相关论文: Low-Rank Isomap Algorithm

An important component of autoencoders is the method by which the information capacity of the latent representation is minimized or limited. In this work, the rank of the covariance matrix of the codes is implicitly minimized by relying on…

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…

Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data…

Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

Multi-task learning, which optimizes performance across multiple tasks, is inherently a multi-objective optimization problem. Various algorithms are developed to provide discrete trade-off solutions on the Pareto front. Recently, continuous…

The Iterative Closest Point (ICP) algorithm is a crucial component of LiDAR-based SLAM algorithms. However, its performance can be negatively affected in unstructured environments that lack features and geometric structures, leading to low…

Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…

While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…

We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. We bridge this gap for a natural and important special case, planar graph isomorphism,…

We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…

We introduce and analyze a lower envelope method (LEM) for the tracking of interfaces motion in multiphase problems. The main idea of the method is to define the phases as the regions where the lower envelope of a set of functions coincides…

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…

Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…

Pooling second-order local feature statistics to form a high-dimensional bilinear feature has been shown to achieve state-of-the-art performance on a variety of fine-grained classification tasks. To address the computational demands of high…

Infomap clustering finds the community structures that minimize the expected description length of a random walk trajectory; algorithms for infomap clustering run fast in practice for large graphs. In this paper we leverage the…