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Formation flight has a vast potential for aerial robot swarms in various applications. However, existing methods lack the capability to achieve fully autonomous large-scale formation flight in dense environments. To bridge the gap, we…
The minimum distance of a linear code is a key concept in information theory. Therefore, the time required by its computation is very important to many problems in this area. In this paper, we introduce a family of implementations of the…
We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Exploration systems are critical for enhancing the autonomy of robots. Due to the unpredictability of the future planning space, existing methods either adopt an inefficient greedy strategy or require a lot of resources to obtain a global…
For a set of $n$ points in $\Re^d$, and parameters $k$ and $\eps$, we present a data structure that answers $(1+\eps,k)$-\ANN queries in logarithmic time. Surprisingly, the space used by the data-structure is $\Otilde (n /k)$; that is, the…
In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set X and a distance d on X, find a Robinsonian distance dR on X minimizing the l\infty-error ||d - dR||\infty…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
We present a simple and easy-to-implement algorithm to detect plan infeasibility in kinematic motion planning. Our method involves approximating the robot's configuration space to a discrete space, where each degree of freedom has a finite…
Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…
In the practice of information extraction, the input data are usually arranged into pattern matrices, and analyzed by the methods of linear algebra and statistics, such as principal component analysis. In some applications, the tacit…
We propose a structured prediction approach for robot imitation learning from demonstrations. Among various tools for robot imitation learning, supervised learning has been observed to have a prominent role. Structured prediction is a form…
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
The accuracy assessment of remote-sensing derived built-up land data represents a specific case of binary map comparison, where class imbalance varies considerably across rural-urban trajectories. Thus, local accuracy characterization of…
Many big-data clusters store data in large partitions that support access at a coarse, partition-level granularity. As a result, approximate query processing via row-level sampling is inefficient, often requiring reads of many partitions.…