Related papers: The Delaunay Density Diagnostic
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
Entropy-type integral functionals of densities are widely used in mathematical statistics, information theory, and computer science. Examples include measures of closeness between distributions (e.g., density power divergence) and…
In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…
A new clustering accuracy measure is proposed to determine the unknown number of clusters and to assess the quality of clustering of a data set given in any dimensional space. Our validity index applies the classical nonparametric…
The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space $\mathbb{R}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite…
Feature selection (FS) is assumed to improve predictive performance and identify meaningful features in high-dimensional datasets. Surprisingly, small random subsets of features (0.02-1%) match or outperform the predictive performance of…
We propose an attentive local feature descriptor suitable for large-scale image retrieval, referred to as DELF (DEep Local Feature). The new feature is based on convolutional neural networks, which are trained only with image-level…
Clustering real world data often faced with curse of dimensionality, where real world data often consist of many dimensions. Multidimensional data clustering evaluation can be done through a density-based approach. Density approaches based…
Density-based distances (DBDs) provide a principled approach to metric learning by defining distances in terms of the underlying data distribution. By employing a Riemannian metric that increases in regions of low probability density,…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
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…
We study the problem of estimating the score function using both implicit score matching and denoising score matching. Assuming that the data distribution exhibiting a low-dimensional structure, we prove that implicit score matching is able…
In the study of depth functions it is important to decide whether we want such a function to be sensitive to multimodality or not. In this paper we analyze the Delaunay depth function, which is sensitive to multimodality and compare this…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
High-dimensional datasets depict a challenge for learning tasks in data mining and machine learning. Feature selection is an effective technique in dealing with dimensionality reduction. It is often an essential data processing step prior…
We seek a practical method for establishing dense correspondences between two images with similar content, but possibly different 3D scenes. One of the challenges in designing such a system is the local scale differences of objects…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Feature matching is a challenging computer vision task that involves finding correspondences between two images of a 3D scene. In this paper we consider the dense approach instead of the more common sparse paradigm, thus striving to find…
Feature selection is a critical step in the analysis of high-dimensional data, where the number of features often vastly exceeds the number of samples. Effective feature selection not only improves model performance and interpretability but…
'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…