Related papers: Central Trajectories
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Understanding the behavior of numerical metaheuristic optimization algorithms is critical for advancing their development and application. Traditional visualization techniques, such as convergence plots, trajectory mapping, and fitness…
Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked…
In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
Trajectory analysis is essential in many applications. In this paper, we address the problem of representing motion trajectories in a highly informative way, and consequently utilize it for analyzing trajectories. Our approach first…
Motivated by an application from geodesy, we introduce a novel clustering problem which is a $k$-center (or k-diameter) problem with a side constraint. For the side constraint, we are given an undirected connectivity graph $G$ on the input…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
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…
Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space…
The degree centrality of a node, defined as the number of nodes adjacent to it, is often used as a measure of importance of a node to the structure of a network. This metric can be extended to paths in a network, where the degree centrality…
Getting a robust time-series clustering with best choice of distance measure and appropriate representation is always a challenge. We propose a novel mechanism to identify the clusters combining learned compact representation of…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
Given a set of points, clustering consists of finding a partition of a point set into $k$ clusters such that the center to which a point is assigned is as close as possible. Most commonly, centers are points themselves, which leads to the…
We study the theoretical and practical runtime limits of k-means and k-median clustering on large datasets. Since effectively all clustering methods are slower than the time it takes to read the dataset, the fastest approach is to quickly…
Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as…
Crowdsourced, or human computation based clustering algorithms usually rely on relative distance comparisons, as these are easier to elicit from human workers than absolute distance information. A relative distance comparison is a statement…
Sampling-based model predictive controllers generate trajectories by sampling control inputs from a fixed, simple distribution such as the normal or uniform distributions. This sampling method yields trajectory samples that are tightly…
In this paper we study the problem of finding hotspots, i.e. regions in which a moving entity has spent a significant amount of time, for polygonal trajectories. The fastest optimal algorithm, due to Gudmundsson, van Kreveld, and Staals…