Related papers: A Novel and Optimal Spectral Method for Permutatio…
This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First,…
The synchronization problem over the special orthogonal group $SO(d)$ consists of estimating a set of unknown rotations $R_1,R_2,...,R_n$ from noisy measurements of a subset of their pairwise ratios $R_{i}^{-1}R_{j}$. The problem has found…
So far, the problem of unmixing large or multitemporal hyperspectral datasets has been specifically addressed in the remote sensing literature only by a few dedicated strategies. Among them, some attempts have been made within a distributed…
Asynchronous distributed algorithms are a popular way to reduce synchronization costs in large-scale optimization, and in particular for neural network training. However, for nonsmooth and nonconvex objectives, few convergence guarantees…
Spectral imaging enables the analysis of optical material properties that are invisible to the human eye. Different spectral capturing setups, e.g., based on filter-wheel, push-broom, line-scanning, or mosaic cameras, have been introduced…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
Active stereo technique using single pattern projection, a.k.a. one-shot 3D scan, have drawn a wide attention from industry, medical purposes, etc. One severe drawback of one-shot 3D scan is sparse reconstruction. In addition, since spatial…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based…
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements -- L_1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized…
This paper investigates the spectral norm version of the column subset selection problem. Given a matrix $\mathbf{A}\in\mathbb{R}^{n\times d}$ and a positive integer $k\leq\text{rank}(\mathbf{A})$, the objective is to select exactly $k$…
Anomaly detection in massive networks has numerous theoretical and computational challenges, especially as the behavior to be detected becomes small in comparison to the larger network. This presentation focuses on recent results in three…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
This paper presents a novel spectral algorithm with additive clustering designed to identify overlapping communities in networks. The algorithm is based on geometric properties of the spectrum of the expected adjacency matrix in a random…
Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…
In many applications including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an $n$-dimensional lattice to get an optimal integer coefficient matrix…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
This paper presents a novel Fourier spectral method that utilizes optimization techniques to ensure the positivity and conservation of moments in the space of trigonometric polynomials. We rigorously analyze the accuracy of the new method…
We present a new method for time series clustering which we call the Hierarchical Spectral Merger (HSM) method. This procedure is based on the spectral theory of time series and identifies series that share similar oscillations or…