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We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…
We present a two-dimensional (2-D) fitting algorithm (GALFIT) designed to extract structural components from galaxy images, with emphasis on closely modeling light profiles of spatially well-resolved, nearby galaxies observed with the…
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…
We generalize the well-known mixtures of Gaussians approach to density estimation and the accompanying Expectation--Maximization technique for finding the maximum likelihood parameters of the mixture to the case where each data point…
We present a statistical analysis of voids in the 2dF galaxy redshift survey (2dFGRS). In order to detect the voids, we have developed two robust algorithms. We define voids as non-overlapping maximal spheres empty of halos or galaxies with…
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…
We consider the regression problem of estimating functions on $\mathbb{R}^D$ but supported on a $d$-dimensional manifold $ \mathcal{M} \subset \mathbb{R}^D $ with $ d \ll D $. Drawing ideas from multi-resolution analysis and nonlinear…
We present DisPerSE, a novel approach to the coherent multi-scale identification of all types of astrophysical structures, and in particular the filaments, in the large scale distribution of matter in the Universe. This method 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…
We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended…
Modern surveys have provided the astronomical community with a flood of high-dimensional data, but analyses of these data often occur after their projection to lower-dimensional spaces. In this work, we introduce a local two-sample…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Accurate density estimation methodologies play an integral role in a variety of scientific disciplines, with applications including simulation models, decision support tools, and exploratory data analysis. In the past, histograms and kernel…
Similarity analysis using neural networks has emerged as a powerful technique for understanding and categorizing complex patterns in various domains. By leveraging the latent representations learned by neural networks, data objects such as…
Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within…
This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions (d.f.'s) when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of…
The key features of the MATPHOT algorithm for precise and accurate stellar photometry and astrometry using discrete Point Spread Functions are described. A discrete Point Spread Function (PSF) is a sampled version of a continuous PSF which…
A novel approach is suggested for improving the accuracy of fault detection in distribution networks. This technique combines adaptive probability learning and waveform decomposition to optimize the similarity of features. Its objective is…