The account for correlations between nearest neighbors in micromagnetic modeling

Quantifying long-range correlations in complex networks beyond nearest neighbors

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied...

Positioning for Online Nearest Neighbors

Tradeoffs for nearest neighbors on the sphere

We consider tradeoffs between the query and update complexities for the (approximate) nearest neighbor problem on the sphere, extending the spherical filters recently introduced by [Becker–Ducas–Gama– Laarhoven, SODA’16] to sparse regimes and generalizing the scheme and analysis to account for different tradeoffs. In a nutshell, for the sparse regime the tradeoff between the query complexity nq...

Nearest-neighbors medians clustering

We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of c...

Boruvka Meets Nearest Neighbors

Computing the minimum spanning tree (MST) is a common task in the pattern recognition and the computer vision fields. However, little work has been done on efficient general methods for solving the problem on large datasets where graphs are complete and edge weights are given implicitly by a distance between vertex attributes. In this work we propose a generic algorithm that extends the classic...