Related papers: Efficient space virtualisation for Hoshen--Kopelma…
This work introduces a kernel-independent, multilevel, adaptive algorithm for efficiently evaluating a discrete convolution kernel with a given source distribution. The method is based on linear algebraic tools such as low rank…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
In this article we consider the graph alignment problem from the perspective of high-dimensional statistics: we aim to estimate an unknown permutation $\pi^*$ from the observation of two correlated random adjacency matrices $A_1$, $A_2$. We…
We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN), the body-centered cubic (BCC), and the…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors…
We consider static, external memory indexes for exact and approximate versions of the $k$-nearest neighbor ($k$-NN) problem, and show new lower bounds under a standard indivisibility assumption: - Polynomial space indexing schemes for…
Visual localization for planar moving robot is important to various indoor service robotic applications. To handle the textureless areas and frequent human activities in indoor environments, a novel robust visual localization algorithm…
Using a recently introduced algorithm for simulating percolation in microcanonical (fixed-occupancy) samples, we study the convergence with increasing system size of a number of estimates for the percolation threshold for an open system…
To overcome the large memory requirement of classical lattice sieving algorithms for solving hard lattice problems, Bai-Laarhoven-Stehl\'{e} [ANTS 2016] studied tuple lattice sieving, where tuples instead of pairs of lattice vectors are…
We consider the problem of embedding unweighted, directed k-nearest neighbor graphs in low-dimensional Euclidean space. The k-nearest neighbors of each vertex provides ordinal information on the distances between points, but not the…
By means of Monte Carlo simulations, we study long-range site percolation on square and simple cubic lattices with various combinations of nearest neighbors, up to the eighth neighbors for the square lattice and the ninth neighbors for the…
We study first-order optimization algorithms under the constraint that the descent direction is quantized using a pre-specified budget of $R$-bits per dimension, where $R \in (0 ,\infty)$. We propose computationally efficient optimization…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4th and the 5th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the…
Similarity search in high-dimensional spaces is an important task for many multimedia applications. Due to the notorious curse of dimensionality, approximate nearest neighbor techniques are preferred over exact searching techniques since…
Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image…
Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…
Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…