Related papers: Depth and depth-based classification with R-packag…
Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…
Depth completion aims at predicting dense pixel-wise depth from an extremely sparse map captured from a depth sensor, e.g., LiDARs. It plays an essential role in various applications such as autonomous driving, 3D reconstruction, augmented…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
As a measure for the centrality of a point in a set of multivariate data, statistical depth functions play important roles in multivariate analysis, because one may conveniently construct descriptive as well as inferential procedures…
Comparative evaluation of several systems is a recurrent task in researching. It is a key step before deciding which system to use for our work, or, once our research has been conducted, to demonstrate the potential of the resulting model.…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…
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…
Linear discriminant analysis (LDA) is a powerful tool in building classifiers with easy computation and interpretation. Recent advancements in science technology have led to the popularity of datasets with high dimensions, high orders and…
Data depth concept offers a variety of powerful and user friendly tools for robust exploration and inference for multivariate socio-economic phenomena. The offered techniques may be successfully used in cases of lack of our knowledge on…
Statistical depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given $d$-dimensional data set for any $d\geq 2$, the algorithm is based on representation of level sets as intersections of balls in $R^d$, and can…
We present a new fast approximate algorithm for Tukey (halfspace) depth level sets and its implementation-ABCDepth. Given a $d$-dimensional data set for any $d\geq 1$, the algorithm is based on a representation of level sets as…
Many research questions can be answered quickly and efficiently using data already collected for previous research. This practice is called secondary data analysis (SDA), and has gained popularity due to lower costs and improved research…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm…