Trajectory segmentation is the process of subdividing a trajectory into parts either by grouping points similar with respect to some measure of interest, or by minimizing a global objective function. Here we present a novel online algorithm for segmentation and summary, based on point density along the trajectory, and based on the nature of the naturally occurring structure of intermittent bouts of locomotive and local activity. We show an application to visualization of trajectory datasets, and discuss the use of the summary as an index allowing efficient queries which are otherwise impossible or computationally expensive, over very large datasets.
Warped k-means @cite_3 adopts a completely different view to the segmentation problem. Since this is essentially a problem of clustering similar points, the method attempts (as in the well known K-means algorithm @cite_27 ) to find centroids and assignments, in order to minimize the mean square distance of each point to the centroid it is assigned to, under the additional constraint that if two points are in the same cluster, so are all the points between them along the trajectory.
@cite_27 @cite_3
2150593711 2116013313
It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for 2^ b quanta, b=1,2, , 7 , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes. Many devices generate large amounts of data that follow some sort of sequentiality, e.g., motion sensors, e-pens, eye trackers, etc. and often these data need to be compressed for classification, storage, and or retrieval tasks. Traditional clustering algorithms can be used for this purpose, but unfortunately they do not cope with the sequential information implicitly embedded in such data. Thus, we revisit the well-known K-means algorithm and provide a general method to properly cluster sequentially-distributed data. We present Warped K-Means (WKM), a multi-purpose partitional clustering procedure that minimizes the sum of squared error criterion, while imposing a hard sequentiality constraint in the classification step. We illustrate the properties of WKM in three applications, one being the segmentation and classification of human activity. WKM outperformed five state-of-the-art clustering techniques to simplify data trajectories, achieving a recognition accuracy of near 97 , which is an improvement of around 66 over their peers. Moreover, such an improvement came with a reduction in the computational cost of more than one order of magnitude.