We propose an algorithm for simultaneously detecting and locating changepoints in a time series, and a framework for predicting the distribution of the next point in the series. The kernel of the algorithm is a system of equations that computes, for each index i, the probability that the last (most recent) change point occurred at i. We evaluate this algorithm by applying it to the change point detection problem and comparing it to the generalized likelihood ratio (GLR) algorithm. We find that our algorithm is as good as GLR, or better, over a wide range of scenarios, and that the advantage increases as the signal-to-noise ratio decreases.
Most recently, Vellekoop and Clark propose a nonlinear filtering approach to the changepoint detection problem (but not estimation or tracking) @cite_0 .
@cite_0
2078450032 2068094367 2183648259 2058148593
A benchmark change detection problem is considered which involves the detection of a change of unknown size at an unknown time. Both unknown quantities are modeled by stochastic variables, which allows the problem to be formulated within a Bayesian framework. It turns out that the resulting nonlinear filtering problem is much harder than the well-known detection problem for known sizes of the change, and in particular that it can no longer be solved in a recursive manner. An approximating recursive filter is therefore proposed, which is designed using differential-geometric methods in a suitably chosen space of unnormalized probability densities. The new nonlinear filter can be interpreted as an adaptive version of the celebrated Shiryayev--Wonham equation for the detection of a priori known changes, combined with a modified Kalman filter structure to generate estimates of the unknown size of the change. This intuitively appealing interpretation of the nonlinear filter and its excellent performance in simulation studies indicates that it may be of practical use in realistic change detection problems. In this paper we propose a robust visual tracking method by casting tracking as a sparse approximation problem in a particle filter framework. In this framework, occlusion, corruption and other challenging issues are addressed seamlessly through a set of trivial templates. Specifically, to find the tracking target at a new frame, each target candidate is sparsely represented in the space spanned by target templates and trivial templates. The sparsity is achieved by solving an l 1 -regularized least squares problem. Then the candidate with the smallest projection error is taken as the tracking target. After that, tracking is continued using a Bayesian state inference framework in which a particle filter is used for propagating sample distributions over time. Two additional components further improve the robustness of our approach: 1) the nonnegativity constraints that help filter out clutter that is similar to tracked targets in reversed intensity patterns, and 2) a dynamic template update scheme that keeps track of the most representative templates throughout the tracking procedure. We test the proposed approach on five challenging sequences involving heavy occlusions, drastic illumination changes, and large pose variations. The proposed approach shows excellent performance in comparison with three previously proposed trackers. In this paper we propose a robust visual tracking method by casting tracking as a sparse approximation problem in a particle filter framework. In this framework, occlusion, corruption and other challenging issues are addressed seamlessly through a set of trivial templates. Specifically, to find the tracking target at a new frame, each target candidate is sparsely represented in the space spanned by target templates and trivial templates. The sparsity is achieved by solving an � 1-regularized least squares problem. Then the candidate with the smallest projection error is taken as the tracking target. After that, tracking is continued using a Bayesian state inference framework in which a particle filter is used for propagating sample distributions over time. Two additional components further improve the robustness of our approach: 1) the nonnegativity constraints that help filter out clutter that is similar to tracked targets in reversed intensity patterns, and 2) a dynamic template update scheme that keeps track of the most representative templates throughout the tracking procedure. We test the proposed approach on five challenging sequences involving heavy occlusions, drastic illumination changes, and large pose variations. The proposed approach shows excellent performance in comparison with three previously proposed trackers. In the past few years there has been increased interest in using data-mining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, which is then mined for interesting episodes. In some cases the rule for determining when a sensor reading should generate an event is well known. However, if the phenomenon is ill-understood, stating such a rule is difficult. Detection of events in such an environment is the focus of this paper. Consider a dynamic phenomenon whose behavior changes enough over time to be considered a qualitatively significant change. The problem we investigate is of identifying the time points at which the behavior change occurs. In the statistics literature this has been called the change-point detection problem. The standard approach has been to (a) upriori determine the number of change-points that are to be discovered, and (b) decide the function that will be used for curve fitting in the interval between successive change-points. In this paper we generalize along both these dimensions. We propose an iterative algorithm that fits a model to a time segment, and uses a likelihood criterion to determine if the segment should be partitioned further, i.e. if it contains a new changepoint. In this paper we present algorithms for both the batch and incremental versions of the problem, and evaluate their behavior with synthetic and real data. Finally, we present initial results comparing the change-points detected by the batch algorithm with those detected by people using visual inspection.