Nested barycentric coordinate system as an explicit feature map for polyhedra approximation and learning tasks

IF 4.3 3区 计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Lee-Ad Gottlieb, Eran Kaufman, Aryeh Kontorovich, Gabriel Nivasch, Ofir Pele
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引用次数: 0

Abstract

We introduce a new embedding technique based on a nested barycentric coordinate system. We show that our embedding can be used to transform the problems of polyhedron approximation, piecewise linear classification and convex regression into one of finding a linear classifier or regressor in a higher dimensional (but nevertheless quite sparse) representation. Our embedding maps a piecewise linear function into an everywhere-linear function, and allows us to invoke well-known algorithms for the latter problem to solve the former. We explain the applications of our embedding to the problems of approximating separating polyhedra—in fact, it can approximate any convex body and unions of convex bodies—as well as to classification by separating polyhedra, and to piecewise linear regression.

Abstract Image

嵌套重心坐标系作为多面体近似和学习任务的显式特征图
我们介绍了一种基于嵌套重心坐标系的新嵌入技术。我们的研究表明,我们的嵌入技术可用于将多面体逼近、片断线性分类和凸回归等问题转化为在高维(但相当稀疏)表示中寻找线性分类器或回归器的问题。我们的嵌入将片面线性函数映射为无处不在的线性函数,并允许我们引用后一个问题的著名算法来解决前一个问题。我们解释了我们的嵌入在近似分离多面体问题上的应用--事实上,它可以近似任何凸体和凸体的联合体--以及在分离多面体分类和分片线性回归中的应用。
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来源期刊
Machine Learning
Machine Learning 工程技术-计算机:人工智能
CiteScore
11.00
自引率
2.70%
发文量
162
审稿时长
3 months
期刊介绍: Machine Learning serves as a global platform dedicated to computational approaches in learning. The journal reports substantial findings on diverse learning methods applied to various problems, offering support through empirical studies, theoretical analysis, or connections to psychological phenomena. It demonstrates the application of learning methods to solve significant problems and aims to enhance the conduct of machine learning research with a focus on verifiable and replicable evidence in published papers.
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