Comparative geochemical study on Furongian-earliest Ordovician

In this part of our experiments we evaluated the efficiency and effective-ness of the proposed indexing scheme. We performed tests over datasets of different sizes and different number of clusters. To generate large realistic datasets, we used real sequences (from the SEALS and ASL datasets) as

“seeds” to create larger datasets that follow the same patterns. To perform tests, we used queries that do not have exact matches in the database, but on the other hand are similar to some of the existing sequences. For each experiment we run 100 different queries and we report the averaged results.

We have tested the index performance for different number of clusters in a dataset consisting of a total of 2000 sequences. We executed a set of K-Nearest Neighbor (K-NN) queries for K 1, 5, 10, 15 and 20 and we plot the fraction of the dataset that has to be examined in order to guarantee

Fig. 20. Performance for increasing number of Nearest Neighbors.

Fig. 21. Index performance for variable number of data clusters.

that we have found the best match for the K-NN query. Note that in this fraction we included the medoids that we check during the search since they are also part of the dataset.

In Figure 20 we show some results for K-Nearest Neighbor queries. We used datasets with 5, 8 and 10 clusters. As we can see the results indicate that the algorithm has good performance even for queries with large K.

We also performed similar experiments where we varied the number of

clusters in the datasets (Figure 21). As the number of clusters increased the performance of the algorithm improved considerably. This behavior is expected and it is similar to the behavior of recent proposed index structures for high dimensional data [6,9,22]. On the other hand if the dataset has no clusters, the performance of the algorithm degrades, since the majority of the sequences have almost the same distance to the query. This behavior follows again the same pattern of high dimensional indexing methods [6,43].

7. Conclusions

We have presented efficient techniques to accurately compute the simi-larity between time-series with significant amount of noise. Our distance measure is based on the LCSS model and performs very well for noisy sig-nals. Since the exact computation is inefficient, we presented approximate algorithms with provable performance bounds. Moreover, we presented an efficient index structure, which is based on hierarchical clustering, for sim-ilarity (nearest neighbor) queries. The distance that we use is not a metric and therefore the triangle inequality does not hold. However, we prove that a similar inequality holds (although a weaker one) that allows to prune parts of the datasets without any false dismissals.

Our experiments indicate that the approximation algorithm can be used to get an accurate and fast estimation of the distance between two time-series even under noisy conditions. Also, results from the index evaluation show that we can achieve good speed-ups for searching similar sequences comparing with the brute force linear scan.

We plan to investigate biased sampling to improve the running time of the approximation algorithms, especially when full rigid transformations (e.g. shifting, scaling and rotation) are necessary. Another approach to index time-series for similarity retrieval is to use embeddings and map the set of sequences to points in a low dimensional Euclidean space [15]. The challenge of course is to find an embedding that approximately preserves the original pairwise distances and gives good approximate results to similarity queries.

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CHAPTER 5

CHANGE DETECTION IN CLASSIFICATION MODELS