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.
We present a framework for supervised subspace tracking, when there are two time series xt and yt, one being the high-dimensional predictors and the other being the response variables and the subspace tracking needs to take into consideration of both sequences. It extends the classic online subspace tracking work…
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.
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.
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. …
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.
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.
Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same time, working with incomplete (partly observed) large scale datasets has recent…
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.
Online detection of abrupt changes in high-dimensional data streams.
problem Detecting abrupt changes in high-dimensional, streaming data with multiple subspaces.
method Dynamic sparse subspace learning approach with multiple structural change-point model, Bayesian information criterion for penalty coefficients selection, and Pruned Exact Linear Time algorithm.
result Effectiveness demonstrated through simulation and real gesture data studies.
Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and internet-of-things. To reduce the communication, sensing and storage complexity, t…
Study quotients of curve complex actions by mapping class group.
problem Understanding actions of mapping class group on curve complex quotients.
method Cone off uniformly quasi-convex subspaces to form symmetric curve sets, non-maximal train track sets, and compression body disc sets. Analyze actions of mapping class group on these quotients.
result Actions of mapping class group on quotients are strongly WPD, non-elementary, and have infinite diameter.
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated with desired accuracy. Nevertheless, inherent to the nonparametric nature of kernel…
This handbook simplifies Grassmann manifold geometry for matrix-based algorithms.
problem Modeling linear subspaces in various applications.
method Expository work on Grassmann manifold geometry, including new algorithms and formulas.
result Improved understanding and computational tools for the Grassmann manifold.
Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found applicati…
New method tracks evolving data metrics.
problem Nonstationary changes in data constraints.
method Online Convex Ensemble StrongLy Adaptive Dynamic Learning (OCELAD).
result Significant performance improvements and robustness.
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a low-rank least-squares problem, and we prove that, under broad sampling conditions,…
A new method for efficiently updating large-scale matrices in real-time.
problem Updating large-scale matrices with evolving data in real-time.
method Incremental SVD approach that handles row/column appends, rank-1 updates, and refresh strategies.
result Incremental SVD achieves accuracy close to full SVD with a fraction of the computational cost.
Reduces memory costs for developing countries by replacing images with text.
problem High memory costs associated with multimodal webpages in developing countries.
method Canonical Correlation Analysis (CCA) to replace high-cost modality (images) with low-cost modality (text).
result Reduces memory costs by at least 83.35% through eye-tracking experiments.
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenge…
RapidPT accelerates permutation testing in neuroimaging by reducing runtime.
problem Significant computational burden in voxel-wise analysis.
method Exploits low-rank structure of permutation testing matrix for efficient recovery.
result Achieves substantial speedups (1.5x - 1000x) over existing methods.
This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the dimensionality of the data, so that a large number of observations are collected after the t…
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
problem Private approximation of symmetric matrices with Gaussian noise.
method Viewing Gaussian noise as Dyson Brownian Motion to track eigenvalue and eigenvector evolution.
result Improved bounds on Frobenius-distance utility for private matrix approximation.
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and adaptive control. A new point of view is offered for the constrained optimization prob…
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
problem Quantum corrections in 3d N=1 vacua from M-theory compactification.
method Use Higgs bundles to analyze 3d N=1 vacua and track corrections.
result Topological anomalies are robust and calculable in 3d effective field theory.
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed to contain multiple components such as (i) linear and nonlinear components, (ii)…
RL approach for target tracking with unknown dynamics and sensor control.
problem Tracking an unknown target with sensor control.
method Track-MDP formulation for RL, compared with POMDP.
result Optimal RL policy tracks all target paths with certainty.
This work uses SVM to identify track component failures in AC Track Circuits.
problem Detecting and identifying specific track component failures in AC Track Circuits.
method Applied SVM classifier to STDS track circuit data.
result Successfully classified 15 different track component failures.
New train tracks for complex homeomorphisms found.
problem Existence of irreducible train tracks for pseudo-Anosov homeomorphisms.
method Starting from a veering triangulation, identify and modify branches to bypass obstructions.
result Construction of invariant train tracks with irreducible transition matrix.
New method uses cluster shapes to improve track finding in particle collisions.
problem Combining timing and additional detector information for efficient track finding.
method Neural networks to analyze cluster shapes for track seeding.
result Cluster shapes reduce fake combinatorial backgrounds while maintaining high track efficiency.
Value-tracking in financial markets breaks down when non-valuation-based traders dominate.
problem Understanding the threshold for value-tracking in financial markets.
method Simple discrete-time model to show how non-valuation-based traders can cause tracking errors.
result A threshold above which value-tracking breaks down without changes in asset value.