Causality in Scale Space as an Approach to Change Detection

Stein Olav Skrøvseth,Johan Gustav Bellika,Fred Godtliebsen,Paul Wrede

doi:10.1371/journal.pone.0052253

Stein Olav Skrøvseth, Johan Gustav Bellika + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0052253

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Abstract

Kernel density estimation and kernel regression are useful ways to visualize and assess the structure of data. Using these techniques we define a temporal scale space as the vector space spanned by bandwidth and a temporal variable. In this space significance regions that reflect a significant derivative in the kernel smooth similar to those of SiZer (Significant Zero-crossings of derivatives) are indicated. Significance regions are established by hypothesis tests for significant gradient at every point in scale space. Causality is imposed onto the space by restricting to kernels with left-bounded or finite support and shifting kernels forward. We show that these adjustments to the methodology enable early detection of changes in time series constituting live surveillance systems of either count data or unevenly sampled measurements. Warning delays are comparable to standard techniques though comparison shows that other techniques may be better suited for single-scale problems. Our method reliably detects change points even with little to no knowledge about the relevant scale of the problem. Hence the technique will be applicable for a large variety of sources without tailoring. Furthermore this technique enables us to obtain a retrospective reliable interval estimate of the time of a change point rather than a point estimate. We apply the technique to disease outbreak detection based on laboratory confirmed cases for pertussis and influenza as well as blood glucose concentration obtained from patients with diabetes type 1.

Highlights

When presented with a signal or time series, the identification of change points is often of high importance
In live surveillance systems such as disease surveillance, early identification of changes in the system is a core task, where the early warning component invariably is a tradeoff between early detection and the false positive rate through the tuning of model parameters
Point data are modeled by kernel density estimation, and measurements modeled by kernel regression

Summary

Introduction

When presented with a signal or time series, the identification of change points is often of high importance. For weak changes there is the chance that the method does not detect a real change, a non-detection chance that must be balanced with the other features of the method. In this manuscript we consider two distinct types of processes, point data and unevenly sampled measurements. The measurements are values yi~f (ti)z[i with ei *iid N (0,s2i ), and the interesting aspect is again changes in the underlying value of f (t). In both cases i~1,2, Á Á Á ,N and ti is increasing with i, strictly increasing in the measurement case

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