99 research outputs found

    LS2W: Implementing the Locally Stationary 2D Wavelet Process Approach in R

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    Locally stationary process representations have recently been proposed and applied to both time series and image analysis applications. This article describes an implementation of the locally stationary two-dimensional wavelet process approach in R. This package permits construction of estimates of spatially localized spectra and localized autocovariance which can be used to characterize structure within images.

    Detection of changes in the characteristics of oceanographic time-series using changepoint analysis.

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    Changepoint analysis is used to detect changes in variability within GOMOS hindcast time-series for significant wave heights of storm peak events across the Gulf of Mexico for the period 1900–2005. To detect a change in variance, the two-step procedure consists of (1) validating model assumptions per geographic location, followed by (2) application of a penalized likelihood changepoint algorithm. Results suggest that the most important changes in time-series variance occur in 1916 and 1933 at small clusters of boundary locations at which, in general, the variance reduces. No post-war changepoints are detected. The changepoint procedure can be readily applied to other environmental time-series

    Divisive clustering of high dimensional data streams

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    Clustering streaming data is gaining importance as automatic data acquisition technologies are deployed in diverse applications. We propose a fully incremental projected divisive clustering method for high-dimensional data streams that is motivated by high density clustering. The method is capable of identifying clusters in arbitrary subspaces, estimating the number of clusters, and detecting changes in the data distribution which necessitate a revision of the model. The empirical evaluation of the proposed method on numerous real and simulated datasets shows that it is scalable in dimension and number of clusters, is robust to noisy and irrelevant features, and is capable of handling a variety of types of non-stationarity

    Innovative and Additive Outlier Robust Kalman Filtering with a Robust Particle Filter

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    In this paper, we propose CE-BASS, a particle mixture Kalman filter which is robust to both innovative and additive outliers, and able to fully capture multi-modality in the distribution of the hidden state. Furthermore, the particle sampling approach re-samples past states, which enables CE-BASS to handle innovative outliers which are not immediately visible in the observations, such as trend changes. The filter is computationally efficient as we derive new, accurate approximations to the optimal proposal distributions for the particles. The proposed algorithm is shown to compare well with existing approaches and is applied to both machine temperature and server data

    Estimating time-evolving partial coherence between signals via multivariate locally stationary wavelet processes

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    We consider the problem of estimating time-localized cross-dependence in a collection of nonstationary signals. To this end, we develop the multivariate locally stationary wavelet framework, which provides a time-scale decomposition of the signals and, thus, naturally captures the time-evolving scale-specific cross-dependence between components of the signals. Under the proposed model, we rigorously define and estimate two forms of cross-dependence measures: wavelet coherence and wavelet partial coherence. These dependence measures differ in a subtle but important way. The former is a broad measure of dependence, which may include indirect associations, i.e., dependence between a pair of signals that is driven by another signal. Conversely, wavelet partial coherence measures direct linear association between a pair of signals, i.e., it removes the linear effect of other observed signals. Our time-scale wavelet partial coherence estimation scheme thus provides a mechanism for identifying hidden dynamic relationships within a network of nonstationary signals, as we demonstrate on electroencephalograms recorded in a visual–motor experiment

    Computationally efficient changepoint detection for a range of penalties

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    In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such methods are typically computationally intensive. Recent work in the penalised optimisation setting has focussed on developing a pruning-based approach which gives an improved computational cost that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. Consequently it is desirable to have an approach that enables us to compare segmentations for different choices of penalty. To this end we present a method to obtain optimal changepoint segmentations of data sequences for all penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitably parsimonious penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. This can be orders of magnitude faster than alternative approaches that find optimal segmentations for a range of the number of changepoints
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