Related papers: Weighted Low-Rank Approximation of Matrices and Ba…
This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…
In this paper, we investigate the generalized low rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $$\underset{ rank(X)\leq k}{\min} \sum^m_{i=1}\left \Vert A_i - B_i XB_i^T \right \Vert^2_F,$$ where…
Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact…
Low rank matrix approximation is an important tool in machine learning. Given a data matrix, low rank approximation helps to find factors, patterns and provides concise representations for the data. Research on low rank approximation…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
In this paper, we look at the problem of cross-domain few-shot classification that aims to learn a classifier from previously unseen classes and domains with few labeled samples. Recent approaches broadly solve this problem by…
Model merging aims to combine multiple fine-tuned models into a single set of weights that performs well across all source tasks. While prior work has shown that merging can approximate the performance of individual fine-tuned models for…
Neural network-based function approximation plays a pivotal role in the advancement of scientific computing and machine learning. Yet, training such models faces several challenges: (i) each target function often requires training a new…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…
We propose a new learning to rank algorithm, named Weighted Margin-Rank Batch loss (WMRB), to extend the popular Weighted Approximate-Rank Pairwise loss (WARP). WMRB uses a new rank estimator and an efficient batch training algorithm. The…
Learning representations of nodes in a low dimensional space is a crucial task with many interesting applications in network analysis, including link prediction and node classification. Two popular approaches for this problem include matrix…
The problem of low rank approximation is ubiquitous in science. Traditionally this problem is solved in unitary invariant norms such as Frobenius or spectral norm due to existence of efficient methods for building approximations. However,…
As a new color image representation tool, quaternion has achieved excellent results in color image processing problems. In this paper, we propose a novel low-rank quaternion matrix completion algorithm to recover missing data of color…
Singular value thresholding (SVT) plays an important role in the well-known robust principal component analysis (RPCA) algorithms which have many applications in computer vision and recommendation systems. In this paper, we formulate and…
A common data analysis task is the reduced-rank regression problem: $$\min_{\textrm{rank-}k \ X} \|AX-B\|,$$ where $A \in \mathbb{R}^{n \times c}$ and $B \in \mathbb{R}^{n \times d}$ are given large matrices and $\|\cdot\|$ is some norm.…
Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $\Vert \cdot \Vert_*$. However, despite the assortment of computational methods for such problems,…