Union of Subspaces (UoS) is a popular model to describe the underlying low-dimensional structure of data. The fine details of UoS structure can be described in terms of canonical angles (also known as principal angles) between subspaces, which is a well-known characterization for relative subspace positions. In this pa…
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48 results for “Subspace Detection Property”
New algorithms improve community detection and parameter estimation for PABM.
problem Improving community detection and parameter estimation for PABM.
method Connecting PABM to GRDPG, constructing new algorithms, and deriving asymptotic properties.
result Absolute number of community detection errors tends to zero as graph vertices increase.
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.
Paper improves -SSC for noisy data by proving SDP and proposing Noisy-DR--SSC.
problem Noisy data and less restrictive subspace affinity in sparse subspace clustering.
method Proposes Noisy-DR--SSC, which projects data onto a lower dimensional space and then applies noisy -SSC.
result Theoretical guarantee on the correctness of noisy -SSC in terms of SDP on noisy data.
We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace detection problem is more challenging because of the intertwined signal dimensions. We s…
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.
Detects domain shifts in datasets using interpretable feature subspaces.
problem Detecting subtle differences in dataset probability distributions.
method Localised density anomaly detection in high-dimensional feature spaces.
result Extracts interpretable feature subspaces for domain shifts.
Perturbations in the Orthogonal Complement Subspace for Efficient Out-of-Distribution Detectionstat.ML
P-OCS detects OOD samples in a low-dimensional subspace, outperforming existing methods.
problem Efficient OOD detection for deep learning models in open-world environments.
method P-OCS operates in the orthogonal complement of the principal subspace, applying a single projected perturbation.
result P-OCS achieves state-of-the-art OOD detection with negligible computational cost and without requiring model retraining.
Detect anomalies in complex networks using topological subspace detectors.
problem Detect anomalies in complex networks defined by simplicial complexes.
method Formulate a hypothesis testing framework using Neyman-Pearson matched topological subspace detectors.
result Effective detection of anomalies in foreign currency exchange networks and other real-world data.
Anomaly detection has numerous applications and has been studied vastly. We consider a complementary problem that has a much sparser literature: anomaly description. Interpretation of anomalies is crucial for practitioners for sense-making, troubleshooting, and planning actions. To this end, we present a new approach c…
Many computer vision tasks involve processing large amounts of data contaminated by outliers, which need to be detected and rejected. While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guar…
Soft and subspace robust multivariate rank tests based on entropy regularized optimal transportstat.ML
Paper extends multivariate rank tests for robust subspace detection.
problem Testing distributional similarity in multivariate data.
method Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport.
result Trade-off between detection power and false alarm rate via projections.
A discriminative approach for finding and characterizing positivity violations using decision treesstat.ML
The assumption of positivity in causal inference (also known as common support and co-variate overlap) is necessary to obtain valid causal estimates. Therefore, confirming it holds in a given dataset is an important first step of any causal analysis. Most common methods to date are insufficient for discovering non-posi…
Rare data in a large-scale database are called outliers that reveal significant information in the real world. The subspace-based outlier detection is regarded as a feasible approach in very high dimensional space. However, the outliers found in subspaces are only part of the true outliers in high dimensional space, in…
We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder …
Discrete return (DR) Laser Detection and Ranging (Ladar) systems provide a series of echoes that reflect from objects in a scene. These can be first, last or multi-echo returns. In contrast, Full-Waveform (FW)-Ladar systems measure the intensity of light reflected from objects continuously over a period of time. In a c…
We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like minimum covaria…
Paper analyzes singular subspace estimation in noisy matrix models.
problem Estimating low-rank signals in noisy matrix data.
method Asymptotic distributional theory, extreme value theory, saddle point approximation, random matrix theory.
result Plug-in test statistic based on two-to-infinity norm has higher power for detecting structured alternatives.
Due to diverse nature of data acquisition and modern applications, many contemporary problems involve high dimensional datum $\x \in \R^\d$ whose entries often lie in a union of subspaces and the goal is to find out which entries of $\x$ match with a particular subspace $\sU$, classically called \emph {matched subspace…
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 consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm intr…
Proposes a new algorithm to estimate invariant subspaces across multilayer networks.
problem Estimating invariant subspaces across heterogeneous multiple networks.
method Bias-corrected joint spectral embedding algorithm that recursively calibrates diagonal bias and iteratively updates the subspace estimator.
result Established entrywise subspace perturbation bound and entrywise eigenvector central limit theorem for the algorithm.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal component methods, namely online moving window robust principal component analysis (OMW…
We briefly review recent progress in techniques for modeling and analyzing hyperspectral images and movies, in particular for detecting plumes of both known and unknown chemicals. For detecting chemicals of known spectrum, we extend the technique of using a single subspace for modeling the background to a "mixture of s…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of dimensionality' phenomenon. Therefore, dimensionality reduction methods are applied to the…
A new model classifies surface anomalies in 3D point cloud data.
problem Accurate classification of surface anomalies in manufacturing processes.
method Deep subspace learning approach for 3D point cloud data.
result The method effectively identifies new types of anomalies.
Sturm theory applied to symplectic geometry and mechanics.
problem Detecting geometric properties of solutions in symplectic geometry and mechanics.
method Generalization of symplectic Sturm theory to Hamiltonians and application to semi-Riemannian manifolds and singular Lagrangian systems.
result Detection of conjugate and focal points on semi-Riemannian manifolds and geometrical properties of solutions space.
Adversarial attacks have always been a serious threat for any data-driven model. In this paper, we explore subspaces of adversarial examples in unitary vector domain, and we propose a novel detector for defending our models trained for environmental sound classification. We measure chordal distance between legitimate a…
This paper investigates differentially private analysis of distance-based outliers. The problem of outlier detection is to find a small number of instances that are apparently distant from the remaining instances. On the other hand, the objective of differential privacy is to conceal presence (or absence) of any partic…
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.
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.
New method learns subspace affinity function for scalable and inductive clustering.
problem Scaling and inductiveness of self-expressiveness methods for high-dimensional data.
method Siamese neural network architecture for metric learning.
result Model scales to larger datasets and clusters out-of-sample data.
Paper proposes CLAIR for efficient LLM fine-tuning across clients.
problem Fine-tuning large language models (LLMs) efficiently and collaboratively.
method Federated LoRA fine-tuning with Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR).
result CLAIR achieves better performance and contamination detection compared to local fine-tuning.
iSearch uses innovation directions for robust PCA and outlier detection.
problem Robust PCA and outlier detection in data with outliers.
method iSearch uses innovation directions to compute optimal data points and identify outliers.
result iSearch provides robust PCA and outlier detection with performance guarantees.
The stable 4-genus of knotsmath.GT
The stable 4-genus of a knot K in 3-space is the limiting value of g_4(nK)/n, where g_4 denotes the 4-genus and n goes to infinity. This induces a seminorm on CQ, the concordance group tensored with the rational numbers. Basic properties of the stable genus are developed, as are examples focused on understanding the un…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data po…
The paper finds Koopman invariant subspaces using personalized PageRank.
problem Selecting a finite dictionary of observables for Koopman-invariant span.
method Exploiting zero-block structure in EDMD matrices and applying PageRank.
result Personalized PageRank can detect Koopman invariant subspaces.
A novel PP algorithm using GMMs and GAs for detecting informative structures.
problem Detecting informative structures in multivariate datasets.
method Gaussian mixture models (GMMs) and Genetic Algorithms (GAs) for optimal projection.
result The approach effectively detects informative structures in multivariate datasets.
WPCA improves subspace recovery robustness to outliers.
problem Improving subspace recovery in the presence of outliers.
method Winsorized PCA (WPCA) with theoretical analysis of accuracy and robustness.
result WPCA provides consistent subspace recovery from contaminated data.
In an era of ubiquitous large-scale streaming data, the availability of data far exceeds the capacity of expert human analysts. In many settings, such data is either discarded or stored unprocessed in datacenters. This paper proposes a method of online data thinning, in which large-scale streaming datasets are winnowed…
KPCA improves OoD detection by separating InD and OoD data.
problem Insufficiency of PCA in detecting OoD data from InD data.
method Kernel PCA (KPCA) with task-specific kernels.
result KPCA achieves superior OoD detection performance.
Framework detects out-of-distribution inputs in regression and survival analysis.
problem Limited OOD detection for regression and survival analysis.
method Model-aware and subspace-aware variable prioritization.
result Consistent improvements over existing methods in synthetic and real data.
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.
Improved spectral method recovers sparse vectors in random subspaces.
problem Recovering a sparse vector in a random subspace with sub-Gaussian entries.
method Improved spectral method with leave-one-out analysis.
result Spectral method recovers sparse vectors with high probability under certain conditions.
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are assumed unknown. We propose a simple low-complexity subspace clustering algorithm, w…
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.
We discuss an "extrinsic" property of knots in a 3-subspace of the 3-sphere to characterize how the subspace is embedded in . Specifically, we show that every knot in a subspace of the 3-sphere is transient if and only if the exterior of the subspace is a disjoint union of handlebodies, i.e. regular neighbor…