Related papers: Sensor network localization has a benign landscape…
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g., low-rank matrix factorization, phase retrieval, and deep…
A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems…
The present work considers the localization problem in wireless sensor networks formed by fixed nodes. Each node seeks to estimate its own position based on noisy measurements of the relative distance to other nodes. In a centralized batch…
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in…
Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning. However, this problem is poorly understood in the…
This paper studies the nonsmooth optimization landscape of the $\ell_1$-norm rank-one symmetric matrix factorization problem using tools from second-order variational analysis. Specifically, as the main finding of this paper, we show that…
Consider $N$ points in $\mathbb{R}^d$ and $M$ local coordinate systems that are related through unknown rigid transforms. For each point we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems.…
We consider the range-based localization problem, which involves estimating an object's position by using $m$ sensors, hoping that as the number $m$ of sensors increases, the estimate converges to the true position with the minimum…
In order to make full use of geographic routing techniques developed for sensor networks, nodes must be localized. However, traditional localization and virtual localization techniques are dependent either on expensive and sometimes…
This paper studies a coordinate alignment problem for cooperative mobile sensor network localization with range-based measurements. The network consists of target nodes, each of which has only access position information in a local fixed…
In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible. In this…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
A practical challenge which arises in the operation of sensor networks is the presence of sensor faults, biases, or adversarial attacks, which can lead to significant errors incurring in the localization of the agents, thereby undermining…
The network localization problem with convex and non-convex distance constraints may be modeled as a nonlinear optimization problem. The existing localization techniques are mainly based on convex optimization. In those techniques, the…
Low-rank matrix sensing is a fundamental yet challenging nonconvex problem whose optimization landscape typically contains numerous spurious local minima, making it difficult for gradient-based optimizers to converge to the global optimum.…
The problem of localizing a set of nodes from relative pairwise measurements is at the core of many applications such as Structure from Motion (SfM), sensor networks, and Simultaneous Localization And Mapping (SLAM). In practical…
This paper addresses the distributed localization problem for a network of sensors placed in a three-dimensional space, in which sensors are able to perform range measurements, i.e., measure the relative distance between them, and exchange…