An Explicit Neural Network Construction for Piecewise Constant Function Approximation
We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions. The proposed FNN has two hidden layers, where the weights and thresholds are explicitly defined and do not require numerical optimization for training. Unlike most of the existing work on explicit FNN construction, the proposed FNN does not rely on tensor structure in multiple dimensions. Instead, it automatically creates Voronoi tessellation of the domain, based on the given data of the target function, and piecewise constant approximation of the function. This makes the construction more practical for applications. We present both theoretical analysis and numerical examples to demonstrate its properties.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
ReLU neural network approximation to piecewise constant functions
This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interf…
Image segmentation by optimal and hierarchical piecewise constant approximations
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approx…
Image SegmentationSemantic SegmentationOnline allocation and homogeneous partitioning for piecewise constant mean-approximation
In the setting of active learning for the multi-armed bandit, where the goal of a learner is to estimate with equal precision the mean of a finite number of arms, recent results show that it is possible to derive strateg…
Active LearningLearning Manifolds with K-Means and K-Flats
We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend pr…
Closed-Form Approximation of the Total Variation Proximal Operator
Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems …
Computed Tomography (CT)DenoisingFormImage Denoising+1