arXiv research

Paper shows affine constraint is unnecessary for high-dimensional data.

Study shows how varying levels of supervision and orthonormality constraints affect generalization errors in subspace fitting.

Dual SVM training with budget constraint for faster accuracy.

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…

Abstract Morse index theorem applied to various optimization problems.

Novel factorization for low-rank matrices in subspaces, improving efficiency.

The paper analyzes SSC on compressed data and sets success conditions.

Unified framework for structured principal subspace estimation with bounds and rates.

Study on robustness of subspace learning from adversarial modifications.

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from "undersampling" due to complexity and speed con…

SIG model identifies invariant variables for MSDA with fewer domain constraints.

A new method clusters multi-view data by sharing a common trace-norm of coefficient matrices.

Paper proposes a new approach for multi-view subspace clustering.

Active learning improves subspace clustering with less labeled data.

In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column outliers, we reformulate the batch mode matrix $L_{2,1}$ norm minimization with…

ALPCAH improves PCA for noisy data samples.

Physics-informed neural networks improve by measuring effective dimensionality of constraints.

The study reveals non-homotopy equivalent subspaces of curves with curvature constraints.

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from unde…

DKLM learns adaptive kernels for robust nonlinear subspace clustering.

A new algorithm for decentralized learning in heterogeneous networks reduces sub-optimality over time.

Matrix rank minimizing subject to affine constraints arises in many application areas, ranging from signal processing to machine learning. Nuclear norm is a convex relaxation for this problem which can recover the rank exactly under some restricted and theoretically interesting conditions. However, for many real-world …

New boundary and point constraints for controlling conformal surfaces.

Agents learn locally, converge globally in online learning with kernels.

Adaptive tensor modeling preserves continuity in multidimensional data.

Survey of algorithms for PCA and subspace tracking with missing data.

Proposes new $\ell_0$-based methods for low-rank sparse subspace clustering.

I construct an algebraic model for a typical fiber on a 1+1 dimensional spacetime. The vector space comprising the fiber is composed of elements formed from the direct product of two copies of an element x in the D2=C2xC2 finite group algebra over the real numbers. The fiber contains subspaces whose elements are associ…

New method clusters multi-view data by squeezing hybrid knowledge.

Paper derives normal approximations for singular subspaces with i.i.d. noise.

Nonnegative matrix factorization (NMF) with group sparsity constraints is formulated as a probabilistic graphical model and, assuming some observed data have been generated by the model, a feasible variational Bayesian algorithm is derived for learning model parameters. When used in a supervised learning scenario, NMF …

New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.

A new geometry-preserving method for interpreting compositional data.

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

New algorithms optimize matrix manifolds, converging faster than existing methods.

The paper proposes a method to balance fairness and prediction accuracy by adjusting data representations.

LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.

Adaptive probabilistic PCA adapts complexity with varying subspaces.

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in a variety of contexts it has been observed that solving the non-convex problem d…

Paper introduces Eden bracket for nonholonomic systems.

Recent work in distance metric learning has focused on learning transformations of data that best align with provided sets of pairwise similarity and dissimilarity constraints. The learned transformations lead to improved retrieval, classification, and clustering algorithms due to the better adapted distance or similar…

LineBO tackles high-dimensional Bayesian optimization by solving 1D subproblems.

Eigen-decomposition simplifies quadratic programming with equality constraints.

PLUMAGE improves large model training efficiency and stability.

Tree-based method selects features from high-dimensional datasets with memory constraints.

This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the…

Paper proposes clustering algorithms for data from Union of Polyhedral Cones model.