New method uses HDP-HMM and multitaper spectral estimation for automated sleep state classification.
problem Manual sleep scoring is subjective, time-consuming, and doesn't capture neural dynamics.
method Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) with multitaper spectral estimation.
result Automated algorithm recovers sleep dynamics and identifies subject-specific microstates.
Deep learning classifies sleep stages from EEG signals, aiding professionals.
problem Manual scoring of sleep stages from EEG signals is tedious and requires trained professionals.
method Multitaper spectral analysis and deep convolutional neural networks for automatic classification.
result System accurately classifies sleep stages in new patients, favorably compared to state-of-the-art.
Binary and multiclass epilepsy detection methods using EEG features.
problem Epilepsy diagnosis from EEG data.
method Feature extraction from power spectrum, spectrogram, and bispectrogram; eight machine learning algorithms used.
result Random forest and backpropagation algorithms achieved highest accuracy for binary and multiclass classification.
We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the generalized word problem in braid groups, in the special case of cyclic subgroups. We ill…
Survey on spectral embeddings for data analysis.
problem None explicitly stated in the abstract.
method Presentation of spectral embeddings from Riemannian geometry to data analysis.
result Survey of spectral embeddings and their applications.
New spectral analysis on non-compact spaces.
problem Analyzing pseudo-Riemannian locally symmetric spaces.
method Initiating spectral analysis beyond classical settings.
result Recent results in non-compact spaces.
Enhanced geographical features improve predictive models for colorectal cancer survival curves.
problem Predicting colorectal cancer survival curves in Iowa.
method Used neural networks to explore feature representations, comparing ABC performance.
result Spectral analysis-based representations improve predictive performance by approximately 40%.
Improved LDA method for better classification and dimensionality reduction.
problem Improving linear discriminant analysis for better classification performance.
method Integrates spectrally-corrected covariance matrix and regularized discriminant analysis.
result SRLDA has a linear classification global optimal solution under spiked model assumption.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
Improved spectral clustering algorithm for better performance.
problem Improving the performance of spectral clustering algorithms.
method Developed a new performance guarantee under a weaker assumption and evaluated using a different spectral embedding map.
result Better performance guarantee under a weaker assumption and evaluation of a new spectral embedding map.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
Improved spectral clustering with fewer eigenvectors performs better.
problem Improving spectral clustering performance under weaker conditions.
method Tighter analysis and using fewer eigenvectors for embedding.
result Spectral clustering can produce better results with fewer eigenvectors.
New spectral triples defined for SU(1,1) using harmonic analysis.
problem Defining new spectral triples for SU(1,1).
method Using harmonic analysis of SU(1,1) to construct pseudo-Riemannian and indefinite spectral triples.
result Triple (A,H,D) forms both pseudo-Riemannian and indefinite spectral triples. Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.
Proposes neural dynamic mode decomposition for end-to-end modeling of nonlinear dynamics.
problem Understanding and modeling nonlinear dynamical systems.
method Trains neural networks to minimize forecast error based on spectral decomposition in the lifted space.
result Demonstrates effectiveness in eigenvalue estimation and forecast performance.
Word2vec analysis reveals spectral underpinnings.
problem Lack of theoretical justification for word2vec.
method Rigorous spectral analysis of word2vec's nonlinear functional.
result Word2vec may be primarily driven by spectral method.
We analyze DMs using spectral methods to design effective noise schedules.
problem Lack of theoretical foundation for synthesis process decisions in DMs.
method Introduced a frequency response perspective based on Gaussianity assumption.
result Proposed a spectral transfer function to understand DM inference process.
Study spectral analysis on lens spaces, proving isospectral lens spaces with prime order fundamental groups.
problem Spectral analysis of the Kohn Laplacian on lens spaces.
method Analog of Weyl's law and isospectral lens spaces with prime order fundamental groups.
result Two 3D lens spaces with prime order fundamental groups are isospectral with respect to the Kohn Laplacian if and only if they are CR isometric.
The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to accommodate most of the existing spectral graph techniques as a consequence of …
Novel spectral embedding considers node weights for graph analysis.
problem Graph node importance quantification.
method Normalized Laplacian eigenvectors for low-energy configurations.
result Weighted embeddings improve graph configurations.
This paper provides theoretical guarantees for spectral clustering using graph cuts.
problem Lack of performance guarantees for spectral clustering.
method Convex relaxation of graph cuts, spectral proximity condition, algebraic connectivity, inter-cluster connectivity.
result Deterministic bounds for successful spectral clustering are derived.
Spectral simplicial theory improves feature selection for complex data.
problem Complex data sets and high-dimensional feature spaces require efficient feature selection methods.
method Extends spectral techniques to abstract simplicial complexes, incorporating topological data analysis.
result Spectral simplicial methods provide a unified approach for feature selection in multi-modal genomic data.
Study magnetic Schrödinger operators in Euclidean space.
problem Semiclassical spectral analysis of magnetic Schrödinger operators.
method Spectral problems for Bochner-Schrödinger operator on manifolds.
result Survey and describe ideas of proofs for magnetic Schrödinger operators.
Develops a new approach to spectral asymmetry using microlocal analysis.
problem Spectral asymmetry on 3-manifolds.
method Constructs an asymmetry operator using microlocal analysis.
result The asymmetry operator generalizes the eta invariant and contains spectral asymmetry information.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
Paper proposes a new method for sparse spectral clustering on Stiefel manifold.
problem Sparse spectral clustering on Stiefel manifold with nonsmooth and nonconvex objective.
method Proposes a manifold proximal linear method (ManPL) to solve the original SSC formulation.
result Demonstrates the advantage of ManPL over existing methods on single-cell RNA sequencing data.
Paper develops a method for estimating spectral density matrices in high-dimensional time series.
problem Estimating spectral density matrices in high-dimensional time series.
method Thresholded versions of averaged periodograms for regularized estimation.
result Consistent estimation of spectral density matrices possible under high-dimensional regime.
New methods avoid spectral pollution in transfer operators for accurate analysis.
problem Spectral pollution in finite-dimensional approximations of transfer operators.
method Algorithms for computing spectral properties of transfer operators without spectral pollution.
result Accurate spectral estimation across various applications, including protein folding models.
BSD is a Bayesian framework for analyzing neural spectral data.
problem Challenges in statistical analysis and group-level comparisons of neural power spectra.
method Bayesian Spectral Decomposition (BSD) for parametric models of neural spectra.
result BSD outperforms existing methods in model selection and parameter estimation.
This work analyzes how different layers in deep neural networks contribute to generalization error.
problem Understanding the role of each layer in deep neural networks for generalization.
method Spectral analysis, Neural Tangent Kernel, Hermite polynomials, Spherical Harmonics.
result Initial layers in deep neural networks have a larger bias towards high-frequency functions.
A new metric measures saturation of neural network layers.
problem Analyzing the quality of latent representations in neural networks.
method Layer Saturation metric based on spectral analysis.
result Saturation is related to generalization and predictive performance.
The paper analyzes how sampling design affects machine learning model generalization.
problem The impact of sampling properties on machine learning model generalization.
method Spectral analysis of the generalization error in Euclidean space using Fourier analysis.
result Estimation of expected error bounds and convergence rates for various sampling patterns.
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
We prove that spherical spectral analysis and synthesis hold in Damek-Ricci spaces and derive two-radius theorems.
The paper studies spectral analysis on complex spaces and finds explicit formulas for eigensections.
problem Understanding eigensections on complex projective spaces and Grassmannians.
method Using creation and annihilation operators, converting higher energy eigensections to lower energy holomorphic sections.
result Explicit formulas for the dimension of higher-level eigensections on Pn. SR-GANs combat mode collapse in GANs by monitoring and compensating spectral distributions.
problem Mode collapse in GANs.
method Spectral regularization (SR-GANs) to combat spectral collapse.
result SR-GANs prevent mode collapse and outperform SN-GANs in experiments.
We identify spectral conditions for reliable neural probe interpretation.
problem Unreliable performance of linear probes in interpreting neural representations.
method Formalized Spectral Identifiability Principle (SIP) based on eigengap and Fisher error.
result Reliability of neural probes depends on the eigengap relative to Fisher estimation error.
Paper proposes a fully data-driven method for Koopman spectral analysis.
problem Manual preparation of nonlinear observables is often required for Koopman spectral analysis.
method Learning Koopman invariant subspaces from observed data using linear least-squares regression.
result Performance evaluated using nonlinear dynamical systems and applications.
Paper tackles functional linear regression using spectral algorithms with discrete observations.
problem Functional linear regression problem with discretely observed data.
method Combines distributed spectral algorithms with Sobolev kernels for regularization.
result Derives matching upper and lower bounds for convergence in Sobolev norm.
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and der…
Spectral methods predict long-term signals from linear and nonlinear systems.
problem Forecasting temporal signals from linear and nonlinear systems with arbitrary sampling.
method Introduces a spectral algorithm for linear signals and extends it to nonlinear systems using Koopman theory.
result The spectral methods achieve high accuracy in forecasting and uncertainty quantification.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Spectral methods simplify data analysis, improving accuracy and stability.
problem Extracting meaningful information from noisy, incomplete data.
method Eigenvalues and eigenvectors of matrices constructed from data.
result Spectral methods are effective and can be analyzed using modern statistical theory.
A theory of feature geometry using spectral analysis of weight matrices.
problem Current methods decompose neural network activations into sparse linear features, losing geometric structure.
method Develops a theory by analyzing the spectra of weight-derived matrices, introducing the frame operator.
result Features collapse onto single eigenspaces, organizing into tight frames, and admit discrete classification.
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity…
CNNs outperform standard chemometric methods for spectral data classification.
problem Reducing the need for pre-processing steps in spectral data analysis.
method Convolutional neural networks (CNNs) compared with SVMs and PLSR for classification and regression of spectral data.
result CNNs outperform standard chemometric methods, especially for classification tasks.
We study topological recursion on the irregular spectral curve xy2−xy+1=0, which produces a weighted count of dessins d'enfant. This analysis is then applied to topological recursion on the spectral curve xy2=1, which takes the place of the Airy curve x=y2 to describe asymptotic behaviour of enumerative proble…
A novel 3D shape registration method using spectral graph embedding and probabilistic matching.
problem Challenges in 3D shape analysis and registration, especially with large variability.
method Combining spectral graph matching with Laplacian embedding for large graphs, using commute-time embedding and PCA.
result A method to register shapes with different samplings and isometric deformations.