method (cont.) Phase 2: k-nn search When there is a new-coming data point of a timeseries stream, segments on the data stream are incrementally normalized and then their coefficients are calculated. These coefficients are matched with the coefficients of query segments already stored in the nodes of R * -tree within each tolerance of the queries from the lowest to upper levels. 25/11/

15 Fig. 3. Query filter through resolution levels 25/11/

16 Proposed method (cont.) Phase 3: Post processing For each query candidate, the real distance between it and the corresponding piece of streaming time series is calculated to find a true k-nn item. If a true k-nn item is found, the k-nn set is updated and the tolerance of the query might be reduced. 25/11/

17 Two options of multi-step k-nn search When the k-nn set of a query is full, the tolerance is the maximum distance in the set and since then, it is not changed (the traditional k- NN search). it might be changed whenever the k-nn set is updated (the proposed k-nn search). Performance of the two options will be evaluated next. 25/11/

18 Range search for many queries at a time Nodes of R * -trees need to include the information of query points that lies in their MBR. The k-nn search on a node of an R * -tree has two steps: o Step 1: get query candidates whose tolerance tl sastifies dt + hmin < tl (cf. Fig. 2) 25/11/

19 Range search for many queries at a time o Step 2: If node is leaf, the real distance between two points are calculated and then the value is compared with the corresponding tolerance to determine if it is a candidate of the k-nn set of the query. Otherwise, the algorithm is called recursively again. 25/11/

20 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/

21 Platform Intel Dual Core i3 M GHz, 4GB RAM PC Programming techniques Using multi-threaded programming in C#. Each threading process handles a time-series stream to implement the proposed method. Threading processes can compete with others to update the same global resources at a time The system must lock the shared resources before updates can be done. 25/11/

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23 Parameters for experiment Buffer length of each stream time series is 1,024. R * -tree with m = 4 and M = 10 There are 1,000 queries whose lengths varies from 8 to 256. There are 5 filter levels and the number of coefficents of each level is 25/11/

24 Evaluation Criteria Compare the proposed method (tolerance reduction) and the traditional k-nn search (no tolerance reduction) accrording to o CPU time for searching k-nn o The number of distance function calls in post processing Compare performance of multi-threading and traditional programming applied to the proposed methoad. 25/11/

25 Fig. 7. CPU search times of k-nn search for the two methods 25/11/

26 Fig. 8. The number of distance function calls in the post- processing step for the two methods 25/11/

27 Fig. 9. The average CPU times for processing a new-coming data point when the system handles time-series streams sequentially 25/11/

28 Fig. 10. The average CPU times for processing a new-coming data point when the system handles time-series streams simultaneously 25/11/

29 Remarks Tolerance reduction is better than no tolerance reduction Multi-threading as a whole offers dramatic improvements in speed (up to roughly 4 times) over traditional programming. 25/11/

30 Contents 1. Introduction 2. Supporting Techniques 3. Proposed Method 4. Experimental Evaluation 5. Conclusions & Future work 25/11/

31 Conclusions The work presents a muti-step k-nn query method for static queries in streaming time series. The method is characterized as follows. A tolerance reduction-based approach, which improves the search performance by tightening the tolerance of a query when its k-nn set is modified Range search in an R * -tree for many queries at a time 25/11/

32 Conclusion (cont.) The experimental results shows that The proposed method outperforms the traditional k-nn search. Applying multi-threading to the proposed method enables the system to have a fast response to high speed time-series streams for the k-nn search of static queries. 25/11/

33 Future Work Adjust the method that can handle k-nn search for streaming queries over high speed time-series streams 25/11/

34 References 1. Korn, F., Sidirapoulos, N., Faloutsos,, Siegel,, Protopapas, Z.: Fast nearest neighbor search in medical databases. In : Proceedings of the 22nd International Conference on Very Large Data Bases, Bombay, India, pp (1996) 2. Lee, S., Kim, B.-S., Choi, M.-J., Moon, Y.-S.: An approximate multi-step k-nn search in time-series databases. Advances in Computer Science and its Applications 279, (2014) 3. Beckmann, N., Kriegel, H.-P., Schneider, R., Seeger, B.: The R * - tree: An efficient and ro-bust access method for points and rectangles. In : ACM SIGMOD International Confer-ence on Management of Data, Atlantic City, New Jersey, USA, pp (1990) 4. Giao, B., Anh, D.: Efficient similarity search for static queries in streaming time series. In : Proceedings of the 2014 International Conference on Green and Human Information Tech-nology, HoChiMinh City, pp (2014)

35 Thanks for listening Questions & Answers