Related papers: Total Variation Depth for Functional Data

A median-radius framework for assessing centrality in multivariate data using median distances is proposed. Based on the proposed framework, a scale invariant measure of radial dispersion is defined and used to establish a depth function…

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as…

Generalization to out-of-distribution (OOD) data is one of the central problems in modern machine learning. Recently, there is a surge of attempts to propose algorithms that mainly build upon the idea of extracting invariant features.…

We present a theory for the construction of out-of-distribution (OOD) detection features for neural networks. We introduce random features for OOD through a novel information-theoretic loss functional consisting of two terms, the first…

Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D…

The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its…

Functional magnetic resonance imaging (fMRI) data contain high levels of noise and artifacts. To avoid contamination of downstream analyses, fMRI-based studies must identify and remove these noise sources prior to statistical analysis. One…

Out-of-distribution (OOD) detection is critical to ensure the safe deployment of deep learning models in critical applications. Deep learning models can often misidentify OOD samples as in-distribution (ID) samples. This vulnerability…

Out-of-distribution (OOD) detection is crucial for ensuring reliable deployment of machine learning models. Recent advancements focus on utilizing easily accessible auxiliary outliers (e.g., data from the web or other datasets) in training.…

Data depth proves successful in the analysis of multivariate data sets, in particular deriving an overall center and assigning ranks to the observed units. Two key features are: the directions of the ordering, from the center towards the…

Anomaly detection or outlier detection is a common task in various domains, which has attracted significant research efforts in recent years. Existing works mainly focus on structured data such as numerical or categorical data; however,…

In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem involving the shape weighted perimeter and an additional term depending on a parameter. Based on recent works and in…

Many real-world applications involve analyzing time-dependent phenomena, which are intrinsically functional, consisting of curves varying over a continuum (e.g., time). When analyzing continuous data, functional data analysis (FDA) provides…

We study a novel outlier detection problem that aims to identify abnormal input-output associations in data, whose instances consist of multi-dimensional input (context) and output (responses) pairs. We present our approach that works by…

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…

Most multivariate outlier detection procedures ignore the spatial dependency of observations, which is present in many real data sets from various application areas. This paper introduces a new outlier detection method that accounts for a…

We present a novel mathematical optimization framework for outlier detection in multimodal datasets, extending Support Vector Data Description approaches. We provide a primal formulation, in the shape of a Mixed Integer Second Order Cone…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…

As a flexible passive 3D sensing means, unsupervised learning of depth from monocular videos is becoming an important research topic. It utilizes the photometric errors between the target view and the synthesized views from its adjacent…

The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular, the sublevel sets of the distance function are used in the computation of persistent homology -- a backbone of the…