arXiv research

New MCMC algorithm reduces subset selection passes to 2 for optimal $k$-dimensional subspace approximation.

One-pass algorithm finds small subset for $\ell_p$ subspace approximation with additive error.

A novel unsupervised feature selection method using subspace clustering and self-expressive model.

LOFT separates subspace rotation and transformation for orthogonal fine-tuning.

RaSE ensemble framework improves sparse classification accuracy.

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same subspace must be identified in order to obtain accurate estimates of the subspace s…

New method reduces high-dimensional data to key features.

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace containing the component means of a GMM with a common covariance matrix also conta…

Algorithm selects public datasets for private machine learning.

Paper proves noise-tolerant SSC using greedy methods under coherence conditions.

Sparse subspace clustering (SSC) is an elegant approach for unsupervised segmentation if the data points of each cluster are located in linear subspaces. This model applies, for instance, in motion segmentation if some restrictions on the camera model hold. SSC requires that problems based on the $l_1$-norm are solved …

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…

A new method for anomaly detection using random subspaces and Gaussian mixture models.

Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of sliced Wasserstein distances), solve the OT problem between these reduced measures, a…

Active sampling selects few points for accurate model reduction of high-fidelity systems.

New method clusters incomplete data by fusing subspaces.

Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on large-scale datasets as they require solving an expensive optimization problem and perfo…

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. We …

Orthogonal Matching Pursuit (OMP) plays an important role in data science and its applications such as sparse subspace clustering and image processing. However, the existing OMP-based approaches lack of data adaptiveness so that the data cannot be represented well enough and may lose the accuracy. This paper proposes a…

AdaSub optimizes with second-order info in low-dims subspace.

Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we propose a variation of the recently introduced thresholding-based subspace clustering…

Optimal smooth subspaces approximate large data sets efficiently.

A new method for faster optimization in high dimensions.

GPS model predicts subspace-valued functions efficiently.

The main contribution of the paper is a new approach to subspace clustering that is significantly more computationally efficient and scalable than existing state-of-the-art methods. The central idea is to modify the regression technique in sparse subspace clustering (SSC) by replacing the $\ell_1$ minimization with a g…

Improved Nyström approximation for kernel quadrature with theoretical guarantees.

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…

Paper extends multivariate rank tests for robust subspace detection.

We propose a conjugate gradient type optimization technique for the computation of the Karcher mean on the set of complex linear subspaces of fixed dimension, modeled by the so-called Grassmannian. The identification of the Grassmannian with Hermitian projection matrices allows an accessible introduction of the geometr…

High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover low-dimensional subspaces and address problems such as clustering, classification, subset sele…

SSVI efficiently trains sparse Bayesian neural networks with minimal compression and performance loss.

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 analyzes and improves GPSP algorithm for block sparse signal recovery.

CobBO optimizes expensive functions in high dimensions by using a two-stage kernel approach.

Sparse Subspace Clustering (SSC) is one of the most popular methods for clustering data points into their underlying subspaces. However, SSC may suffer from heavy computational burden. Orthogonal Matching Pursuit applied on SSC accelerates the computation but the trade-off is the loss of clustering accuracy. In this pa…

New algorithm reduces dimensionality in federated learning.

Proposes a neural network model to learn active subspaces and interpret important features.

New method clusters variables using robust nodewise regression.

Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature engineering method, Randomized Union of Locally Linear Subspaces (RULLS). We generat…

In the supervised high dimensional settings with a large number of variables and a low number of individuals, one objective is to select the relevant variables and thus to reduce the dimension. That subspace selection is often managed with supervised tools. However, some data can be missing, compromising the validity o…

In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a new approach for partitioning such high-dimensional data. Our assumption is that…

Paper introduces S-SSE for stable sparse subspace embedding.

Paper develops a consistent model selection framework for learning Hypotheses Space from data.

PAS method improves UDA by progressively refining subspaces for reliable pseudo-labels.

In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures corresponding to several classes or categories the data belongs to. In this paper, we…

The paper finds Koopman invariant subspaces using personalized PageRank.

A new method routes EEG covariance matrices across domains using adaptive subspace selection.

Paper proposes a new approach to Model Selection using a U-curve algorithm.