论文标题
旋转对称模型中卷积神经网络图像分类器的分析
Analysis of convolutional neural network image classifiers in a rotationally symmetric model
论文作者
论文摘要
定义了卷积神经网络图像分类器，并分析了估计值对最佳错误分类风险的分类风险的收敛速率。在这里，我们将图像视为在某些功能空间中具有值的随机变量，在某些功能空间中，我们只会在某些有限网格上观察到离散的样本为函数值。在功能性A后验概率的合适结构和平滑度假设下，其中包括某种对称性反对输入图像的子部分旋转的对称性，这表明，如果我们忽略了二进制图像分类的诅咒，则基于卷积神经网络的最小二乘插件分类器，如果我们忽略了解决方案错误术语，则可以避免biartial图像分类的诅咒。通过将其应用于模拟和真实数据来分析分类器的有限样本量行为。
Convolutional neural network image classifiers are defined and the rate of convergence of the misclassification risk of the estimates towards the optimal misclassification risk is analyzed. Here we consider images as random variables with values in some functional space, where we only observe discrete samples as function values on some finite grid. Under suitable structural and smoothness assumptions on the functional a posteriori probability, which includes some kind of symmetry against rotation of subparts of the input image, it is shown that least squares plug-in classifiers based on convolutional neural networks are able to circumvent the curse of dimensionality in binary image classification if we neglect a resolution-dependent error term. The finite sample size behavior of the classifier is analyzed by applying it to simulated and real data.
