Related papers: Efficient randomized algorithms for PageRank probl…
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…
Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually…
Singular value decomposition (SVD) and matrix inversion are ubiquitous in scientific computing. Both tasks are computationally demanding for large scale matrices. Existing algorithms can approximatively solve these problems with a given…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix…
Rank-based Learning with deep neural network has been widely used for image cropping. However, the performance of ranking-based methods is often poor and this is mainly due to two reasons: 1) image cropping is a listwise ranking task rather…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very different intervals. Sometimes, this is evident even within a…
Ranking problem of web-based rating system has attracted many attentions. A good ranking algorithm should be robust against spammer attack. Here we proposed a correlation based reputation algorithm to solve the ranking problem of such…
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a…
The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…
This work studies a fully distributed algorithm for computing the PageRank vector, which is inspired by the Matching Pursuit and features: 1) a fully distributed implementation 2) convergence in expectation with exponential rate 3) low…
The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$. Although this problem can be solved efficiently, we study an…
Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…
We give a new link spam detection and PageRank demotion algorithm called MaxRank. Like TrustRank and AntiTrustRank, it starts with a seed of hand-picked trusted and spam pages. We define the MaxRank of a page as the frequency of visit of…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking…