相关论文: Fast Eigenspace Approximation using Random Signals

In this paper, we cast the scribble-based interactive image segmentation as a semi-supervised learning problem. Our novel approach alleviates the need to solve an expensive generalized eigenvector problem by approximating the eigenvectors…

This paper characterizes the difficulty of estimating a network's eigenvector centrality only from data on the nodes, i.e., with no information about the topology of the network. We model this nodal data as graph signals generated by…

The volume of image repositories continues to grow. Despite the availability of content-based addressing, we still lack a lightweight tool that allows us to discover images of distinct characteristics from a large collection. In this paper,…

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering…

In this paper we give the first efficient algorithms for the $k$-center problem on dynamic graphs undergoing edge updates. In this problem, the goal is to partition the input into $k$ sets by choosing $k$ centers such that the maximum…

Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…

We consider semi-supervised regression when the predictor variables are drawn from an unknown manifold. A simple two step approach to this problem is to: (i) estimate the manifold geodesic distance between any pair of points using both the…

We study the problem of sampling and reconstructing spectrally sparse graph signals where the objective is to select a subset of nodes of prespecified cardinality that ensures interpolation of the original signal with the lowest possible…

Spectral methods that are based on eigenvectors and eigenvalues of discrete graph Laplacians, such as Diffusion Maps and Laplacian Eigenmaps are often used for manifold learning and non-linear dimensionality reduction. It was previously…

We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful…

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…

We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent…

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…

In this paper, we propose an adaptive finite element method for computing the first eigenpair of the $p$-Laplacian problem. We prove that starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete…

We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…

Range-filtering approximate $k$-nearest neighbor (RFAKNN) search takes as input a vector and a numeric value, returning $k$ points from a database of $N$ high-dimensional points. The returned points must satisfy two criteria: their numeric…

We provide faster algorithms and improved sample complexities for approximating the top eigenvector of a matrix. Offline Setting: Given an $n \times d$ matrix $A$, we show how to compute an $\epsilon$ approximate top eigenvector in time…

We develop here an algorithmic framework for constructing consistent multiscale Laplacian eigenfunctions (vectors) on data. Consequently, we address the unsupervised machine learning task of finding scalar functions capturing consistent…