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In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node.…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
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…
We present canonical quantiles and depths for directional data following a distribution which is elliptically symmetric about a direction $\mu$ on the sphere $\mathcal{S}^{d-1}$. Our approach extends the concept of Ley et al. [1], which…
A method for extracting multiscale geometric features from a data cloud is proposed and analyzed. The basic idea is to map each pair of data points into a real-valued feature function defined on $[0,1]$. The construction of these feature…
Chirality information (i.e. information that allows distinguishing left from right) is ubiquitous for various data modes in computer vision, including images, videos, point clouds, and meshes. While chirality has been extensively studied in…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…
In this paper we introduce the concept of \emph{multivector functionals.} We study some possible kinds of derivative operators that can act in interesting ways on these objects such as, e.g., the $A$-directional derivative and the…
Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models…
We propose a new assumption in outlier detection: Normal data instances are commonly located in the area that there is hardly any fluctuation on data density, while outliers are often appeared in the area that there is violent fluctuation…
John W. Tukey (1975) defined statistical data depth as a function that determines centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved…
We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…
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.…
This paper presents an approach to analyzing two-dimensional temporal datasets focusing on identifying observations that are significant in calculating the outliers of a scatterplot. We also propose a prototype, called Outliagnostics, to…
Light curves of astrophysical objects frequently contain strictly periodic signals. In those cases we can use that property to aid the detrending algorithm to fully disentangle an unknown periodic signal and an unknown baseline signal with…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Light curves feature many kinds of variability, including instrumental systematics, intrinsic stellar variability such as pulsations, and flux changes caused by transiting exoplanets or eclipsing binary stars. Detrending is a key…