2 Linear Algebra 3 2.1 Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Vector norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Induced matrix norms. . . . . . . . . . . . . . . . . . . . . . . . ....

We propose a new subspace clustering model to segment data which is drawn from multiple linear or affine subspaces. Unlike the well-known sparse subspace clustering (SSC) and low-rank representation (LRR) which transfer the subspace clustering problem into two steps’ algorithm including building the affinity matrix and spectral clustering, our proposed model directly learns the different subspa...

In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W . Instances of this problem in machine learning include multi-task learning, collaborative filtering and...

In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W . Instances of this problem in machine learning include multi-task learning, collaborative filtering and...

Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used for image restoration. However, NNM tends to over-shrink the rank components and treats the different rank components equally, thus limits its capability and flexibility. This paper proposes a new approach for image restoration based ADMM framework via ...

The robust estimation of the low-dimensional subspace that spans the data from a set of high-dimensional, possibly corrupted by gross errors and outliers observations is fundamental in many computer vision problems. The state-of-the-art robust principal component analysis (PCA) methods adopt convex relaxations of `0 quasi-norm-regularised rank minimisation problems. That is, the nuclear norm an...

Let $${\mathcal {H}}={\mathcal {H}}_+\oplus {\mathcal {H}}_-$$ be a fixed orthogonal decomposition of the complex separable Hilbert space {H}}$$ in two infinite-dimensional subspaces. We study geometry set {P}}^p$$ selfadjoint projections Banach algebra {A}}^p=\{A\in {B}}({\mathcal {H}}): [A,E_+]\in {B}}_p({\mathcal {H}})\},$$ where $$E_+$$ is projection onto {H}}_+$$ and {H}})$$ Schatten ideal...

We correct a formula of Gavish and Donoho for singular value shrinkage with operator norm loss non-square matrices. also observe that in the classical regime, optimal any Schatten converges to best linear predictor.