Reconstruction based subspace clustering methods compute a self reconstruction matrix over the samples and use it for spectral clustering to obtain the final clustering result. Their success largely relies on the assumption that the underlying subspaces are independent, which, however, does not always hold in the appli…
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48 results for “matrix reconstruction”
3d-SMRnet speeds up MPI system matrix recovery to 1 minute with high quality.
problem Slow system matrix recovery in MPI due to recalibration.
method 3d-System Matrix Recovery Network using deep learning.
result 3d-SMRnet recovers 3d system matrix with 64x subsampling in 1 minute.
We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-no…
Graph filtering improves data reconstruction performance.
problem Data reconstruction and dimensionality reduction.
method Formulate data tasks as graph filtering operations, optimize mean-square error cost involving adjacency matrix, update filters via gradient descent.
result Better reconstruction performance of novel method compared to PCA.
3-manifold triangulation can be reconstructed from its intersection matrix.
problem Reconstructing the triangulation of 3-manifolds from their intersection matrix.
method Using the intersection matrix of a simplicial complex to determine the triangulation of a 3-manifold up to isomorphism.
result The intersection matrix is sufficient to determine the triangulation of a 3-manifold up to isomorphism.
A1GM method improves efficiency in reconstructing missing data using KL divergence.
problem Efficiently reconstructing missing data in matrices.
method Fast non-gradient-based rank-1 NMF using KL divergence.
result A1GM outperforms gradient methods in efficiency with competitive reconstruction errors.
Paper proposes a new method for fast matrix completion.
problem Challenges in matrix completion, especially for images with heterogeneous data.
method Sparse reverse of principal component analysis.
result The method efficiently reconstructs matrices with missing data.
New method reconstructs network topology from node-dynamics data.
problem Reconstructing network topology from time-resolved observations of node-dynamics.
method Feature ranking using Random forest and RReliefF to rank node importance.
result Method is robust to various system parameters and depends on dynamical regime.
Boosts neural network performance by improving weight separability.
problem Improving the separability of weight vectors in neural networks.
method Proposes a new evaluation metric and feed-backward reconstruction loss to encourage weight separability.
result Improves visual recognition performance across various tasks.
We develop a method to factorize symmetric sparse Boolean matrices efficiently.
problem Finding a symmetric factorization of a given matrix into a sparse, Boolean matrix.
method Polynomial-time algorithm based on bootstrapping higher-order information and tensor decomposition.
result A matrix with full column rank can be recovered with high probability when the matrix size is sufficiently large.
We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank , has positive bounded entries, and the graph $\mathcal{G…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…
We develop latent variable models for Bayesian learning based low-rank matrix completion and reconstruction from linear measurements. For under-determined systems, the developed methods are shown to reconstruct low-rank matrices when neither the rank nor the noise power is known a-priori. We derive relations between th…
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
problem Optimal model structure reconstruction from weighted colored graph adjacency matrix.
method Uses prize-collecting Steiner tree algorithm to reconstruct minimum spanning tree.
result Demonstrates the effectiveness of the prize-collecting Steiner tree algorithm for model structure reconstruction.
We introduce a new family of matrix norms, the "local max" norms, generalizing existing methods such as the max norm, the trace norm (nuclear norm), and the weighted or smoothed weighted trace norms, which have been extensively used in the literature as regularizers for matrix reconstruction problems. We show that this…
PACE-GGM uses Gaussian mechanism for private covariance estimation.
problem Private estimation of covariance matrices in high dimensions.
method Data-adaptive selection of entries, Gaussian mechanism, maximum-entropy reconstruction.
result Consistent improvements in estimation error compared to Gaussian mechanism and baselines.
New model reconstructs networks by identifying regular components.
problem Uncovering the complexity of network structures.
method Low-rank pursuit based self-representation network model.
result Reconstructs networks and measures their regulability.
Paper recovers multi-subspace matrices from permuted data.
problem Recovering a multi-subspace matrix from permuted data with corrupted columns.
method Four-stage algorithm pipeline: outlier identification, subspace reconstruction, outlier classification, unsupervised sensing.
result The pipeline provides theoretical guarantees for reliable multi-subspace matrix recovery.
This article gives matrix factorizations for the trivalent diagrams and double line appearing in quantum link invariant. These matrix factorizations reconstruct Khovanov-Rozansky homology. And we show that the Euler characteristic of the matrix factorization for a double loop equals the quantum dimens…
Random Fourier Features reduce kernel matrix reconstruction error without dimensionality dependence.
problem Error reduction in kernel matrix reconstruction for high-dimensional data.
method Random Fourier Features with theoretical error bounds.
result Error probability is independent of data dimensionality.
Study uses ML to reconstruct stock market sentiment from trading data.
problem Reconstructing underlying sentiment states from stock price behavior.
method Applied Hidden Markov Models and Recurrent Neural Networks.
result Recovered sentiment states from observed stock price behavior.
ME-Net defends neural nets against adversarial attacks by reconstructing images.
problem Adversarial attacks on deep neural networks.
method ME-Net uses matrix estimation to preprocess images, destroying adversarial noise while preserving global structure.
result ME-Net consistently outperforms state-of-the-art defenses on various benchmarks.
Paper proposes a method to break symmetries in Bayesian matrix factorization.
problem Symmetries in posterior distribution reduce MCMC sampling efficiency.
method Modification to Gaussian prior mean and covariance to break symmetries.
result Breaking symmetries leads to lower autocorrelation and reconstruction errors.
A new method for feature selection in high-dimensional data.
problem Dealing with noise and high-dimensional data in unsupervised feature selection.
method Sparse PCA via -norm regularization, combined with an efficient optimization algorithm.
result The proposed method effectively selects features from real-world data sets.
The paper explores how kernel eigenalignments affect generalization in KRR.
problem Achieving robust generalization in kernel methods.
method Direct connection between generalization and matrix eigenvectors/eigenvalues, focusing on finite-sample settings.
result Strong generalization requires increasing eigenvector alignment, eigenvalue magnitude, or gaps between eigenvalues.
Study on tensor signal estimation from incomplete data.
problem Estimating a rank-one tensor signal from noisy, incomplete data.
method Reduction to random matrix model for spectral analysis.
result Loss of performance due to incomplete data.
Fetal ECG (FECG) telemonitoring is an important branch in telemedicine. The design of a telemonitoring system via a wireless body-area network with low energy consumption for ambulatory use is highly desirable. As an emerging technique, compressed sensing (CS) shows great promise in compressing/reconstructing data with…
New quantum state reconstruction method accelerates convergence.
problem Quantum state reconstruction for larger systems.
method Momentum-Inspired Factored Gradient Descent (MiFGD) combining compressed sensing, non-convex optimization, and acceleration.
result Converges to true density matrix at an accelerated linear rate, provably close to the true matrix.
Selective sampling improves matrix completion with known structure.
problem Reconstructing a low-rank matrix with incomplete data.
method Designing observation sets based on matrix structure and selective sampling.
result Improved reconstruction accuracy with selective sampling.
New method improves efficiency of non-convex matrix reconstruction.
problem Reconstructing a low-rank matrix from few linear measurements.
method Factorized gradient descent with spectral initialization.
result Non-convex approaches can match the sample complexity of convex methods.
New algorithm predicts missing matrix entries using side information, outperforming existing methods.
problem Learning a partially observed matrix with side information.
method Mixed-projection ADMM algorithm for optimization.
result Our algorithm achieves 2.3% lower objective value and 41% lower reconstruction error than benchmarks.
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. More…
Paper proposes a new model for robust feature extraction.
problem Developing a robust method for feature representation.
method Double Denoising Auto-Encoders (DDAEs) model, using corruption and reconstruction on both input and hidden representation.
result The proposed model achieves better robustness and feature learning than state-of-the-art models.
Noiseless linear estimation results are found to be universal across various structured matrices.
problem Reconstructing a vector from linear projections with noiseless data.
method Development of message passing methods to analyze the l1 transition and optimal Bayesian reconstruction.
result The l1 transition and optimal Bayesian reconstruction are universal across various structured matrices.
New iterative solvers speed up Gaussian process regression with derivatives.
problem Scaling Gaussian process regression with derivatives for high-dimensional problems and large budgets.
method Iterative solvers using fast matrix-vector multiplications and pivoted Cholesky preconditioning.
result Bayesian optimization with derivatives can now scale to high-dimensional problems and large evaluation budgets.
A machine-learning approach solves CS data reconstruction for structural health monitoring.
problem Optimal solution for sparse optimization in compressive sensing.
method Formalizing CS data reconstruction as a supervised-learning task, using l1-norm regularization and a multi-neuron layer.
result High reconstruction accuracy achieved by the machine learning-based approach.
UA-LQE improves value function learning by selectively erasing uncertain entries in Q-matrix.
problem Improving value function learning in complex reinforcement learning tasks.
method Uncertainty-aware low-rank Q-matrix estimation (UA-LQE) algorithm.
result UA-LQE selectively erases uncertain entries in Q-matrix to improve value function approximation.
Let M be a random (alpha n) x n matrix of rank r<<n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(rn) observed entries with relative root mean square error RMSE <= C(rn/|E|)^0.5 . Further, if r=O(1), M can be reconstructed ex…
OnAIR reconstructs dynamic images from sparse measurements online.
problem Reconstructing dynamic images from limited or corrupted measurements.
method Online adaptive reconstruction using sparsity and low-rank models with dictionary learning.
result Memory-efficient online algorithms for sequential estimation of dictionary and images.
We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix . This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix rec…
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…
Simpler method for separating and manipulating latent attributes in autoencoders.
problem Separating and manipulating latent attributes in autoencoders.
method Matrix subspace projection
result Our method allows for changing selected attributes while preserving other information.
Robust SPA improves NMF robustness to outliers.
problem Non-robustness to outliers in SPA.
method Integrates outlier robustness and data fitting into SPA.
result RSPA is robust to outliers and maintains low-noise robustness.
Study exact limits of matrix reconstruction from noisy projections.
problem Reconstructing matrices from linear projections with high-dimensional data.
method Asymptotic analysis, universality properties, and generalized linear models.
result Exact asymptotic equations for optimal learning performance.
Optimal estimation of low-rank matrices from contaminated data.
problem Reconstructing a low-rank matrix from a contaminated version of itself.
method Developed an asymptotically optimal algorithm to estimate the original matrix from the singular values of the contaminated matrix.
result Found an explicit signal-to-noise cutoff below which estimation fails.
A method extracts binary features directly from CS measurements for compressive image classification.
problem Efficiently classify images using compressive sensing without reconstruction.
method DCT-based approach for binary feature extraction from CS measurements, feature fusion with CNN features.
result Fused features outperform state-of-the-art methods in image classification.
APGD algorithm reconstructs point set from partial distance measurements.
problem Reconstructing point set configuration from partial Euclidean distance measurements.
method Asymmetric Projected Gradient Descent (APGD) for EDMC problem.
result Global convergence and exact recovery with observations.