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The Gromov-Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW…
Learning generic joint representations for video and text by a supervised method requires a prohibitively substantial amount of manually annotated video datasets. As a practical alternative, a large-scale but uncurated and narrated video…
The geometric transportation problem takes as input a set of points $P$ in $d$-dimensional Euclidean space and a supply function $\mu : P \to \mathbb{R}$. The goal is to find a transportation map, a non-negative assignment $\tau : P \times…
Among many existing distance measures for time series data, Dynamic Time Warping (DTW) distance has been recognized as one of the most accurate and suitable distance measures due to its flexibility in sequence alignment. However, DTW…
Edit distance is a measurement of similarity between two sequences such as strings, point sequences, or polygonal curves. Many matching problems from a variety of areas, such as signal analysis, bioinformatics, etc., need to be solved in a…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
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…
One approach to studying the Fr\'echet distance is to consider curves that satisfy realistic assumptions. By now, the most popular realistic assumption for curves is $c$-packedness. Existing algorithms for computing the Fr\'echet distance…
The Fr\'{e}chet distance is a well-studied similarity measure between curves that is widely used throughout computer science. Motivated by applications where curves stem from paths and walks on an underlying graph (such as a road network),…
We propose the Deep Distance Measurement Method (DDMM) to improve retrieval accuracy in unsupervised multivariate time series similarity retrieval. DDMM enables learning of minute differences within states in the entire time series and…
The discrete Fr{\'e}chet distance is a measure of similarity between point sequences which permits to abstract differences of resolution between the two curves, approximating the original Fr{\'e}chet distance between curves. Such distance…
Color descriptors are one of the important features used in content-based image retrieval. The Dominant Color Descriptor (DCD) represents a few perceptually dominant colors in an image through color quantization. For image retrieval based…
It has been alleged in several papers that the so called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since…
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of…
Time series with large discontinuities are common in many scenarios. However, existing distance-based algorithms (e.g., DTW and its derivative algorithms) may perform poorly in measuring distances between these time series pairs. In this…
Modern networks are highly dynamic, and temporal graphs capture these changes through discrete edge appearances on a fixed vertex set, known in advance up to the graph's lifetime. The Vertex Cover problem extends to the temporal setting as…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…
Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…
It is unlikely that the discrete Fr\'echet distance between two curves of length $n$ can be computed in strictly subquadratic time. We thus consider the setting where one of the curves, $P$, is known in advance. In particular, we wish to…