TRAJEDI
The vast increase in our ability to obtain and store trajectory data necessitates trajectory analytics techniques to extract useful information from this data. Pair-wise distance functions are a foundation building block for common operations on trajectory datasets including constrained SELECT queries, k-nearest neighbors, and similarity and diversity algorithms. The accuracy and performance of these operations depend heavily on the speed and accuracy of the underlying trajectory distance function, which is in turn affected by trajectory calibration. Current methods either require calibrated data, or perform calibration of the entire relevant dataset first, which is expensive and time consuming for large datasets. We present TRAJEDI, a calibrationaware pair-wise distance calculation scheme that outperforms naive approaches while preserving accuracy. We also provide analyses of parameter tuning to trade-off between speed and accuracy. Our scheme is usable with any diversity, similarity or k-nearest neighbor algorithm. …

k-meansNet
In this paper, we study how to make clustering benefiting from differentiable programming whose basic idea is treating the neural network as a language instead of a machine learning method. To this end, we recast the vanilla $k$-means as a novel feedforward neural network in an elegant way. Our contribution is two-fold. On the one hand, the proposed \textit{k}-meansNet is a neural network implementation of the vanilla \textit{k}-means, which enjoys four advantages highly desired, i.e., robustness to initialization, fast inference speed, the capability of handling new coming data, and provable convergence. On the other hand, this work may provide novel insights into differentiable programming. More specifically, most existing differentiable programming works unroll an \textbf{optimizer} as a \textbf{recurrent neural network}, namely, the neural network is employed to solve an existing optimization problem. In contrast, we reformulate the \textbf{objective function} of \textit{k}-means as a \textbf{feedforward neural network}, namely, we employ the neural network to describe a problem. In such a way, we advance the boundary of differentiable programming by treating the neural network as from an alternative optimization approach to the problem formulation. Extensive experimental studies show that our method achieves promising performance comparing with 12 clustering methods on some challenging datasets. …

Fan Chart
In time series analysis, a fan chart is a chart that joins a simple line chart for observed past data, by showing ranges for possible values of future data together with a line showing a central estimate or most likely value for the future outcomes. As predictions become increasingly uncertain the further into the future one goes, these forecast ranges spread out, creating distinctive wedge or ‘fan’ shapes, hence the term. Alternative forms of the chart can also include uncertainty for past data, such as preliminary data that is subject to revision. The term ‘fan chart’ was coined by the Bank of England, which has been using these charts and this term since 1997 in its ‘Inflation Report’ to describe its best prevision of future inflation to the general public. Fan charts have been used extensively in finance and monetary policy, for instance to represent forecasts of inflation. …

2T-graph
A 2T-graph is a graph whose edge set can be decomposed into two edge-disjoint spanning trees. …