Efficient time series matching by wavelets
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Citations
Stock time series pattern matching: Template-based vs. rule-based approaches
Finding Structural Similarity in Time Series Data Using Bag-of-Patterns Representation
Mining asynchronous periodic patterns in time series data
An improvement of symbolic aggregate approximation distance measure for time series
Fuzzy clustering of time series in the frequency domain
References
An introduction to the bootstrap
R-trees: a dynamic index structure for spatial searching
An Introduction to the Bootstrap
Mining sequential patterns
Related Papers (5)
Frequently Asked Questions (14)
Q2. What are the contributions in "Efficient time series matching by wavelets" ?
While the use of DFT and K-L transform or SVD have been studied in the literature, to their knowledge, there is no in-depth study on the application of DWT. In this paper, the authors propose to use Haar Wavelet Transform for time series indexing. The major contributions are: ( 1 ) the authors show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, ( 2 ) they show that Haar transform can outperform DFT through experiments, ( 3 ) a new similarity model is suggested to accommodate vertical shift of time series, and ( 4 ) a two-phase method is proposed for efficient -nearest neighbor query in time series databases.
Q3. How do the authors obtain the -point Haar transform?
The authors obtain the -point Haar transform by applying Equation (2) with the normalization factor, for each subsequences with a sliding window of size to each sequence in the database.
Q4. How can the authors avoid missing any qualifying object?
To avoid missing any qualifying object, the Euclidean distance in the reduced C -dimensional space should be less than or equal to the Euclidean distance between the two original time sequences.
Q5. What are the results of the experiments?
Experiments show that their method outperforms the F-index (Discrete Fourier Transform) method in terms of pruning power, number of page accesses, scalability, and complexity.
Q6. How many coefficients can be found in the Haar transform?
After the first multiplication of and , half of the Haar transform coefficients can be found which are and in interleaving with some intermediate coefficients and .
Q7. What is the importance of the precision in a query?
As most of the page accesses of a query are devoted to removing false alarm, the precision is crucial to the overall performance of query evaluation.
Q8. What is the effect of sliding window on a trail?
Feature points in nearby offsets will form a trail due to the effect of stepwise sliding window, the minimum bounding rectangle (MBR) of a trail is then being indexed in an R-Tree instead of the feature points themselves.
Q9. What is the effect of the poorer precision of DFT?
The poorer precision of DFT creates more work in the post-processing step and this affects the overall performance, especially in terms of the amount of disk accesses for large databases with long sequences.
Q10. What is the way to build an index?
An index structure such as an R-Tree is built, using the first Haar coefficients where is an optimal value found by experiments based on the number of page accesses.
Q11. How can the authors improve the performance of the R-Tree?
The extra step introduced in Phase 2 to update can enhance the performance by pruning more non-qualifying MBRs during the traversal of R-Tree.
Q12. What is the way to accommodate v-shift similarity?
Apart from Euclidean distance, their model can easily accommodate v-shift similarity of two time sequences (Definition 2) at a little more cost.
Q13. What are the main reasons why time series data are of growing importance in many new database applications?
Time series data are of growing importance in many new database applications, such as data warehousing and data mining [3, 8, 2, 12].
Q14. What are the other wavelets that the authors have found?
From experiments,we find that the other wavelets seem to also preserve Euclidean distances, however, so far the authors have a proof of this property only for the Haar wavelets.