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.
This work tackles phaseless subspace tracking, recovering time-varying signals from phaseless projections.
problem Recovering time-varying signals from phaseless linear projections under gradual subspace change.
method Dynamic subspace tracking approach, leveraging gradual subspace change over time.
result Demonstrates feasibility of phaseless subspace tracking with gradual subspace change.
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.
Online tensor subspace tracking algorithm for incomplete data.
problem Online subspace tracking of partially observed high-dimensional data.
method OLSTEC algorithm based on CP decomposition and recursive least squares.
result OLSTEC outperforms state-of-the-art algorithms in convergence rate.
Develops a new algorithm for robustly tracking data vectors in a subspace, even with outliers.
problem Tracking data vectors in a slowly changing low-dimensional subspace robustly against outliers.
method ReProCS-NORST, a recursive projected compressive sensing algorithm.
result Achieves a near optimal tracking delay of O(rlognlog(1/ε)). Fast robust subspace tracking in sparse data-dependent noise with near-optimal delay.
problem Robustly tracking time-varying subspaces in the presence of sparse outliers.
method Introduces a fast mini-batch robust ST solution under mild assumptions.
result Provably correct subspace tracking with near-optimal delay and same time complexity as simple PCA.
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations. GROUSE requires only basic linear algebraic manipulations at each iteration, and each subspace update can be performed in linear time in the dimension of…
This paper presents GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm), an efficient and robust online algorithm for tracking subspaces from highly incomplete information. The algorithm uses a robust l1-norm cost function in order to estimate and track non-stationary subspaces when the streaming data …
Proves subspace tracking with missing data and improves matrix completion.
problem Subspace tracking in the presence of missing data.
method Modified robust subspace tracking algorithm.
result Proves subspace estimates are close to true subspaces under mild assumptions.
New algorithm tracks subspaces with missing and corrupted data, simpler and federated.
problem Subspace tracking with missing and corrupted data.
method Proposes a novel algorithm that does not assume piecewise constant subspace changes and is simpler.
result Guarantees for both subspace tracking with missing data and outliers.
A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspa…
New algorithm tracks changing data subspaces with sparse outliers.
problem Tracking changing data subspaces in the presence of sparse outliers.
method Simple-ReProCS algorithm based on ReProCS framework.
result First guarantee for dynamic RPCA under weakened assumptions.
Survey of algorithms for PCA and subspace tracking with missing data.
problem Handling missing data in streaming Principal Component Analysis and subspace tracking.
method Review of classical and recent algorithms with low computational and memory complexities.
result Algorithms need careful adjustment for missing data.
Bicycle paths form geodesics in 3D subspaces, related to Kirchhoff rods.
problem Optimizing bicycle paths between two points.
method Variational equations and geometric analysis of bicycle paths.
result Bicycle geodesics are contained in 3D subspaces and relate to Kirchhoff rods.
Study shows how varying levels of supervision and orthonormality constraints affect generalization errors in subspace fitting.
problem Effects of varying levels of supervision and orthonormality constraints on generalization errors in subspace fitting.
method Flexible family of problems connecting unsupervised and supervised subspace fitting tasks, explored over a supervision-orthonormality plane.
result Generalization errors of subspace fitting problems follow double descent trends as they become more supervised and less orthonormally constrained.
Paper proposes efficient online data thinning for expert analysis.
problem Large-scale streaming data exceeds human analysis capacity.
method Online anomaly detection using dynamic low-rank Gaussian mixture models.
result Proposed method reduces data to unique elements for timely analysis.
Review of robust PCA and matrix completion methods.
problem Robust Principal Component Analysis and matrix completion with outliers.
method Various provably correct, fast, and practical solutions to RPCA and matrix completion.
result Exhaustive review of recent literature on RPCA and dynamic RPCA.
New framework tracks communities in dynamic networks.
problem Discovering and tracking communities in evolving networks.
method Spectral framework on Grassmann manifold for subspace tracking.
result Improved dynamic community detection results across various network types.
LASER compresses recursive model activations by exploiting their low-dimensional structure.
problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.
New method disentangles hidden data structures using HSIC and supervision.
problem Tackles the challenge of interpreting high-dimensional data.
method Supervised Independent Subspace Principal Component Analysis (sisPCA) using HSIC.
result Identifies and separates hidden data structures effectively.
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.
Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
problem Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
method Analyzing the behavior of memory-efficient optimizers like GaLore, which project gradients onto a rank-r subspace recomputed every T steps.
result Memory-efficient optimizers fail to track a subspace, leading to unpredictable model performance.
Many applications in data analysis rely on the decomposition of a data matrix into a low-rank and a sparse component. Existing methods that tackle this task use the nuclear norm and L1-cost functions as convex relaxations of the rank constraint and the sparsity measure, respectively, or employ thresholding techniques. …
Efficiently extracts features from large datasets using budgeted nonlinear subspace tracking.
problem Handling large-scale datasets with kernel-based methods while maintaining computational and memory efficiency.
method Low-rank, budgeted online subspace learning for feature extraction.
result Approximates high-dimensional features with a low-rank nonlinear subspace, leading to efficient kernel function approximation.
Geometric theory of projection heads in self-supervised learning.
problem Dimensional collapse and information invariance trade-off in projection heads.
method Geometric modeling of projection heads as Riemannian metrics, analyzing Hessian eigenvalues, and tracking optimization geometry.
result Smooth nonlinear heads induce negative curvature, preventing collapse; linear and ReLU heads cannot.
New architecture tracks objects in cluttered scenes without supervision.
problem Learning to track objects in large scenes with many objects.
method Spatially invariant computations and representations.
result Outperforms competing methods in tracking objects in cluttered scenes.
New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.
problem Inaccurate first principle models for complex systems due to data complexity.
method Bayesian prediction error bound for Gaussian process regression, derived from kernel-based data density.
result Achieves vanishing tracking error with increasing data density, providing time-varying accuracy guarantees.
Paper proposes S2ConvSCN for robust subspace clustering and classification.
problem Insufficient handling of nonlinear manifolds, data corruptions, and out-of-sample data.
method Self-supervised convolutional subspace clustering network (S2ConvSCN) with FC layer, CIM for robustness, and BD regularization. result Robust S2ConvSCN outperforms baseline on unseen data. Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subs…
We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jo…
Paper tackles anomaly detection in large-scale networks.
problem Inferring network-level anomalies from indirect link measurements.
method Online subspace tracking of Hankelized traffic tensor using Candecomp/PARAFAC decomposition and RLS algorithm for normal flows; outlier detection for abnormal flows.
result Proposed algorithm achieves faster convergence and better anomaly detection performance.
A new method generalizing subspace learning for improved classification.
problem Improving classification accuracy using subspace learning methods.
method Roweis Discriminant Analysis (RDA) which generalizes PCA, SPCA, and FDA.
result RDA and kernel RDA improve classification accuracy on benchmark datasets.
Develops an efficient online robust PCA method for big data.
problem Efficiency and robustness in processing big data with changing subspaces.
method Online moving window robust principal component analysis (OMWRPCA) with change point detection.
result Successfully tracks both slowly and abruptly changing subspaces and detects change points.
Proposes CMP method for reducing tensor object dimensions in binary classification.
problem Reduction of tensor object dimensions while maintaining class separability.
method Proposes Common Mode Patterns (CMP) method considering class labels.
result CMP method increases inter-class separability compared to MPCA.
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.
Proposes a new regularizer for semi-supervised learning on multilayer graphs.
problem Semi-supervised learning on multilayer graphs with labeled and unlabeled data.
method Generalized matrix mean regularizer and matrix-free numerical scheme.
result The regularizer outperforms state-of-the-art methods numerically.
Bayesian approach for online subspace learning from incomplete data.
problem Handling incomplete large-scale datasets for subspace learning.
method Online variational Bayes subspace learning with low-rank and sparsity constraints.
result The proposed algorithm outperforms state-of-the-art methods in estimation accuracy.
Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.
problem Need for basic methods in 3D action recognition.
method Roweisposes uses Roweis discriminant analysis for generalized subspace learning.
result Roweisposes is effective for 3D action recognition.
ProSub uses angles in feature space to classify data as in- or out-of-distribution.
problem Open-set semi-supervised learning with unknown classes.
method Probabilistic approach based on angles in feature space, estimating conditional distributions of scores.
result ProSub achieves state-of-the-art performance on benchmark problems.
End-to-end unsupervised MOT from videos.
problem Challenging online Multi-Object Tracking from videos.
method Differentiable neural model for tracking and animation, end-to-end learning.
result End-to-end learning of MOT from videos without labeled data.
DeepDA uses LSTM to track multiple targets in clutter.
problem NP-hard combinatorial optimization in multi-target tracking with clutter.
method LSTM-based deep learning for data association.
result Significant performance on association ratio, target ID switching, and time-consuming tracking.
New subspace methods resist limited adversary corruption on test instances.
problem Adversary can corrupt up to l features in test instances.
method Subspace voting techniques to transform algorithms.
result Significant fraction of voting hypotheses do not contain corrupt features.
Weakly-supervised RL identifies meaningful tasks, improving performance in complex environments.
problem Learning to efficiently explore and distinguish between meaningful and irrelevant tasks.
method Weak supervision to automatically disentangle meaningful tasks from a large space of nonsensical tasks.
result The learned subspace of meaningful tasks leads to substantial performance gains, especially in complex environments.
Neural network models of early sensory processing typically reduce the dimensionality of streaming input data. Such networks learn the principal subspace, in the sense of principal component analysis (PCA), by adjusting synaptic weights according to activity-dependent learning rules. When derived from a principled cost…
Detects changes in low-rank signals from high-dimensional data.
problem Detecting changes in low-rank signals from high-dimensional data.
method Sketching-based approach to reduce dimensionality; uses largest eigenvalue of sketch covariance matrices.
result Detects low-rank changes with high probability using sketching of high-dimensional observations.
V-SysId identifies keypoints and 3D system from unlabeled videos.
problem Identifying keypoints and 3D system from unlabeled videos.
method Alternates between parameter estimation and extrinsic camera calibration, using motion equations as weak supervision.
result Utility of the approach demonstrated across various settings.
A new method projects patterns into class subspaces for supervised dimensionality reduction.
problem Lack of a simple model for projecting patterns into a space defined by classes.
method Projects each class into a 1D subspace of the feature space, ensuring orthogonality and class discrimination.
result The approach guarantees class discrimination and optimizes the projection of features into class subspaces.
EXoN creates an explainable latent space for semi-supervised learning.
problem Creating an explainable latent space for semi-supervised learning.
method EXoN combines VAE with SCI (Soft-label Consistency Interpolation) to create an explainable latent space.
result EXoN reduces the cost of investigating representation patterns on the latent space.