Flow Matching models help generative models stay within the subspace of real data.
problem How do generative models stay within the subspace of real data?
method Flow Matching models using a learned velocity field to transform a simple prior into a complex target distribution.
result Generated samples memorize real data points and represent the sample data subspace exactly.
New research shows SSC fails when points on the same subspace are mislabeled.
problem Failure of SSC when points on the same subspace are mislabeled.
method Analyzed the effect of different distributions of points on the same subspace.
result SSC fails to infer correct labels when points on the same subspace fall into more than one cluster.
New algorithm clusters 2D data like images from multilinear subspaces.
problem Clustering 2D data like images from multilinear subspaces.
method Developed Multilinear Subspace Clustering (MSC) algorithm.
result MSC algorithm performs competitively with UOS models in clustering performance.
This paper covers robust subspace learning and tracking methods.
problem Learning and tracking subspaces in the presence of outliers.
method Robust PCA, Robust Subspace Tracking, Robust Subspace Recovery.
result Effective methods for handling outliers in subspace learning and tracking.
Study extends matrix completion under clustered subspaces, impacting subspace clustering.
problem Improving matrix completion under clustered subspaces for big-data applications.
method Extends recent results on matrix completion under subspaces, focusing on non-disjoint or independent clusters.
result Direct implications for subspace clustering with missing data.
GPS model predicts subspace-valued functions efficiently.
problem Accurate and efficient prediction of subspace-valued functions.
method Gaussian Process Subspace regression (GPS) model, using multivariate Gaussian distributions on Euclidean space.
result GPS provides accurate, smooth predictions with uncertainty quantification.
A new method for anomaly detection using random subspaces and Gaussian mixture models.
problem Anomaly detection in high-dimensional data.
method Statistical estimation of probability density using random subspaces combined with geometric averaging.
result The method achieves competitive AUC scores and is interpretable.
Improves RL learning speed by leveraging subspace generalization.
problem Slow learning in RL due to limited state-space generalization.
method Model-based RL method using subspaces to enhance learning speed.
result MoBLeS improves learning speed in early trials through subspace generalization.
DCFSC uses a simple auto-encoder for subspace clustering without parameters.
problem Subspace clustering for large-scale high-dimensional datasets.
method Closed-form shallow auto-encoder for data-driven self-expressive layer, no parameters or optimization.
result Significant memory benefits over existing methods on large datasets.
Theoretical guarantees for STE, a robust subspace recovery method.
problem Recovering a low-dimensional subspace from corrupted data.
method Subspace-constrained Tyler's estimator (STE) with initialization conditions.
result STE can effectively recover the subspace under certain conditions.
Paper uses random projection to preserve subspace structure for efficient data analysis.
problem Efficiently analyzing data with low-dimensional structure.
method Compressed Subspace Learning (CSL) framework based on Johnson-Lindenstrauss property.
result Random projection preserves the UoS structure of data, enabling efficient analysis.
Paper explores tradeoffs in classification using tensor subspaces.
problem Supervised classification with sample, computation, and storage complexities.
method Use of tensor subspaces, particularly hierarchical Kronecker structured subspaces.
result Hierarchical Kronecker structured subspaces improve classification tradeoffs.
GMM with constrained component means in pre-selected subspaces for classification and clustering.
problem Efficiently modeling data with constrained component means in subspaces.
method EM-type estimation algorithm, weighted PCA, multiple kernel densities, maximum likelihood selection.
result Subspace containing component means also contains modes and class means, leading to improved classification/clustering.
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…
Paper models dynamic multivariate functional data with sparse subspace learning.
problem Complex, high-dimensional multivariate functional data with evolving cross-correlations.
method Sparse subspace learning for automatic subspaces formulation and cross-correlation dynamics description.
result Efficient estimation and feature extraction of multivariate functional data.
Stochastic Sparse Subspace Clustering improves subspace clustering by reducing over-segmentation through dropout.
problem Over-segmentation in subspace clustering.
method Introducing dropout regularization to enforce denser connections between points from the same subspace.
result Stochastic Sparse Subspace Clustering effectively handles large datasets and reduces over-segmentation.
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric structure of the clusters …
Kernel models learn low-dimensional predictive subspaces from input data.
problem Learning effective feature transformations in kernel models.
method Study of a compositional kernel ridge regression model.
result Global minimizers of the objective function identify the subspace with high probability.
Bayesian methods reduce variance in subspace identification for small data sets.
problem High variance in traditional subspace identification methods for large models or small sample sizes.
method Investigation of Bayesian estimation solutions (regularized and shrinkage estimators) for subspace identification.
result Bayesian estimators reduce estimation risk by up to 40% compared to traditional methods.
New forms of symmetric shift-invariant subspaces found for harmonic maps.
problem Understanding harmonic maps into symmetric and k-symmetric spaces. method Imposing a symmetry condition on shift-invariant subspaces of a Hilbert space.
result Obtained new general forms for symmetric shift-invariant subspaces and extended solutions.
Paper develops a method to identify minimal sample subspaces from limited data.
problem Challenging task of subspace segmentation with minimal sample subspaces.
method Develops a theoretical framework and optimization algorithms for MSS.
result The MSS model can retrieve minimal sample subspaces even when they are heavily intersected.
New method estimates active subspaces for jump-discontinuous functions.
problem Estimating active subspaces for discontinuous functions like ABMs.
method Extending active subspaces to discontinuous functions, using Gaussian process.
result Identifies important parameters in ABM simulations of refugee movement.
A new model reduces noise and speeds up subspace segmentation.
problem Subspace segmentation from noisy data.
method Group norm regularized factorization model (GNRFM) with AALM algorithm.
result The method is faster and more robust to noise.
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…
Paper analyzes neural networks using active subspace for structural analysis and vulnerability, reducing model size and improving attacks.
problem Analyzing and reducing the complexity of neural networks.
method Active subspace method for measuring active neurons, network structure modification, and additive universal adversarial attack vector.
result ASNet achieves significant parameter and flops reduction, and improves universal adversarial attack performance.
Paper analyzes subspace clustering with missing data under UoS model.
problem Subspace clustering under missing data with UoS model.
method Deterministic analysis of conditions for clustering in two cases.
result Dual conditions for Case II provide perfect clustering under missing data.
New method discovers concepts in hidden feature layers using sparse subspace clustering.
problem Local attribution methods fail to identify coherent model behavior across samples.
method Sparse Subspace Clustering (SSCC) for concept discovery.
result Empirically validated method for various image classification tasks.
In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coefficients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active (i.e., …
Active learning improves subspace clustering with less labeled data.
problem Efficiently incorporating labeled data to improve subspace clustering models.
method Proposes an active learning framework for subspace clustering that queries informative points and updates the subspace model.
result Demonstrates the advantage of the proposed active strategy over state-of-the-art methods.
CSVAE learns interpretable latent subspaces for binary labels.
problem Learning interpretable latent representations correlated to specific labels.
method Conditional Subspace VAE (CSVAE) using mutual information minimization.
result CSVAE extracts interpretable latent subspaces for binary labels.
The paper analyzes SSC on compressed data and sets success conditions.
problem Analyzing SSC on compressed data.
method Formal analysis of SSC on dimensionality-reduced data.
result Established formal success conditions of SSC on dimensionality-reduced data.
Paper presents conditions for SSC success with missing data.
problem Determining success of SSC under missing data in UoS model.
method Two variants of SSC with zero-filling, providing deterministic conditions.
result Deterministic conditions for perfect clustering under various missing data patterns.
We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their correspondi…
Bayesian method for semi-structured models accounts for both types of uncertainty.
problem Lack of work on epistemic uncertainty in semi-structured regression models.
method Bayesian approximation with subspace inference for joint posterior sampling.
result Validated approach recovers structured effect posteriors and approaches full-space posterior.
Study explores GAN dynamics for high-dimensional subspace learning.
problem Subspace learning in high-dimensional datasets.
method Single-layer GAN model with multi-feature discriminators.
result GANs outperform conventional methods in capturing informative subspace.
New method uses word subspaces and term-frequency to improve text classification.
problem Lack of semantic meaning in bag-of-words features.
method Proposes word subspaces and term-frequency weighted word subspaces for text classification.
result Improved text classification performance compared to state-of-the-art algorithms.
Paper develops a method to identify feature subspaces contributing to local data complexity.
problem Identifying feature subspaces that contribute to local data complexity.
method Develops an estimator of Local Intrinsic Dimension (LID) along axis projections to identify feature subspaces.
result Preliminary evidence suggests LID decomposition can indicate axis-aligned data subspaces supporting cluster formation.
We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l_p-averaged distances of the sampled data points from any K subspaces. Under…
Extends active subspace analysis to infinite dimensions.
problem Dimension reduction in infinite dimensional functionals.
method Defines an operator for Hilbert space, extends Euclidean properties, proposes Monte Carlo procedure.
result Desirable properties extend to infinite dimensional setting.
Gradient descent mostly converges to a small subspace of eigenvectors.
problem Understanding the dynamics of gradient descent in deep learning.
method Analyzing the convergence of gradients in various deep learning scenarios.
result Gradient descent converges to a small subspace spanned by a few top eigenvectors of the Hessian.
Efficiently clusters millions of data points with learnable subspace clustering.
problem Large-scale subspace clustering with high-dimensional data.
method Develops a learnable subspace clustering paradigm using a parametric function and RPCM.
result Outperforms state-of-the-art methods in efficiency and effectiveness.
Framework for tracking high-dimensional predictors and responses.
problem Tracking high-dimensional predictors and responses in time series data.
method Online sufficient dimensionality reduction (OSDR) using alternating minimization and gradient descent on Grassmannian manifold.
result OSDR outperforms conventional unsupervised subspace tracking methods.
KSS method converges and recovers correct clustering under certain conditions.
problem Subspace clustering for semi-randomly sampled data.
method Local convergence analysis and recovery guarantee for KSS method.
result KSS method converges superlinearly and finds correct clustering within loglog N iterations.
Active sampling selects few points for accurate model reduction of high-fidelity systems.
problem Efficiently identify dominant subspaces for model reduction of large training sets.
method Proposes an active sampling strategy to select a few points from the training set to estimate dominant subspaces accurately.
result Active sampling can provide 17x speed-up without sacrificing accuracy.
Paper examines how principal angles affect subspace classification accuracy.
problem Determining the probability of misclassification in subspace models.
method Analyzes the geometry of subspaces and signal energy distribution to optimize principal angles.
result Optimizing principal angles leads to smaller classification error and superior accuracy.
RaSE ensemble framework improves sparse classification accuracy.
problem Sparse classification challenges in high-dimensional data.
method Random Subspace Ensemble (RaSE) framework with subspace selection via RIC.
result RaSE achieves low misclassification rates and accurate feature ranking.
New method for active subspace analysis reduces gradient evaluations needed.
problem Efficiently perform subspace sensitivity analysis on expensive or noisy functions.
method Develops acquisition functions for sequential learning of active subspaces using Gaussian process surrogate models.
result ASM estimator can be computed in closed form for Gaussian process surrogates, reducing need for finite differencing.
A new method for generative modeling of discrete data using geometric latent subspaces.
problem Learning generative models for discrete data with statistical dependencies.
method Geometric latent-subspace framework in exponential parameter space of product manifolds of categorical distributions.
result Low-dimensional latent space encodes statistical dependencies and accurately models high-dimensional discrete data.