论文标题
矫形单调规范，通用的TOP-K和K-Suport Norms和L0伪型
Orthant-Strictly Monotonic Norms, Generalized Top-k and k-Support Norms and the L0 Pseudonorm
论文作者
论文摘要
欧几里得空间Rd上的所谓的L0假型计数矢量的非零组分的数量。 我们说，如果规范序列不足，则严格越来越分级（相对于L0伪型），并且矢量〜x的规范序列恰好在索引L0（x）处固定。 在本文中，我们将通用的TOP-K和K-Support规范的序列与任何（源）规范相关联，我们还介绍了新的矫形单调单调规范（涵盖LP规范，但对于极端的单调规范）。 然后，我们表明，矫形单调源标准会产生一系列广义的TOP-K规范，这些序列严格越来越分级。 因此，我们提供了一种系统的方式来生成规范序列，通过该序列，L0伪型的水平集通过两个规范的差异表示。 我们的结果依赖于对矫形单调规范的研究。
The so-called l0 pseudonorm on the Euclidean space Rd counts the number of nonzero components of a vector. We say that a sequence of norms is strictly increasingly graded (with respect to the l0 pseudonorm) if it is nondecreasing and that the sequence of norms of a vector~x becomes stationary exactly at the index l0(x). In this paper, with any (source) norm, we associate sequences of generalized top-k and k-support norms, and we also introduce the new class of orthant-strictly monotonic norms (that encompasses the lp norms, but for the extreme ones). Then, we show that an orthant-strictly monotonic source norm generates a sequence of generalized top-k norms which is strictly increasingly graded. With this, we provide a systematic way to generate sequences of norms with which the level sets of the l0 pseudonorm are expressed by means of the difference of two norms. Our results rely on the study of orthant-strictly monotonic norms.
