This work improves group data analysis using modified tensor decompositions.
problem Improving group data analysis models for better signal modeling.
method Introduces a new generalization of block tensor decomposition for group data analysis.
result Demonstrates improved performance in multilabel classification and clustering tasks.
BT-Nets simplify DNNs by reducing parameter count.
problem Redundancy in DNN weights limits deployment to resource-constrained environments.
method Replaces FC-layers with BT-layers using block term decomposition.
result BT-layers achieve high compression ratios while maintaining performance.
This paper improves fMRI analysis by modeling higher-order tensors.
problem Ineffective tensor-based methods in spatially folded fMRI data.
method Higher-order Block Term Decomposition (BTD) applied to 4 or 5 order tensors.
result Demonstrated effectiveness of BTD in fMRI analysis through simulations.
Compact RNNs reduce parameters and improve efficiency.
problem High computational cost of RNNs with large inputs.
method Block-Term Tensor Decomposition (BT-TD) to reduce RNN parameters.
result BT-RNN achieves better accuracy and faster convergence than standard RNNs.
A new probabilistic BTD method for tensor data.
problem Modeling higher-order tensors with robust inference.
method Probabilistic Block-Term Decomposition using variational Bayesian inference and von-Mises Fisher distribution.
result The proposed pBTD can quantify multi-linear structures robustly.
P-moves connect different 3-manifold decompositions.
problem Connecting different 3-manifold decompositions.
method Using P-complex and Morse 2-functions, we show P-moves between pants-block decompositions.
result Any two pants-block decompositions are related by a finite sequence of P-moves.
MONet learns to decompose scenes into meaningful components without supervision.
problem Learning meaningful scene decompositions without labeled data.
method MONet combines a VAE and recurrent attention network to learn decompositions of 3D scenes.
result MONet can learn to represent 3D scenes into meaningful components like objects and background.
This paper improves SVD for recommender systems using block-based matrix factorization.
problem Scalability and performance issues in recommender systems.
method Block-based Singular Value Decomposition (BMF) for matrix factorization.
result BMF paired with SVD enhances performance and scalability.
Core-Halo solves large-scale fixed-point problems by decentralizing updates.
problem Large-scale fixed-point equations with block dependencies.
method Core-Halo decomposition separates write ownership from read-only context, aligning with block-dependence structure.
result Core-Halo achieves near-centralized performance while retaining parallelism.
Efficient algorithm for Bayesian estimation from few samples, focusing on community detection.
problem Bayesian estimation problems, especially community detection in graphs.
method Meta-algorithm based on low-degree polynomials, semidefinite programming, and tensor decomposition.
result Best recovery guarantees for community detection in sparse stochastic block models and mixed-membership stochastic block models.
Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection f…
Paper compares optimization methods for sparse NCP decomposition of tensors.
problem Efficiently extract meaningful nonnegative and sparse components from tensors.
method Sparse NCP decomposition with l1-norm regularization and block coordinate descent.
result Comparison of optimization methods for tensor decomposition effectiveness and speed.
New method for geodesics of multivariate normals, derived from a Toda lattice.
problem Computing geodesics of multivariate normal distributions.
method Using block Cholesky decomposition and a natural Riemannian submersion, a new Toda lattice type Lax pair is derived.
result A new Toda lattice type Lax pair derived from geodesics and block Cholesky decomposition.
Unified framework for coupled tensor completion improves recovery accuracy.
problem Improving recovery accuracy in coupled tensor completion.
method Unified framework using tensor ring (TR) decomposition with shared latent factors and novel optimization model.
result The proposed method achieves superior recovery accuracy on real-world data compared to state-of-the-art methods.
TGCCA analyzes higher-order tensors using orthogonal rank-R CP decomposition.
problem Handling higher-order structures in multi-block data analysis.
method Tensor Generalized Canonical Correlation Analysis (TGCCA) with orthogonal rank-R CP decomposition.
result TGCCA outperforms state-of-the-art methods on simulated and real data.
Algorithm determines spatial graph isomorphism with vertex, edge colorings and orientations.
problem Algorithmic recognition of spatial graphs with various colorings and orientations.
method Proved existence of an algorithm for isomorphic spatial graphs, decomposed into canonical blocks, and applied Haken and Matveev's result.
result Algorithmic recognition of spatial graphs with colorings and orientations.
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result, we then propose penalty decomposition methods for general rank minimization pro…
Tensor method robustly decomposes tensors with sparse perturbations.
problem Robust tensor decomposition under block sparse perturbations.
method Non-convex iterative algorithm alternating low-rank CP decomposition and hard thresholding.
result Proves convergence to globally optimal solution under natural conditions.
New method improves MAP inference efficiency and reliability.
problem Efficient inference in systems with latent variables or missing data.
method Generalized dual decomposition on a convex decomposition bound.
result Framework converges monotonically and is faster/reliable than previous methods.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
problem Nonlinear spiked random matrix models with rank-one signal and noise.
method Signal-plus-noise decomposition and phase transition analysis.
result Identified precise phase transitions in signal components at critical thresholds.
Develops a new model to better predict corporate bond yields.
problem Persistent shifts in interest rates undermine single-regime models.
method Regime-switching generalized CIR model with two-state short-rate process and credit factors.
result The model improves joint curve fit and delivers interpretable probabilities.
Proposes BHT-ARIMA for forecasting multiple short time series.
problem Forecasting multiple short time series with mutual correlations.
method Block Hankel tensors, Tucker decomposition, generalized tensor ARIMA.
result Improves forecasting accuracy and reduces computational cost.
Diagrammatic approach to Springer fibers for types C and D.
problem Understanding Springer representations on fiber homology.
method Topological construction and diagrammatic description of Weyl and component group actions.
result Decomposition of Springer representations into irreducibles and presentations of cohomology rings.
New algorithm approximates large matrices by sampling column blocks, reducing overhead.
problem Approximating large matrices using limited row or column sampling.
method Sampling predefined blocks of columns, providing guarantees for approximation quality.
result Effective algorithm for distributed matrix approximation, demonstrated with real-world biometric data.
New method optimizes MAP inference for structured problems.
problem Structured energy minimization problems
method Proximal bundle method with block-coordinate Frank-Wolfe
result Empirically outperforms state-of-the-art algorithms
We show that for every spherical category $\C$ with invertible dimension, the Turaev-Viro TQFT admits a splitting into blocks which come from an HQFT, called the Turaev-Viro HQFT. The Turaev-Viro HQFT has the classifying space $B\grad$ as target space, where $\grad$ is a group obtained from the category $\C$. This cons…
This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a manifold constructed from these blocks must be hyperbolic. The main application…
The study develops methods to summarize team passing strategies from soccer data.
problem Modeling spatial passing networks across multiple games with varying positions.
method Multiresolution tensor decomposition and Poisson nonnegative block term decomposition.
result Automatic production of network motifs at different levels of detail.
The one-term distributive homology was introduced by J.H.Przytycki as an atomic replacement of rack and quandle homology, which was first introduced and developed by R.Fenn, C.Rourke and B.Sanderson, and J.S.Carter, S.Kamada and M.Saito. This homology was initially suspected to be torsion-free, but we show in this pape…
We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…
TWIST algorithm detects communities in multi-layer networks with tensor decomposition.
problem Community detection in multi-layer networks with multiple node-modality relationships.
method Tensor-based TWIST algorithm for global/local node and layer memberships.
result Accurate community detection with small misclassification error as network size increases.
The article develops a method to learn sparse and low rank PARAFAC decomposition robust to noise.
problem Learning sparse and low rank PARAFAC decomposition for tensors with missing values.
method Bayesian model with elastic net regularization, efficient algorithms for large scale problems.
result The method finds true rank and sparse factor matrix robust to noise.
Study handles in 3D shapes, applies to material patterns.
problem Understanding 3D shapes through handlebody decompositions.
method Introduced handlebody decompositions, showed stability, applied to materials.
result Stable equivalence of handlebody decompositions in 3-manifolds.
Paper studies randomized spectral clustering for large-scale networks.
problem Computational challenges in large-scale network community detection.
method Randomized sketching algorithms for spectral clustering.
result Theoretical bounds for approximation, misclassification, and link probability estimation.
New solutions found for elliptic systems with mixed couplings.
problem Existence of fully nontrivial solutions to elliptic systems with mixed couplings.
method Study of fully nontrivial solutions to the system with mixed couplings in a bounded or unbounded domain.
result New existence and multiplicity results of fully nontrivial solutions.
LazySVD improves SVD decomposition speed and efficiency.
problem Efficiently computing the first k singular vectors of a matrix.
method LazySVD framework using block Krylov method, variance-reduction stochastic method, and accelerated alternating minimization.
result Faster gap-free method and first accelerated stochastic method.
A method reduces dimensionality for multi-block data, enhancing feature extraction and classification accuracy.
problem Tractable feature extraction from large-scale, multi-dimensional data.
method Common and individual feature extraction from multi-block data structures using tensor decompositions.
result Significant reduction in dimensionality and enhanced accuracy in feature extraction and classification.
New algorithms accelerate solving nonlinear matrix decomposition with ReLU.
problem Nonlinear matrix decomposition with ReLU function.
method Two new algorithms: A-NMD and 3B-NMD, with adaptive extrapolation and block parametrization.
result Effective algorithms accelerate solving ReLU-NMD problems.
In a previous work arXiv:0903.4512, we have built an homotopical Turaev-Viro invariant and an HQFT from the universal graduation of a spherical category. In the present paper, we show that every graduation (G,p) of a spherical category $\C$ defines an homotopical Turaev-Viro invariant $HTV_{\C}^{(G,p)}$ and an HQFT $…
MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…
Study finds conditions for operator fields to be in strictly upper triangular form in small dimensions.
problem Jordan-Chevalley decomposition for operator fields in small dimensions.
method Tensorial conditions and proof of conjecture for higher order brackets.
result Proves Tempesta-Tondo conjecture for higher order brackets.
FreDN separates trends and periodicities in non-stationary time series forecasts.
problem Spectral entanglement and computational burden in frequency-domain methods for non-stationary time series.
method FreDN introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain, and uses a ReIm Block to reduce complexity.
result FreDN outperforms state-of-the-art methods by up to 10% on long-term forecasting benchmarks.
Sparse spectral decomposition identifies overlapping communities in networks.
problem Estimating overlapping community memberships in networks where nodes can belong to multiple communities.
method Sparse principal subspace estimation with iterative thresholding.
result The fixed point of the algorithm corresponds to correct node memberships under the stochastic block model.
Paper analyzes spectral clustering for large graphs using random signals.
problem Complex eigen decomposition for large graphs.
method Graph filtering of random signals for approximate spectral embedding.
result Consistency of spectral clustering in stochastic block model.
Study on determinants of unitary Brownian motion and their asymptotic laws.
problem Understanding determinants of unitary Brownian motion and their behavior over time.
method Using Stiefel fibration and skew-product decomposition of the Stiefel Brownian motion.
result Prove asymptotic laws for determinants of block entries of unitary Brownian motion.
A novel algorithm converges for solving a specific matrix decomposition problem.
problem Nonlinear matrix decomposition with ReLU function for sparse data.
method Introduced a reparametrization of the Latent-RMD model and developed eBCD for convergence proof.
result eBCD converges and outperforms state-of-the-art methods on various data sets.
Simple optimization method for Poisson likelihood models.
problem Optimizing Poisson likelihood models with non-Lipschitz continuity.
method Saddle point reformulation, gradient-based optimization, randomized block-decomposition.
result Gradient-based optimization with O(1/t) convergence rate for large-scale problems. Homogeneous links were introduced by Peter Cromwell, who proved that the projection surface of these links, that given by the Seifert algorithm, has minimal genus. Here we provide a different proof, with a geometric rather than combinatorial flavor. To do this, we first show a direct relation between the Seifert matrix…