Related papers: Projection pursuit for discrete data

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit…

Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic…

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

Recently, diffusion models have gained popularity and attention in trajectory optimization due to their capability of modeling multi-modal probability distributions. However, addressing nonlinear equality constraints, i.e, dynamic…

Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional…

The accelerated deployment of service robots have spawned a number of algorithm variations to better handle real-world conditions. Many local trajectory planning techniques have been deployed on practical robot systems successfully. While…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

Trajectory prediction is a fundamental and challenging task for numerous applications, such as autonomous driving and intelligent robots. Currently, most of existing work treat the pedestrian trajectory as a series of fixed two-dimensional…

Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics, combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle…

The observation of objects located in inaccessible regions is a recurring challenge in a wide variety of important applications. Recent work has shown that indirect diffuse light reflections can be used to reconstruct objects and…

Machine teaching often involves the creation of an optimal (typically minimal) dataset to help a model (referred to as the `student') achieve specific goals given by a teacher. While abundant in the continuous domain, the studies on the…

The approximate discrete Radon transform (ADRT) is a hierarchical multiscale approximation of the Radon transform. In this paper, we factor the ADRT into a product of linear transforms that resemble convolutions and derive an explicit…

Efficient explorative data analysis systems must take into account both what a user knows and wants to know. This paper proposes a principled framework for interactive visual exploration of relations in data, through views most informative…

Effective tracking of surrounding traffic participants allows for an accurate state estimation as a necessary ingredient for prediction of future behavior and therefore adequate planning of the ego vehicle trajectory. One approach for…

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…

We propose two distributed set-based observers using strip-based and set-propagation approaches for linear discrete-time dynamical systems with bounded modeling and measurement uncertainties. Both algorithms utilize a set-based diffusion…

Few-shot object detection, learning to adapt to the novel classes with a few labeled data, is an imperative and long-lasting problem due to the inherent long-tail distribution of real-world data and the urgent demands to cut costs of data…