Change detection

In statistical analysis, change detection or change point detection tries to identify times when the probability distribution of a stochastic process or time series changes. In general the problem concerns both detecting whether or not a change has occurred, or whether several changes might have occurred, and identifying the times of any such changes.

Specific applications, like step detection and edge detection, may be concerned with changes in the mean, variance, correlation, or spectral density of the process. More generally change detection also includes the detection of anomalous behavior: anomaly detection.

Online change detection

Using the sequential analysis ("online") approach, any change test must make a trade-off between these common metrics:

• False alarm rate
• Misdetection rate
• Detection delay

In a Bayes change-detection problem, a prior distribution is available for the change time.

Online change detection is also done using streaming algorithms.

Minimax change detection

In minimax change detection, the objective is to minimize the expected detection delay for some worst-case change-time distribution, subject to a cost or constraint on false alarms.

A key technique for minimax change detection is the CUSUM procedure.

Offline change detection

Basseville (1993, Section 2.6) discusses offline change-in-mean detection with hypothesis testing based on the works of Page^[1] and Picard^[2] and maximum-likelihood estimation of the change time, related to two-phase regression. Other approaches employ clustering based on maximum likelihood estimation.

"Offline" approaches cannot be used on streaming data because they need to compare to statistics of the complete time series, and cannot react to changes in real time but often provide more accurate estimation of the change time and magnitude.

Applications of change detection

Change detection tests are often used in manufacturing (quality control), intrusion detection, spam filtering, website tracking, and medical diagnostics.

Linguistic change detection

Linguistic change detection refers to the ability to detect word-level changes across multiple presentations of the same sentence. Researchers have found that the amount of semantic overlap (i.e., relatedness) between the changed word and the new word influences the ease with which such a detection is made (Sturt, Sanford, Stewart, & Dawydiak, 2004). Additional research has found that focussing one's attention to the word that will be changed during the initial reading of the original sentence can improve detection. This was shown using italicized text to focus attention, whereby the word that will be changing is italicized in the original sentence (Sanford, Sanford, Molle, & Emmott, 2006), as well as using clefting constructions such as "It was the tree that needed water." (Kennette, Wurm, & Van Havermaet, 2010). These change-detection phenomena appear to be robust, even occurring cross-linguistically when bilinguals read the original sentence in their native language and the changed sentence in their second language (Kennette, Wurm & Van Havermaet, 2010). Recently, researchers have detected word-level changes in semantics across time by computationally analyzing temporal corpora (for example:the word "gay" has acquired a new meaning over time) using change point detection.^[3]

See also

• Structural break—Change in model structure
• Detection theory
• Hypothesis testing
• Recall rate
• Receiver operating characteristic

Notes and references

1. ↑ Page, E. S. (1957). On problems in which a change in a parameter occurs at an unknown point. Biometrika, 44(1/2), 248-252.
2. ↑ Picard, Dominique. "Testing and estimating change-points in time series." Advances in applied probability (1985): 841-867.
3. ↑ Kulkarni Vivek; Rfou Rami; Perozzi Bryan; Skiena Steven (2015). "Statistically Significant Detection of Linguistic Change". WWW '15 Proceedings of the 24th International Conference on World Wide Web. 

• Michèle Basseville; Igor V. Nikiforov (April 1993). Detection of Abrupt Changes: Theory and Application. Prentice-Hall, Englewood Cliffs, N.J. ISBN 0-13-126780-9. 
• Kennette, L. N., Wurm, L. H., & Van Havermaet, L. R. (2010). "Change detection: The effects of linguistic focus, hierarchical word level and proficiency", The Mental Lexicon, 5(1), 47–86. Abstract
• H. Vincent Poor; Olympia Hadjiliadis (2009). Quickest Detection. Cambridge University Press. ISBN 978-0-521-62104-5. 
• Sanford, A. J. S., Sanford, A. J., Molle, J., & Emmott, C. (2006). "Shallow processing and attention capture in written and spoken discourse", Discourse Processes, 42(2), 109-130.
• Sturt, P., Sanford, A. J., Stewart, A., & Dawydiak, E. (2004). "Linguistic focus and good-enough representations: An application of the change-detection paradigm", Psychonomic Bulletin & Review, 11(5), 882-888.