In current molecular biology, it becomes more and more important to identify differentially expressed genes closely correlated with a key biological process from gene expression data. In this paper, based on the Schatten p-norm and Lp-norm, a novel p-norm robust feature extraction method is proposed to identify the differentially expressed genes. In our method, the Schatten p-norm is used as th...

In the recent years, the trace norm of graphs has been extensively studied under the name of graph energy. In this paper some of this research is extended to more general matrix norms, like the Schatten p-norms and the Ky Fan k-norms. Whenever possible the results are given both for graphs and general matrices. In various contexts a puzzling fact was observed: the Schatten p-norms are widely di...

We conjecture the following so-called norm compression inequality for 2×N partitioned block matrices and the Schatten p-norms: for p ≥ 2,

We define Schatten classes of adjointable operators on Hilbert modules over abelian C⁎-algebras. Many key features carry from the space case. In particular, form two-sided ideals compact and are equipped with a Banach norm C⁎-valued trace expected properties. For trivial bundles, we show that our Schatten-class can be identified bijectively Schatten-norm–continuous maps base into fiber, fiberwi...

The first main result in this article provides an error bound for balanced truncation where the matrix norm used is a general Schatten norm rather than the usual operator norm. The second main result in this article is that for the Schatten 1-norm (the trace class norm) this bound, for systems with a semi-definite Hankel operator, is in fact an equality. This class of systems for which we obtai...

Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for large-scale problems. To address this difficulty, we therefore propose an efficient and scalable core tensor Schatten 1-norm minimization method for simultaneous tensor decompositi...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

Suppose that we observe entries or, more generally, linear combinations of entries of an unknown m×T -matrix A corrupted by noise. We are particularly interested in the high-dimensional setting where the numbermT of unknown entries can be much larger than the sample size N . Motivated by several applications, we consider estimation of matrix A under the assumption that it has small rank. This c...