arXiv research

Paper bounds subspace estimator error from noisy projections.

Develops accelerated methods for optimization using low-dimensional projected-gradient information.

Paper introduces S-SSE for stable sparse subspace embedding.

Low-rank matrix regression refers to the instances of recovering a low-rank matrix based on specially designed measurements and the corresponding noisy outcomes. In the last decade, numerous statistical methodologies have been developed for efficiently recovering the unknown low-rank matrices. However, in some applicat…

New algorithm updates eigenvectors of evolving graphs efficiently.

Simpler method for separating and manipulating latent attributes in autoencoders.

A method for identifying joint and individual subspaces from multi-view data.

We describe ways to define and calculate $L_1$-norm signal subspaces which are less sensitive to outlying data than $L_2$-calculated subspaces. We focus on the computation of the $L_1$ maximum-projection principal component of a data matrix containing N signal samples of dimension D and conclude that the general proble…

A new method for Bayesian inference in high dimensions using projected Stein variational gradient descent.

This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The formula is neat and holds for deterministic matrix perturbations. Second, we calculate…

The paper updates SVD of evolving matrices using projection techniques.

Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image), efficiently determine the nearest subspace to the query in $\ell^1$ distance. In…

We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estima…

A new method compresses NLP networks by using multiple subspaces instead of a single one.

Paper proposes estimators for sparse PCA with oracle property.

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…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the leading eigenvectors of the covariance matrix. This projection can be used either…

We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the nu…

FSPA bypasses eigenvalue estimation for quantum PCA, achieving optimal complexity and robustness.

Proposes TS-NMF for 2D clustering, preserving spatial info.

Paper analyzes and improves GPSP algorithm for block sparse signal recovery.

Optimizes parameters in high-dimensional spaces for practical applications.

Survey of Laplacian-based methods for data dimensionality reduction and embedding.

A geometric analysis of the time series of returns has been performed in the past and it implied that the most of the systematic information of the market is contained in a space of small dimension. Here we have explored subspaces of this space to find out the relative performance of portfolios formed from the companie…

Investigates projections onto explicit subspaces and their variance effects.

Paper recovers multi-subspace matrices from permuted data.

Proposes MFPC for cross-manifold clustering.

A new method for clustering high-dimensional data into subspaces efficiently and accurately.

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. …

Solves kernel dimension reduction while making features interpretable.

This paper considers the problem of completing a matrix with many missing entries under the assumption that the columns of the matrix belong to a union of multiple low-rank subspaces. This generalizes the standard low-rank matrix completion problem to situations in which the matrix rank can be quite high or even full r…

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…

Study on robustness of subspace learning from adversarial modifications.

Adapts POD basis for parametric ROMs using pGP.

As an alternative to variable selection or shrinkage in high dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low dimensional linear subspace with minimal l…

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…

Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using for instance projections on random real lines, or a preliminary quantization of…

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

Paper proposes a clustering algorithm for nonnegative data.

Paper analyzes singular subspace estimation in noisy matrix models.

A method to visualize multidimensional local subspaces using implicit differentiation.

The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.

Research explores flat subspaces in complex projective manifolds using Okounkov bodies.

Unified theory and debiasing framework for random oblique projections in high dimensions.

A fast method for sparse PCA reduces computation time.

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accura…

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…

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from the typical assumption prevalent in the literature dealing with compression and r…