arXiv research

New method unifies and formalizes data partitioning using a single vector.

Study shows generative priors improve rank-one matrix recovery with optimal sample complexity.

Convex optimization method recovers low-rank matrices from rank-one projections efficiently.

This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.

Paper shows no spurious local minima in a specific matrix factorization problem.

We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm conve…

We consider worker skill estimation for the single-coin Dawid-Skene crowdsourcing model. In practice, skill-estimation is challenging because worker assignments are sparse and irregular due to the arbitrary and uncontrolled availability of workers. We formulate skill estimation as a rank-one correlation-matrix completi…

Improved stability for matrix recovery from rank-one measurements.

We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The algorithm we propose first uses the geometric assumption to obtain an exact clus…

Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.

SON-NMF estimates nonnegative rank on-the-fly for NMF.

The paper develops algorithms for Boolean matrix factorization using IP and heuristics.

Study shows how fast a specific matrix completion method works.

We consider the decomposition of a compact-type symmetric space into a product of factors and show that the rank-one factors, when considered as totally geodesic submanifolds of the space, are isolated from inequivalent minimal submanifolds.

Rank-one measurements limit feasible sets for low-rank PSD matrices.

Proposes a new model for image restoration combining deep learning and total variation.

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$ columns and a …

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …

Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.

Algorithm recovers factors of rank-1 matrices from noisy measurements.

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous theoretical analysis. We show that the proposed algorithms enjoy linear convergence a…

Novel algorithm for Markov decision processes using rank-one approximation.

New algorithms improve rank one signal estimation from noisy data.

Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best possible approximation of $M$ according to some metric. In this paper, we study th…

We formulate and solve a tensor model using a latent-variable approach.

Study robust recovery of low-rank matrices from corrupted measurements without rank prior.

Estimates the probability of a random symmetric tensor being close to rank-one.

Non-negative matrix factorization (NMF) approximates a non-negative matrix $X$ by a product of two non-negative low-rank factor matrices $W$ and $H$. NMF and its extensions minimize either the Kullback-Leibler divergence or the Euclidean distance between $X$ and $W^T H$ to model the Poisson noise or the Gaussian noise.…

Study on signal-plus-noise decomposition in nonlinear spiked random matrices.

Paper proposes a tensor model for clustering noisy multi-view data.

Study on tensor signal estimation from incomplete data.

Estimates rank-one spikes from heavy-tailed noise using self-avoiding walks.

AMP method reconstructs rank-one matrices from noisy data efficiently.

We show that S-arithmetic lattices in semisimple Lie groups with no rank one factors are quasi-isometrically rigid.

Item recommendation is the task of predicting a personalized ranking on a set of items (e.g. websites, movies, products). In this paper, we investigate the most common scenario with implicit feedback (e.g. clicks, purchases). There are many methods for item recommendation from implicit feedback like matrix factorizatio…

New methods estimate covariance for matrix data without assuming fixed size or specific distributions.

New insights into compact rank-one ECS manifolds, proving they are bundles over circles.

New method solves matrix completion problems to certifiable optimality.

We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does no…

This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.

Study linear perturbations of Spin(7) metrics, finding only rank one nilpotent matrices.

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization method for stable recovery of low-rank matrices in the noisy case. The procedure is…

M4L-JMF tackles multi-typed objects learning, improving on M3L.

New algorithms detect and estimate rank-one signals with prior directional information.

The digital revolution of the banking system with evolving European regulations have pushed the major banking actors to innovate by a newly use of their clients' digital information. Given highly sparse client activities, we propose CPOPT-Net, an algorithm that combines the CP canonical tensor decomposition, a multidim…

Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least squares regression, canonical-correlation analysis and Fisher discriminant analysis. R…

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the go…

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…