Constrained clustering has been well-studied for algorithms such as -means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode many constraints is to use spectral clustering, which remains a developing area. I…
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48 results for “spectral constraints”
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the recently proposed -spectral clustering for the unconstrained problem, our method is…
On consistency of constrained spectral clustering under representation-aware stochastic block modelstat.ML
New method finds balanced clusters in graphs using auxiliary information.
problem Finding balanced clusters in graphs with population-level constraints.
method Proposes individual-level balancing constraint and develops spectral clustering algorithms.
result Establishes first statistical consistency result for constrained spectral clustering.
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 discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopole…
Paper tackles graph structure learning via spectral constraints.
problem Learning graphs with specific structures from data.
method Convert structural constraints to Laplacian eigenvalue constraints, integrate with Gaussian graphical modeling.
result Unified framework for learning various graph structures, convergent and scalable.
A novel nonstationary permanental process relaxes kernel constraints and captures complex data patterns.
problem Limitations of existing permanental processes in terms of kernel types and stationarity.
method Sparse spectral representation of nonstationary kernels and hierarchical stacking of spectral feature mappings.
result Enhanced model expressiveness and reduced computational complexity.
Consistent spectral clustering with fairness constraints on representation graphs.
problem Finding balanced clusters in similarity graphs with fairness constraints.
method Developed variants of unnormalized and normalized spectral clustering for fair planted partitions.
result Consistency results for constrained spectral clustering under fair planted partitions.
Muon optimizer improves deep learning with spectral norm constraints.
problem Improving optimization algorithms in deep learning.
method Theoretical analysis of Muon optimizer within the Lion- family.
result Muon implicitly solves an optimization problem enforcing spectral norm constraints.
Proposes RNSE for clustering with adaptive similarity matrix learning.
problem Sub-optimal results due to mismatch between stages in Spectral Clustering.
method End-to-end single-stage learning with adaptive similarity matrix and non-negative constraints.
result Superior clustering performance on synthetic and real-world datasets.
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding co…
Bayesian parametric matrix models provide uncertainty quantification for spectral learning.
problem Uncertainty quantification in spectral learning for safety-critical applications.
method Bayesian parametric matrix models (B-PMMs) that extend PMMs to provide uncertainty estimates.
result B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling.
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…
Proposes CRG_IMSC for better clustering of multi-view data.
problem Lack of effective connectivity in clustering results.
method Directly obtains clustering result with nonnegative constraint; constructs connectivity matrix based on spectral clustering result; uses multiplicative update algorithm.
result Improves clustering performance on benchmark datasets.
Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores that prevent discrimination in predictions. This paper develops computationally…
New algorithm speeds up fair clustering by 12x.
problem Achieving fair clustering in scalable algorithms.
method s-FairSC algorithm incorporating nullspace projection and Hotelling's deflation.
result s-FairSC is 12x faster and maintains fairness.
New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.
problem Bounding Bartnik mass for surfaces with spectral non-negativity condition.
method Proving upper bound on Bartnik mass using spectral non-negativity condition.
result Bounded above by √(|S²|_g/16π) under spectral non-negativity.
In this paper we construct compact manifolds with fixed boundary geometry which admit Riemannian metrics of unit volume with arbitrarily large Steklov spectral gap. We also study the effect of localized conformal deformations that fix the boundary geometry. For instance, we prove that it is possible to make the spectra…
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
If a curve in R^3 is closed, then the curvature and the torsion are periodic functions satisfying some additional constraints. We show that these constraints can be naturally formulated in terms of the spectral problem for a 2x2 matrix differential operator. This operator arose in the theory of the self-focusing Nonlin…
Classifies charge-3 monopoles with symmetry, identifying new spectral curves.
problem Classifying charge-3 monopoles with symmetry.
method Constructing Nahm data and identifying spectral curves with elliptic quotients.
result New monopole spectral curves with and symmetry identified.
Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for …
Deep networks reveal colour opponent cells under retinal constraints.
problem Understanding colour vision in deep neural networks.
method Classifying cells in early layers of anatomically constrained convolutional neural networks.
result Emergence of single and double opponent cells in deep networks.
The paper finds extremum values for mixed Laplacian eigenvalues on triangles and trapezoids.
problem Finding extremum values for mixed eigenvalues of the Laplacian on triangles and trapezoids.
method Characterizations obtained under suitable geometric constraints.
result Characterizations of extremum values for mixed eigenvalues of the Laplacian on triangles and trapezoids.
Paper improves MVSC using tensor low-rank modeling.
problem Improving multi-view spectral clustering.
method Structured tensor low-rank norm for MVSC optimization.
result Proposed method outperforms state-of-the-art methods.
Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interferenceeess.SP
A robust method for decomposing spectral peaks robust to distortion and interference.
problem Decomposing spectral peaks in the presence of distortion and interference.
method Optimizing a nonparametric approach using pseudo-symmetric functions with nonincreasing behavior.
result Decomposed spectral peaks show pseudo-orthogonal behavior and power preserving equality.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
Multi-view spectral clustering, which aims at yielding an agreement or consensus data objects grouping across multi-views with their graph laplacian matrices, is a fundamental clustering problem. Among the existing methods, Low-Rank Representation (LRR) based method is quite superior in terms of its effectiveness, intu…
A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.
problem Optimization problems over binary matrices with injectivity constraints.
method Non-negative spherical relaxation followed by conditional power iteration.
result Automatic adjustment of the continuous parameter related to universe size.
The paper studies hyperbolic three-manifolds and their geometric constraints.
problem Understanding the interaction between hyperbolic geometry and homology cobordism.
method Derived explicit bounds on relative grading and invariants in monopole Floer homology.
result Explicit bounds on numerical invariants and subgroup structure of homology cobordism.
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank approximations, similar algorithms appears recently in the literature under different name…
We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a numb…
Spectral portfolio theory links neural networks to wealth dynamics via SGD weight matrices.
problem Understanding wealth dynamics from neural network training.
method Direct identification of weight matrices as portfolio allocation matrices, linking SGD forces to portfolio dynamics.
result Spectral properties of SGD weight matrices transition between additive and multiplicative regimes, influencing wealth dynamics.
Several isoperimetric inequalities of Dirichlet and Neumann eigenvalues of the Witten-Laplacianmath.AP
Paper derives inequalities for eigenvalues of Witten-Laplacian under fixed volume constraint.
problem Eigenvalue inequalities of Witten-Laplacian on bounded domains.
method Rearrangement technique and trial functions under fixed weighted volume constraint.
result Several isoperimetric inequalities for eigenvalues of Witten-Laplacian.
Spectral images captured by satellites and radio-telescopes are analyzed to obtain information about geological compositions distributions, distant asters as well as undersea terrain. Spectral images usually contain tens to hundreds of continuous narrow spectral bands and are widely used in various fields. But the vast…
In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writi…
Paper tackles efficient BAI in graph-smooth bandits.
problem Best arm identification with graph smoothness constraint.
method Gradient ascent algorithm for sample complexity.
result Asymptotically optimal strategy for BAI.
On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminantsstat.ML
Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.
problem Improving discriminant analysis for multilabel classification with enhanced dimensionality and robustness.
method Unified theoretical analysis of multilabel Fisher discriminants with algebraic and statistical guarantees.
result Unified characterization of multilabel Fisher objectives and their equivalence under orthogonality constraints.
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of con…
Proves Hölder-type inequality for Lagrangians' distance.
problem Understanding the symplectic geometry of Lagrangians.
method Developed methods from previous works to establish the inequality.
result Established a Hölder-type inequality for the Hausdorff distance between Lagrangians.
This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding…
Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known method for clustering which utilizes the spectrum of the data similarity matrix to pe…
Optimal estimates for spectral projection norms on compact manifolds.
problem Estimating norms of spectral projection operators on compact manifolds.
method Analyzing spectral windows with logarithmic growth and applying curvature constraints.
result Optimal estimates for norms are derived, saturating on flat or negatively curved manifolds.
Optimizes risk measures given known marginal distributions of two unknown factors.
problem Determining an upper bound for spectral risk measures with unknown joint distribution.
method Introduces Maximum Spectral Measure (MSP) as a worst-case risk measure, formulated as an optimization problem with a more general objective function.
result Characterizes the continuity properties of the optimal value function and optimal solution set with respect to marginal distributions.
Researchers approximate spectral targets on manifolds with constant negative curvature.
problem Prescribing an arbitrary finite portion of the Laplace-Beltrami spectrum on manifolds of constant negative curvature.
method Constructing macroscopically heterogeneous hyperbolic covering manifolds in and using discrete spectral limit theorems in .
result Any finite strictly increasing target list can be approximated to arbitrary precision by a closed manifold of constant negative curvature.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many members up to orbifold homeomorphism. Furthermore, any class of isospectral Riemannian orbifolds with a lower bound on the sectional curvature is …
Federated PCA and Estimation for Spiked Covariance Matrices: Optimal Rates and Efficient Algorithmmath.ST
Paper optimizes federated PCA for covariance estimation under privacy constraints.
problem Privacy-preserving covariance estimation in federated learning.
method Federated PCA, matrix version of van Trees' inequality, three-layer spectral decomposition.
result Optimal rates of convergence for central server's estimation, robust to inconsistent local estimators.