Related papers: Multi-Subspace Matrix Recovery from Permuted Data

Many machine learning problems encode their data as a matrix with a possibly very large number of rows and columns. In several applications like neuroscience, image compression or deep reinforcement learning, the principal subspace of such…

Modern data sets, such as those in healthcare and e-commerce, are often derived from many individuals or systems but have insufficient data from each source alone to separately estimate individual, often high-dimensional, model parameters.…

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…

The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is…

This paper considers the problem of clustering a collection of unlabeled data points assumed to lie near a union of lower-dimensional planes. As is common in computer vision or unsupervised learning applications, we do not know in advance…

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

The most important purpose of this article is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by matrix methods. To this end, first we obtain more structures of the canonical…

Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including $\ell_1$ and nuclear norm minimization as well as…

We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…

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…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…

A multivariate dataset consists of $n$ cases in $d$ dimensions, and is often stored in an $n$ by $d$ data matrix. It is well-known that real data may contain outliers. Depending on the situation, outliers may be (a) undesirable errors which…

In this paper, we explore the theoretical properties of subspace recovery using Winsorized Principal Component Analysis (WPCA), utilizing a common data transformation technique that caps extreme values to mitigate the impact of outliers.…

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

Modern inference and learning often hinge on identifying low-dimensional structures that approximate large scale data. Subspace clustering achieves this through a union of linear subspaces. However, in contemporary applications data is…

With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…

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…

We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…