New method estimates sparse eigenvectors without sacrificing orthogonality.
problem Estimating sparse eigenvectors of a symmetric matrix.
method Developed a new method using MM framework and Procrustes reformulation.
result Improves support recovery and explained variance compared to existing methods.
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous (i.e. corresponding to each other), as far as possible, and the Procrust…
Alternative method proposed to avoid Procrustes in regularized MVA.
problem Optimizing regularized MVA solutions while preserving feature uncorrelation.
method Solves an eigenvalue problem instead of the Procrustes approach.
result Ensures preservation of feature uncorrelation in regularized MVA.
We solve a key problem in cross-lingual learning using a novel approach.
problem Aligning word embeddings across different languages.
method We devise a direct solution to the Wasserstein-Procrustes problem.
result Our method improves existing UCL approaches significantly.
Method preserves correlations in synthetic data.
problem Preserving dependence structure of original data.
method Orthogonal Procrustes problem for restoring Pearson correlation.
result Restores Pearson correlation structure while preserving feature distributions and downstream tasks performance.
We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al, 2000)). The measure also serves as a natural tool when choosing dimension-reduction …
A new method for computing shape barycenters from point clouds using Procrustes-Wasserstein distance.
problem Computing representative shapes from point clouds with precise alignment and shape preservation.
method Developed a new distance metric (Procrustes-Wasserstein) and algorithms for computing barycenters.
result Superior performance in precise alignment and shape preservation compared to existing OT approaches.
Extends metrics for SPD matrices to infinite dimensions.
problem Lack of generalized forms for Riemannian metrics.
method Unitized Hilbert-Schmidt operators and extended Mahalanobis norm.
result Improved performance in high-dimensional comparisons.
Paper proposes a KGE framework that reduces training time and carbon footprint.
problem Efficient KGE learning with reduced computational cost and environmental impact.
method Full batch learning, Orthogonal Procrustes Analysis, non-negative-sampling training.
result Significant reduction in training time and carbon footprint compared to state-of-the-art approaches.
Researchers mapped clinical jargon to consumer language using embeddings alignment.
problem Mapping and translating clinical jargon to consumer language for better communication.
method Trained embeddings on clinical and consumer language corpora, aligned them using Procrustes algorithm, and refined with adversarial training.
result Procrustes algorithm effectively aligned clinical and consumer language embeddings.
Study matches two noisy point clouds with geometric transformations and relabeling.
problem Matching two noisy point clouds with orthogonal transformations and relabeling.
method Information-theoretic results and Ping-Pong algorithm for computational alignment.
result The Ping-Pong algorithm retrieves the planted signal after one step.
Solves a fundamental problem in statistics and imaging with new methods.
problem Generalized Orthogonal Procrustes Problem (GOPP)
method Semidefinite relaxation (SDR) and generalized power method (GPM)
result GPM converges linearly to the global minimizer under large signal-to-noise ratio.
Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.
problem Recovering permutations of high-dimensional Gaussian vectors with constant correlation.
method Computing and comparing weighted counts of specially chosen wide trees.
result Polynomial-time algorithm for exact recovery at constant correlation.
The paper provides robustness bounds for manifold learning techniques.
problem Understanding the robustness of manifold learning methods.
method Derives perturbation bounds for Procrustes, Classical Scaling, and Trilateration.
result Performance bounds for Isomap, Landmark Isomap, and Maximum Variance Unfolding are derived.
New method visualizes brain activity changes over time.
problem Understanding representational dynamics in neural responses.
method Procrustes-aligned Multidimensional Scaling (pMDS) on RDM movies.
result Multidimensional scaling alignment captures representational dynamics.
New algorithm reduces sample and computational complexities for matrix completion.
problem Recovering a rank-r matrix from n features. method Gradient-based non-convex optimization algorithm with linear convergence rate.
result Linear sample complexity and logarithmic computational complexity.
A new algorithm reduces communication in distributed SVD by p factors.
problem Efficiently compute SVD in distributed systems.
method LocalPower algorithm with weighted aggregation and periodic decay of iterations.
result Reduces communication cost by a factor of p. LDLE embeds manifolds in lower dimensions with low distortion.
problem Embedding manifolds in lower dimensions with low distortion.
method Constructs local views using global eigenvectors of the graph Laplacian, registers them using Procrustes analysis, and tears manifolds apart for intrinsic dimension embedding.
result LDLE preserves distances up to a constant scale with low distortion.
Novel method detects changes in noisy dynamic networks.
problem Change detection in noisy dynamic networks with sparsity and degree heterogeneity.
method Adapted Procrustes analysis to embedded points for vertices in spectral embedding.
result CDP successfully detects various types of vertex-based changes.
A new method for aligning datasets without known correspondences.
problem Aligning datasets from different domains without labeled correspondences.
method Integrates MDS and Wasserstein Procrustes for joint optimization of embeddings and correspondences.
result Maps datasets to a common low-dimensional space without labeled correspondences.
New method aligns word embeddings without supervision.
problem Aligning word embeddings trained on monolingual data.
method Wasserstein Procrustes approach with orthogonal and permutation matrices.
result Obtains state-of-the-art results in unsupervised word translation.
New measures link neural representation geometry to decoding ability.
problem Understanding how neural representations relate to decoding ability.
method Showed that popular similarity measures can be interpreted from a decoding perspective.
result Proved that measures like CKA and CCA quantify alignment between optimal linear readouts.
Deep model predicts shapes of curves with multiple covariates.
problem Predicting shapes of planar curves with various covariates.
method Deep learning model using complex-valued functions, conditional covariance smoother with modality-specific encoders.
result Model accurately predicts shapes of curves with multimodal covariates.
We have observed an interesting, yet unexplained, phenomenon: Semidefinite programming (SDP) based relaxations of maximum likelihood estimators (MLE) tend to be tight in recovery problems with noisy data, even when MLE cannot exactly recover the ground truth. Several results establish tightness of SDP based relaxations…
Proposes BONMI for integrating noisy matrices from multi-source data.
problem Integrating noisy matrices from multi-source data with block-wise missingness.
method Exploits orthogonal Procrustes problem to align eigenspaces and completes missing blocks.
result Statistical rate for eigenspace of underlying matrix comparable to independently missing assumption.
We reformulate linear systems into stochastic problems for faster solutions.
problem Efficiently solving linear systems with stochastic methods.
method Developed a family of reformulations into stochastic problems, analyzed algorithms with global linear convergence rates.
result Found parameters leading to a sufficiently small condition number for faster solutions.
The paper introduces metrics for robust unsupervised learning of vehicle interactions.
problem Robust representation learning of temporal dynamic interactions in robotics.
method Geometric approach using Procrustes distance and optimal transport for comparing interaction distributions.
result Metrics for assessing stability and comparing interaction learning algorithms.
Reformulated Markov's conjecture in combinatorial terms.
problem Markov's uniqueness conjecture in integral necklaces.
method Geometric reformulation and combinatorial description.
result Explicitly described set of lengths on modular torus.
Modified Wasserstein metric for Gaussian distributions, invariant to isometries.
problem Distance measurement for latent Gaussian distributions invariant to isometries.
method Modified Benamou-Brenier approach leading to a Procrustes Wasserstein metric.
result For Gaussian distributions, the metric reduces to Euclidean distance between eigenvalues.
Robustly computes intrinsic coordinates on point clouds using resampling and averaging.
problem Computing intrinsic coordinates on noisy or outlier-prone point clouds.
method Subsample data, vary hyperparameters, cluster candidate embeddings, identify representative embeddings, and average them using Procrustes analysis.
result Robust to noise and outliers, validated on synthetic and real data.
A method for efficient reinforcement learning query reformulation.
problem Efficiently learn diverse strategies for query reformulation.
method A framework with specialized sub-agents and a meta-agent trained on full data.
result Improved generalization performance and diversity of reformulation strategies.
A new framework improves solving mixed-integer convex problems with binary indicators.
problem Optimizing mixed-integer convex problems with binary indicators controlling continuous variables.
method Coordinate Optimality Reformulation (CORe) framework, incorporating coordinate-wise optimality information.
result CORe reformulations improve branch-and-bound performance, especially in sparse and structured settings.
After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample and similar counterexamples in the light of the reformulated conjecture.
Reformulates RBM for unified linear and nonlinear dimensionality reduction.
problem Traditional RBM limitations in handling both linear and nonlinear data.
method Reformulates RBM using MAP and EM, introduces deterministic CD algorithm.
result Reformulated RBM can outperform PCA in nonlinear dimensionality reduction.
We reformulate LIPs as min-max problems for easier solution.
problem Recovering signals from few linear measurements.
method Proposed a min-max reformulation of LIPs.
result Saddle points characterize solutions to LIPs.
Proposes a method to align language and image data.
problem Aligning language and image data for better understanding.
method Uses triplet loss to learn consistent embeddings of language and images.
result Outperforms four baselines across multiple metrics.
Virtual index cocycles reformulate virtual link invariants.
problem No specific problem stated; focuses on reformulation.
method Using virtual index cocycles to reformulate invariants.
result Unified reformulation of virtual link invariants.
In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigat…
DNNs with L2 regularization reveal feature learning dynamics and sparsity.
problem Understanding feature learning in DNNs with L2 regularization. method Reformulating loss in terms of layerwise activations and covariances.
result Proving sparsity of local minima in L2-regularized DNNs. Reformulated sigma models for complex Grassmannians using Gross-Neveu formalism.
problem Classical aspects of N=(2,2) supersymmetric sigma models with Hermitian symmetric target spaces. method Reformulation using Gross-Neveu formalism, proposing two types of equivalent Lagrangians.
result Proposed two types of equivalent Lagrangians for maximal isotropic Grassmannians, making either supersymmetry or geometry manifest.
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
Python package for SPD matrix distances, reproducible and extensible.
problem Computing distances between SPD matrices for various applications.
method Unified, extensible framework supporting multiple SPD metrics.
result Reproducible and accessible SPD matrix comparison tool.
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
The paper reformulates an invariant and calculates it for lens spaces.
problem Classifying lens spaces using an invariant.
method Reformulation of an invariant and calculation for lens spaces.
result The invariant Δ(M,ω) is calculated for lens spaces. Quaternionic reformulation simplifies surface curvature theory.
problem Prescribed extrinsic curvature of surfaces.
method Quaternionic reformulation of Labourie's theory.
result Simpler proofs and higher-dimensional generalization.
Paper tackles SMPC for linear systems with unknown noise distribution.
problem Stochastic MPC for linear systems with chance state constraints and unknown noise distribution.
method Reformulate chance constraints, design robust benchmark SMPC, and develop adaptive SMPC with online noise statistics learning.
result Adaptive SMPC guarantees time-uniform satisfaction of unknown reformulated state constraints with high probability.
The paper explores handlebody versions of various diagram algebras.
problem None explicitly stated, but related to algebraic structures.
method Study of handlebody versions of classical diagram algebras and reformulation of cellular algebras.
result All mentioned algebras are part of the reformulated cellular algebra theory.
Study reformulates Finsler metrizability problems using geodesic invariance.
problem Finsler metrizability problems for sprays.
method Reformulate problems in terms of geodesic invariance of tensors (metric and angular).
result Gyroscopic sprays have geodesically invariant angular metric.