Related papers: Distance-based Depths for Directional Data
We introduce derivative sensitivity, an analogue to local sensitivity for continuous functions. We use this notion in an analysis that determines the amount of noise to be added to the result of a database query in order to obtain a certain…
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and…
We present techniques to characterize which data is important to a recommender system and which is not. Important data is data that contributes most to the accuracy of the recommendation algorithm, while less important data contributes less…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…
We present efficient data structures for approximate nearest neighbor searching and approximate 2-point shortest path queries in a two-dimensional polygonal domain $P$ with $n$ vertices. Our goal is to store a dynamic set of $m$ point sites…
Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
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…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
Depth information is useful for many applications. Active depth sensors are appealing because they obtain dense and accurate depth maps. However, due to issues that range from power constraints to multi-sensor interference, these sensors…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…
Modern cloud-based data infrastructures open new vistas for the deployment of scientometric data into the hands of practitioners. These infrastructures lower barriers to entry by making data more available and compute capacity more…
Local differential privacy (LPD) is a distributed variant of differential privacy (DP) in which the obfuscation of the sensitive information is done at the level of the individual records, and in general it is used to sanitize data that are…
For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the…
If $X$ is a convex surface in a Euclidean space, then the squared intrinsic distance function $\dist^2(x,y)$ is DC (d.c., delta-convex) on $X\times X$ in the only natural extrinsic sense. An analogous result holds for the squared distance…