Chapter 3 Proposed Subsequence Similarity Matching Method
4.2 Experiments of EPLR Similarity Retrieval
Figure 4-7 Comparison of error rate between EPLR with 1/2 overlapping and PAA
Our experiments demonstrate that data overlapping is necessary. Besides, overlapping 1/2 data of previous segment is good enough to beat Euclidean distance.
We do not need more data overlap because it can cause more overhead. The comparisons between EPLR and PAA and PLR are also shown that EPLR is superior to PAA and PLR in most of the data sets.
4.2 Experiments of EPLR Similarity Retrieval
Since the superiority of EPLR is proven, the following experiments are all based on EPLR. In this section, we use pruning rate, miss rate and CPU cost to test our similarity retrieval. Pruning rate refers to efficiency that how many time series pruned by major trends match. In order to verify effectiveness, we compare the time series matched by major trends and the ground truth is acquired by DTW distance applied to
Euclidean distance and the proposed method without major trends match. The experimental results are presented based on 24 data sets out of 32 benchmark data sets used in [22]. Table 4-3 shows the parameter settings for 24 data sets. The symbol mix( ) means mix the items in ( ).
Table 4-3 Parameter settings for 24 data sets
Number of data sets 24
Time series length of query data 64, 128, 256, mix(64, 128 ,256) Time series length of database 512, mix(512,1024)
Size of query data for each length 400 Size of database for each length 1000
Each data set contains query data and database data and the length of query data is less than the length of database data. Before experimenting, there are still some parameters needed to define. Parameters a and b in Def 3 for major trends match are set to 0.4 and 0.2. For simplicity, each time series is divided into equal segments with 16 data points. We define a DTW distance threshold ε as a ground truth for similarity.
Each time series in query data and each time series in database have a minimum subsequence distance, called MSSD. ε is set to 1/5 of average MSSD. Figure 4-8, 4-9, 4-10 and 4-11 show the results of four combinations of different length of query data and database, respectively. In Figure 4-8, the length of query data is 64 and the length of database is 512. We change the length of query data to 128 and 256 in Figure 4-9 and Figure 4-10. In Figure 4-11, we mix the length of 64, 128 and 256 for query data and the length of 512 and 1024 for database. As for CPU cost, two data sets, Fetal ECG and Power Data, are chosen to compare. CPU cost of Fetal ECG is shown in Figure 4-12 and CPU cost of Power Data is described in Figure 4-13.
Table 4-4 Summarization of pruning rates and miss rates for different length of data
Data Set Pruning Miss Pruning Miss Pruning Miss Pruning Miss
64-512 64-512 128-512 128-512 256-512 256-512 mix-mix mix-mix
Figure 4-8 Pruning rate and Miss rate withlength of query = 64, and length of
time series in Database = 512
Figure 4-9 Pruning rate and Miss rate with length of query = 128, and length
of time series in Database = 512
Figure 4-10 Pruning rate and Miss rate with length of query = 256, and length
of time series in Database = 512
Figure 4-11 Pruning rate and Miss rate with length of query = mix of 64, 128,
256 and length of time series in Database = 512
Figure 4-12 CPU cost of Fetal ECG between Euclidean Distance, Proposed Method
and MDTW
Figure 4-13 CPU cost of Power Data between Euclidean Distance, Proposed Method
and MDTW
Observe that the miss rates of all data sets are low enough for different length of query. The miss rate rises a little only on the condition that the pruning rate is too high, such as tide and winding in Figure 4-10. Besides, the results indicate that pruning rates are quite satisfactory for most data sets. By Figure 4-12 and Figure 4-13, we can further prove that our proposed method is much faster than Euclidean distance. Even
Chapter 5
Conclusion and Future Work
5.1 Conclusion of Our Proposed Work
In this thesis, we proposed a subsequence similarity retrieval mechanism to deal with the shape-based similarity. A new representation EPLR is presented and for similarity retrieval, a similarity measure for EPLR is proposed. EPLR is a kind of segmentation technique, divides a time series of the length n into m segments with equal length k. Each segment overlaps parts of data with previous segment and is represented by the angle of its best-fit line segment. Since segments are equally split and presented by angles, there are many advantages, such as easy to implementation, retaining information of trends and dimensionality reduction. Experimental results show that the representation EPLR not only reduces the dimension but is also reliable to handle shape or trend of time series. In contrast with PLR and PAA, EPLR is superior to them.
We define 2-level similarity measure based on EPLR. On first level, the major trends of two subsequences have to be matched because if two time series are similar, their shape should be similar. We can prune a lot of non-qualified time series to speed the retrieval. We assign each segment a segment trend in accordance with its angle.
Then a merge mechanism is applied to segment trends to form major trends. After that, we can perform major trends match by specific rules. As regards to the second level, the distance of two subsequences which is the sum of all major trend distance must
conditions are met. Experiments demonstrate that the pruning rate of our similarity measure is satisfactory with acceptable miss rates and CPU cost is of the proposed method is low enough.
5.2 Future Work
Our work uses angles as the representation of shape or trend of time series and the similarity retrieval based on this representation is discussed. There is an extended research on applying EPLR to other data mining tasks such as anomaly detection and motif discovery. As for EPLR, how many data points in a segment is highly data dependent. We may analyze the data distribution to decide the number of data points in a segment. Furthermore, only the trends but not the real values of data are concerned in the work. It may be possible to combine the real values with angles to make the similarity retrieval more robust and powerful.
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