# Time Series

**DOI:**https://doi.org/10.1007/978-0-387-30164-8_835

## Synonyms

## Definition

A *Time Series* is a sequence *T* = (*t*_{1}, *t*_{2}*,…,t*_{n}) which is an ordered set of *n* real-valued numbers. The ordering is typically temporal; however, other kinds of data such as color distributions (Hafner, Sawhney, Equitz, Flickner, & Niblack, 1995), shapes (Ueno, Xi, Keogh, & Lee, 2006), and spectrographs also have a well-defined ordering and can be fruitfully considered “time series” for the purposes of machine learning algorithms.

## Motivation and Background

The special structure of time series produces unique challenges for machine learning researchers.

It is often the case that each individual time series object has a very high dimensionality. Whereas classic algorithms often assume a relatively low dimensionality (for example, a few dozen measurements such as “height, weight, blood sugar,” etc.), time series learning algorithms must be able to deal with dimensionalities in hundreds or thousands. The problems created by...

## References

- Ding, H., Trajcevski, G., Scheuermann, P., Wang, X., & Keogh, E. A. (2008). Querying and mining of time series data: Experimental comparison of representations and distance measures.
*In Proceeding of the VLDB*. VLDB Endowment.Google Scholar - Hafner, J., Sawhney, H., Equitz, W., Flickner, M., & Niblack, W. (1995). Efficient color histogram indexing for quadratic form distance functions.
*IEEE Transactions on Pattern Analysis and Machine Intelligence,17*(7), 729–736.CrossRefGoogle Scholar - Ueno, K., Xi, X., Keogh, E., & Lee, D. (2006). Anytime classification using the nearest neighbor algorithm with applications to stream mining. In Proceedings of IEEE international conference on data mining (ICDM).Google Scholar