Related papers: Visualization of High-dimensional Scalar Functions…

This article investigates a new procedure to estimate the influence of each variable of a given function defined on a high-dimensional space. More precisely, we are concerned with describing a function of a large number $p$ of parameters…

Our human sense of touch enables us to manipulate our surroundings; therefore, complex robotic manipulation will require artificial tactile sensing. Typically tactile sensor arrays are used in robotics, implying that a straightforward way…

We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…

Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever…

Nanophotonics finds ever broadening applications requiring complex component designs with a large number of parameters to be simultaneously optimized. Recent methodologies employing optimization algorithms commonly focus on a single design…

Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…

There has recently been great interest in neural rendering methods. Some approaches use 3D geometry reconstructed with Multi-View Stereo (MVS) but cannot recover from the errors of this process, while others directly learn a volumetric…

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…

We present two diagnostic methods based on ideas of Principal Component Analysis and demonstrate their efficiency for sophisticated processing of multicolour photometric observations of variable objects.

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

Scalar features in time-dependent fluid flow are traditionally visualized using 3D representation, and their topology changes over time are often conveyed with abstract graphs. Using such techniques, however, the structural details of…

We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…

We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

In this paper we propose a novel variable selection method for two-view settings, or for vector-valued supervised learning problems. Our framework is able to handle extremely large scale selection tasks, where number of data samples could…

In the context of optimization, visualization techniques can be useful for understanding the behaviour of optimization algorithms and can even provide a means to facilitate human interaction with an optimizer. Towards this goal, an…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

Data visualizations summarize high-dimensional distributions in two or three dimensions. Dimensionality reduction entails a loss of information, and what is preserved differs between methods. Existing methods preserve the local or the…

The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…

Hypergraph visualization has many applications in network data analysis. Recently, a polygon-based representation for hypergraphs has been proposed with demonstrated benefits. However, the polygon-based layout often suffers from excessive…