Related papers: One-Pass Trajectory Simplification Using the Synch…
Nowadays, various sensors are collecting, storing and transmitting tremendous trajectory data, and it is known that raw trajectory data seriously wastes the storage, network band and computing resource. Line simplification (LS) algorithms…
Location-aware devices continuously generate massive volumes of trajectory data, creating demand for efficient compression. Line simplification is a common solution but typically assumes 2D trajectories and ignores time synchronization and…
Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
Nowadays, there are ubiquitousness of GPS sensors in various devices collecting, transmitting and storing tremendous trajectory data. However, such an unprecedented scale of GPS data has posed an urgent demand for not only an effective…
Long-term location tracking, where trajectory compression is commonly used, has gained high interest for many applications in transport, ecology, and wearable computing. However, state-of-the-art compression methods involve high space-time…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…
Trajectories represent the mobility of moving objects and thus is of great value in data mining applications. However, trajectory data is enormous in volume, so it is expensive to store and process the raw data directly. Trajectories are…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
Tree-Sliced methods have recently emerged as an alternative to the traditional Sliced Wasserstein (SW) distance, replacing one-dimensional lines with tree-based metric spaces and incorporating a splitting mechanism for projecting measures.…
Compressive sensing (CS) has attracted significant attention in parameter estimation tasks, where parametric dictionaries (PDs) collect signal observations for a sampling of the parameter space and yield sparse representations for signals…
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…
Increasing and massive volumes of trajectory data are being accumulated that may serve a variety of applications, such as mining popular routes or identifying ridesharing candidates. As storing and querying massive trajectory data is…
Sequential Convex Programming (SCP) has recently gained popularity as a tool for trajectory optimization due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are…
Modern GPUs are equipped with tensor cores (TCs) that are commonly used for matrix multiplication in artificial intelligence workloads. However, because they have high computational throughput, they can lead to significant performance gains…
To overcome computational challenges of Optimal Transport (OT), several variants of Sliced Wasserstein (SW) has been developed in the literature. These approaches exploit the closed-form expression of the univariate OT by projecting…
In this paper, we investigate the properties of the Sliced Wasserstein Distance (SW) when employed as an objective functional. The SW metric has gained significant interest in the optimal transport and machine learning literature, due to…
The sliced Wasserstein distance (SW) reduces optimal transport on $\mathbb{R}^d$ to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work…
Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…
Persistence diagrams (PD)s play a central role in topological data analysis. This analysis requires computing distances among such diagrams such as the $1$-Wasserstein distance. Accurate computation of these PD distances for large data sets…