Related papers: Multiscale geometric feature extraction for high-d…

With the explosive growth of multi-source data, multi-view clustering has attracted great attention in recent years. Most existing multi-view methods operate in raw feature space and heavily depend on the quality of original feature…

Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…

The points on the point clouds that can entirely outline the shape of the model are of critical importance, as they serve as the foundation for numerous point cloud processing tasks and are widely utilized in computer graphics and…

Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…

We propose a method for speeding up a 3D point cloud registration through a cascading feature extraction. The current approach with the highest accuracy is realized by iteratively executing feature extraction and registration using deep…

Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

Outlier or anomaly detection is an important task in data analysis. We discuss the problem from a geometrical perspective and provide a framework that exploits the metric structure of a data set. Our approach rests on the manifold…

The features used in many image analysis-based applications are frequently of very high dimension. Feature extraction offers several advantages in high-dimensional cases, and many recent studies have used multi-task feature extraction…

We are surrounded by huge amounts of large-scale high dimensional data. It is desirable to reduce the dimensionality of data for many learning tasks due to the curse of dimensionality. Feature selection has shown its effectiveness in many…

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

This study introduces a novel unsupervised medical image feature extraction method that employs spatial stratification techniques. An objective function based on weight is proposed to achieve the purpose of fast image recognition. The…

Several machine learning models are defined for inputs of any size, such as graphs with different numbers of nodes and point clouds containing varying numbers of points. The universality properties of such any-dimensional models remain…

The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point…

We introduce a new method of performing high dimensional discriminant analysis, which we call multiDA. We achieve this by constructing a hybrid model that seamlessly integrates a multiclass diagonal discriminant analysis model and feature…

The amount of information in the form of features and variables avail- able to machine learning algorithms is ever increasing. This can lead to classifiers that are prone to overfitting in high dimensions, high di- mensional models do not…

LiDAR point clouds can effectively depict the motion and posture of objects in three-dimensional space. Many studies accomplish the 3D object detection by voxelizing point clouds. However, in autonomous driving scenarios, the sparsity and…

Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…