arXiv research

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely used in data analysis. To gain a better understanding of why spectral clustering i…

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

Spectral algorithms improve under covariate shift with novel weighted techniques.

This paper proposes a spectral clustering algorithm for hyperbolic spaces, improving efficiency over Euclidean methods.

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods …

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue decompositions. Several algorithms have been proposed in the recent past to accelerate spec…

Spectral methods predict long-term signals from linear and nonlinear systems.

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, whe…

ARFF reduces spectral bias in SGD-trained neural networks.

New algorithms improve spectral clustering for finite mixture models.

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the principal subspaces in the neighborhoods, and then applies spectral clustering. …

New spectral clustering method for graphs with uneven node degrees.

Spectral algorithms on manifolds using diffusion kernels improve convergence rates.

Enhanced spectral clustering for geometric graphs improves clustering accuracy.

Study confirms learning rates for vector-valued spectral algorithms, proving consistency.

Spectral algorithms solve optimal community detection and related problems.

Paper tackles functional linear regression using spectral algorithms with discrete observations.

Algorithm learns dynamics from past observations.

We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm…

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…

We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a…

In spectral clustering and spectral image segmentation, the data is partioned starting from a given matrix of pairwise similarities S. the matrix S is constructed by hand, or learned on a separate training set. In this paper we show how to achieve spectral clustering in unsupervised mode. Our algorithm starts with a se…

A simple linear algebraic explanation of the algorithm in "A Spectral Algorithm for Learning Hidden Markov Models" (COLT 2009). Most of the content is in Figure 2; the text just makes everything precise in four nearly-trivial claims.

A fast, robust AMP algorithm for quadratic optimization problems.

This paper explores saturation effects in spectral algorithms over large dimensions.

The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.

Spectral clustering adapted for mixed data types without preprocessing.

Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the in…

SPEDER extracts state-action abstraction from dynamics for reinforcement learning.

We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. The spectral algorithm consists of multiple algorithmic steps, named as "{edges}", to which noise cou…

Interpolates mean shift and spectral clustering on graphs.

New spectral clustering method handles discrete covariates for better community detection.

Randomized spectral co-clustering speeds up large-scale directed networks.

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a…

New methods rank players using covariates and comparisons, outperforming existing algorithms.

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous statistical…

The study analyzes spectral algorithms for kernel methods and derives generalization error.

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading eigenvectors, where $k$ is the desired number of clusters among $n$ objects. This is pro…

This paper improves spectral clustering for large datasets using the Nystrom method.

Study spectral learning for odeco tensors, addressing initialization bottlenecks.

Spectral clustering is robust to helpful model changes but not to random changes.

Spectral clustering with edge counting detects communities in sparse models.

New methods for clustering graphs using spectral analysis.

A fast spectral algorithm detects community structure in evolving graphs.

New method shows spectral clustering is consistent with theoretical guarantees.

Accelerates optimal transport computation by 10x with spectral insights.

KCoreMotif clusters large networks efficiently by exploiting k-core decomposition and motifs.

In the past decades, spectral clustering (SC) has become one of the most effective clustering algorithms. However, most previous studies focus on spectral clustering tasks with a fixed task set, which cannot incorporate with a new spectral clustering task without accessing to previously learned tasks. In this paper, we…