Related papers: Fast Quadratic Manifold Learning For Nonlinear Dim…

In order to avoid the curse of dimensionality, frequently encountered in Big Data analysis, there was a vast development in the field of linear and nonlinear dimension reduction techniques in recent years. These techniques (sometimes…

Landing methods have recently emerged in Riemannian matrix optimization as efficient schemes for handling nonlinear equality constraints without resorting to costly retractions. These methods decompose the search direction into tangent and…

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…

This paper considers an optimization problem that components of the objective function are available at different nodes of a network and nodes are allowed to only exchange information with their neighbors. The decentralized alternating…

In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

We examine a wide class of stochastic approximation algorithms for solving (stochastic) nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study of Riemannian optimization, game theory and optimal transport,…

We study the properties of stochastic approximation applied to a tame nondifferentiable function subject to constraints defined by a Riemannian manifold. The objective landscape of tame functions, arising in o-minimal topology extended to a…

The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…

Optimization problems on the Stiefel manifold, ranging from principal component analysis to enhancing neural network robustness, are ubiquitous in machine learning. The Landing algorithm avoids computationally expensive retraction…

An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…

Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…

In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Riemannian optimization with random initialization. We use the…

Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging.…

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However,…