Related papers: Directional Outlyingness for Multivariate Function…
In this paper, we address the problem of class-generalizable anomaly detection, where the objective is to develop a unified model by focusing our learning on the available normal data and a small amount of anomaly data in order to detect…
This paper establishes the existence of observable footprints that reveal the "causal dispositions" of the object categories appearing in collections of images. We achieve this goal in two steps. First, we take a learning approach to…
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…
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats the fundamentals of the multivector differential…
Realizations of stochastic process are often observed temporal data or functional data. There are growing interests in classification of dynamic or functional data. The basic feature of functional data is that the functional data have…
We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the…
Multivariate functional data are becoming ubiquitous with advances in modern technology and are substantially more complex than univariate functional data. We propose and study a novel model for multivariate functional data where the…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
For a function $f$ from $\mathbb{F}_2^n$ to $\mathbb{F}_2^n$, the planarity of $f$ is usually measured by its differential uniformity and differential spectrum. In this paper, we propose the concept of vanishing flats, which supplies a…
In this paper, we propose a novel approach for outlier detection, called local projections, which is based on concepts of Local Outlier Factor (LOF) (Breunig et al., 2000) and RobPCA (Hubert et al., 2005). By using aspects of both methods,…
Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, $u_t = L(u_x)_x$, where $L$ is merely a monotone function. We also expose the basic properties of solutions,…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
We consider models for network indexed multivariate data involving a dependence between variables as well as across graph nodes. In the framework of these models, we focus on outliers detection and introduce the concept of edgewise…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…
Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…
Outlier detection is one of the most important processes taken to create good, reliable data in machine learning. The most methods of outlier detection leverage an auxiliary reconstruction task by assuming that outliers are more difficult…
Machine learning techniques can automatically identify outliers in massive datasets, much faster and more reproducible than human inspection ever could. But finding such outliers immediately leads to the question: which features render this…
Out-of-distribution (OOD) detection and segmentation are crucial for deploying machine learning models in safety-critical applications such as autonomous driving and robot-assisted surgery. While prior research has primarily focused on…