# Piecewise Chebyshev Factorization based Nearest Neighbour Classification for Time Series

### Qinglin Cai, Ling Chen, Jianling Sun

#### Abstract

In the research field of time series analysis and mining, the nearest neighbour classifier (1NN) based on dynamic time warping distance (DTW) is well known for its high accuracy. However, the high computational complexity of DTW can lead to the expensive time consumption of classification. An effective solution is to compute DTW in the piecewise approximation space (PA-DTW), which transforms the raw data into the feature space based on segmentation, and extracts the discriminatory features for similarity measure. However, most of existing piecewise approximation methods need to fix the segment length, and focus on the simple statistical features, which would influence the precision of PA-DTW. To address this problem, we propose a novel piecewise factorization model for time series, which uses an adaptive segmentation method and factorizes the subsequences with the Chebyshev polynomials. The Chebyshev coefficients are extracted as features for PA-DTW measure (ChebyDTW), which are able to capture the fluctuation information of time series. The comprehensive experimental results show that ChebyDTW can support the accurate and fast 1NN classification.

#### References

- Esling P., Agon C., 2012. Time-series data mining. ACM Computer Survey, 45(1).
- Fu T., 2011. A review on time series data mining. Engineering Applacations of Artificial Intelligence, 24(1): 164-181.
- Ding H., Trajcevski G., Scheuermann P., Wang X., Keogh E., 2008. Querying and mining of time series data: experimental comparison of representations and distance measures. In Proceedings of the VLDB Endowment, New Zealand, pp. 1542-1552.
- Hills J., Lines J., Baranauskas E., Mapp J., Bagnall A., 2014. Classification of time series by shapelet transformation. Data Mining and Knowledge Discovery, 28(4): 851-881.
- Serra J., Arcos J L., 2014. An empirical evaluation of similarity measures for time series classification. Knowledge-Based System, 67: 305-314.
- Keogh E., Chakrabarti K., Pazzani M., Mehrotra S., 2001. Dimensionality reduction for fast similarity search in large time series databases. Knowledge Information System, 3(3): 263-286.
- Keogh E., Chu S., Hart D., Pazzani M., 2004. Segmenting time series: A survey and novel approach. Data Mining in Time Series Databases. London: World Scientific.
- Chakrabarti K., Keogh E., Mehrotra S., Pazzani M., 2002. Locally adaptive dimensionality reduction for indexing large time series databases. ACM Transactions on Database System, 27(2): 188-228.
- Gullo F., Ponti G., Tagarelli A., Greco S., 2009. A time series representation model for accurate and fast similarity detection. Pattern Recognition, 42(11): 2998-3014.
- Li H., Guo C., 2011. Piecewise cloud approximation for time series mining. Knowledge-Based System, 24(4): 492-500.
- Ullman S., Poggio T., 1982. Vision: A computational investagation into the human representation and processing of visual information, MIT Press.
- Gao J., Sultan H., Hu J., Tung W., 2010. Denoising nonlinear time series by adaptive filtering and wavelet shrinkage: a comparison. IEEE Signal Processing Letters, 17(3): 237-240.
- Keogh E., Zhu Q., Hu B., Hao. Y., Xi X., Wei L., Ratanamahatana C. A., 2011. UCR time series classification/clustering homepage: www.cs.ucr.edu/eamonn/time_series_data/.
- Cai Y., Ng R., 2004. Indexing spatio-temporal trajectories with Chebyshev polynomials. In Proceedings of the 2004 ACM SIGMOD international conference on Management of data, France, pp. 599-610.
- Björkman M., Holmström K., 1999. Global optimization using the DIRECT algorithm in matlab. Advanced Model. Optimization, 1(2): 17-37.
- Keogh E., Pazzani M. J., 1999. Relevance feedback retrieval of time series data. In Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval, USA, pp. 183-190.
- Lin J., Vlachos M., Keogh E., 2005. A MPAA-based iterative clustering algorithm augmented by nearest neighbors search for time-series data streams. Advances in Knowledge Discovery and Data Mining. Springer Berlin Heidelberg.
- Rakthanmanon T., Campana B., Mueen A., 2012. Searching and mining trillions of time series subsequences under dynamic time warping. In Proceedings of the 18th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, China, pp. 262-270.
- Keogh E. J., Pazzani M. J., 2000. Scaling up dynamic time warping for data mining applications. In Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, USA, pp. 285-289.
- Keogh E. J., Pazzani M. J., 1999. Scaling up dynamic time warping to massive datasets. Principles of Data Mining and Knowledge Discovery. Springer Berlin Heidelberg.

#### Paper Citation

#### in Harvard Style

Cai Q., Chen L. and Sun J. (2015). **Piecewise Chebyshev Factorization based Nearest Neighbour Classification for Time Series** . In *Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR, (IC3K 2015)* ISBN 978-989-758-158-8, pages 84-91. DOI: 10.5220/0005611900840091

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR, (IC3K 2015)

TI - Piecewise Chebyshev Factorization based Nearest Neighbour Classification for Time Series

SN - 978-989-758-158-8

AU - Cai Q.

AU - Chen L.

AU - Sun J.

PY - 2015

SP - 84

EP - 91

DO - 10.5220/0005611900840091

#### in Bibtex Style

@conference{kdir15,

author={Qinglin Cai and Ling Chen and Jianling Sun},

title={Piecewise Chebyshev Factorization based Nearest Neighbour Classification for Time Series},

booktitle={Proceedings of the 7th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management - Volume 1: KDIR, (IC3K 2015)},

year={2015},

pages={84-91},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005611900840091},

isbn={978-989-758-158-8},

}