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The key to device-edge co-inference paradigm is to partition models into computation-friendly and computation-intensive parts across the device and the edge, respectively. However, for Graph Neural Networks (GNNs), we find that simply…

Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

Clusters form the basis of a number of research study designs including survey and experimental studies. Cluster-based designs can be less costly but also less efficient than individual-based designs due to correlation between individuals…

Although quadrotor navigation has achieved high performance in trajectory planning and control, real-time adaptability in unknown complex environments remains a core challenge. This difficulty mainly arises because most existing planning…

Data driven algorithm design is an important aspect of modern data science and algorithm design. Rather than using off the shelf algorithms that only have worst case performance guarantees, practitioners often optimize over large families…

This paper proposes a locally differentially private federated learning algorithm for strongly convex but possibly nonsmooth problems that protects the gradients of each worker against an honest but curious server. The proposed algorithm…

This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization…

Worldwide visual geo-localization aims to determine the geographic location of an image anywhere on Earth using only its visual content. Despite recent progress, learning expressive representations of geographic space remains challenging…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…

The past few years have witnessed a remarkable rise in interest in driver-less cars; and naturally, in parallel, the demand for an accurate and reliable object localization and mapping system is higher than ever. Such a system would have to…

This paper presents a sampling-based motion planning framework that leverages the geometry of obstacles in a workspace as well as prior experiences from motion planning problems. Previous studies have demonstrated the benefits of utilizing…

Synthetic data generation is a fundamental task for many data management and data science applications. Spatial data is of particular interest, and its sensitive nature often leads to privacy concerns. We introduce GeoPointGAN, a novel…

Understanding human behavior is a fundamental goal of social sciences, yet its analysis presents significant challenges. Conventional methodologies employed for the study of behavior, characterized by labor-intensive data collection…

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and…

During the rapid urbanization construction of China, acquisition of urban geographic information and timely data updating are important and fundamental tasks for the refined management of cities. With the development of domestic remote…

Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…

Geocoding systems are widely used in both scientific research for spatial analysis and everyday life through location-based services. The quality of geocoded data significantly impacts subsequent processes and applications, underscoring the…

We present an optimization-based framework for multicopter trajectory planning subject to geometrical configuration constraints and user-defined dynamic constraints. The basis of the framework is a novel trajectory representation built upon…