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

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and…

The convex hull of a set of points, $C$, serves to expose extremal properties of $C$ and can help identify elements in $C$ of high interest. For many problems, particularly in the presence of noise, the true vertex set (and facets) may be…

Convolutional neural networks (CNNs) have achieved superior performance but still lack clarity about the nature and properties of feature extraction. In this paper, by analyzing the sensitivity of neural networks to frequencies and scales,…

A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…

Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and…

Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…

Dimensionality effects pose major challenges in high-dimensional and non-Euclidean data analysis. Graph-based two-sample tests and change-point detection are particularly attractive in this context, as they make minimal distributional…

Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based…

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the…

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional…

This paper introduces Multiscale Anisotropic Harmonic Filters (MAHFs) aimed at extracting signal variations over non-Euclidean domains, namely 2D-Manifolds and their discrete representations, such as meshes and 3D Point Clouds as well as…

Point cloud shape completion is a challenging problem in 3D vision and robotics. Existing learning-based frameworks leverage encoder-decoder architectures to recover the complete shape from a highly encoded global feature vector. Though the…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

Texture is an important spatial feature which plays a vital role in content based image retrieval. The enormous growth of the internet and the wide use of digital data have increased the need for both efficient image database creation and…

A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension ($N_{_{D}}>3$). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering…

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…

Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…

Deep neural networks have achieved significant success in 3D point cloud classification while relying on large-scale, annotated point cloud datasets, which are labor-intensive to build. Compared to capturing data with LiDAR sensors and then…

This paper introduces a new technique to measure the feature dependency of neural network models. The motivation is to better understand a model by querying whether it is using information from human-understandable features, e.g.,…