代码收藏家 Python深度学习实战：基于PyTorch的簇分类、圆环分类与月牙分类详解
一、引言
深度学习的重要性
深度学习是一种通过模拟人脑神经元结构来进行数据学习和模式识别的技术，在分类任务中展现出强大的能力。
分类任务的多样性
分类任务涵盖了各种场景，例如簇分类、圆环分类和月牙分类，每种任务都有不同的特征和应用。
二、分类任务详解
2.1、簇分类
簇分类旨在将数据点分为多个簇或类别，目标是在特征空间中找到数据点的天然聚集。
通常数据聚集在不同的区域形成簇，这些簇可能具有不同的形状和大小。
数据挖掘、市场细分、社交网络分析等。
簇分类数据
class1_points = np.array(
[[3.2, 3.0], [2.6, 3.4], [3.5, 4.9], [2.5, 3.4], [1.8, 2.7], [1.3, 1.9], [1.1, 3.4], [1.0, 4.0],
[1.2, 5.0], [2.8, 4.1],
[2.7, 3.1], [2.6, 4.5], [2.1, 3.3], [2.3, 2.4], [2.6, 3.1], [1.9, 3.0], [0.7, 4.2], [1.4, 3.3],
[1.6, 4.6], [2.3, 2.0],
[1.3, 4.2], [1.9, 3.8], [3.6, 6.0], [1.2, 3.1], [1.6, 3.1], [3.5, 4.1], [1.7, 2.6], [2.4, 3.3],
[0.8, 2.2], [1.5, 4.3],
[1.3, 3.9], [1.6, 5.4], [3.4, 3.7], [2.3, 3.4], [2.6, 2.4], [1.8, 2.5], [1.1, 4.1], [1.8, 2.8],
[0.7, 4.4], [1.1, 3.4],
[1.9, 3.6], [1.5, 4.9], [1.0, 3.3], [1.4, 3.6], [2.8, 3.3], [3.1, 4.2], [2.7, 3.8], [3.3, 2.6],
[3.0, 2.7], [0.8, 3.0],
[1.1, 3.8], [1.8, 3.5], [1.9, 2.8], [0.7, 3.1], [2.5, 2.6], [1.3, 2.5], [2.9, 2.9], [3.1, 2.3],
[2.4, 2.8], [1.5, 4.0],
[1.2, 3.8], [2.4, 2.3], [2.1, 1.9], [2.6, 4.2], [2.1, 2.8], [1.6, 2.6], [0.9, 3.8], [1.5, 2.1],
[1.7, 3.0], [3.0, 2.9],
[2.3, 2.6], [1.5, 2.9], [2.9, 2.9], [1.9, 2.7], [0.9, 2.7], [1.0, 4.9], [3.3, 4.0], [2.3, 2.7],
[2.2, 4.0], [1.7, 4.2],
[1.5, 3.4], [2.1, 3.5], [2.7, 3.9], [1.0, 4.8], [2.4, 2.8], [1.5, 2.6], [2.2, 3.2], [2.5, 2.6],
[3.9, 2.8], [2.9, 4.1],
[2.1, 4.3], [1.9, 3.4], [1.3, 1.9], [0.7, 3.3], [1.8, 4.2], [1.7, 3.2], [3.9, 2.9], [1.6, 4.2],
[2.4, 4.4], [1.8, 1.3],
[3.5, 2.0], [2.2, 3.1], [3.0, 3.5], [2.9, 3.3], [1.9, 2.9], [1.6, 2.7], [2.8, 3.6], [3.0, 2.7],
[2.9, 4.4], [3.1, 3.4],
[1.9, 1.2], [3.0, 1.6], [2.0, 3.7], [1.3, 3.1], [2.8, 2.4], [1.5, 2.6], [2.2, 3.1], [3.0, 3.7],
[0.9, 4.3], [3.4, 3.6],
[1.0, 2.4], [2.1, 3.3], [0.7, 2.3], [2.9, 2.3], [2.7, 3.5], [1.3, 2.6], [1.7, 4.2], [2.5, 4.1],
[2.2, 3.4], [3.3, 3.0],
[2.2, 3.5], [1.7, 3.1], [1.9, 2.8], [1.7, 2.9], [3.4, 3.0], [1.6, 4.9], [2.8, 3.7], [1.3, 3.7],
[2.6, 2.6], [4.1, 3.5],
[4.1, 3.1], [1.2, 2.6], [2.5, 3.0], [1.8, 4.0], [3.6, 4.0], [2.1, 4.3], [1.8, 3.2], [3.3, 1.9],
[2.4, 3.5], [1.4, 3.9]])
class2_points = np.array(
[[8.8, 7.2], [7.8, 7.3], [6.8, 7.8], [8.1, 7.5], [7.8, 5.4], [7.6, 8.1], [8.3, 7.5], [6.9, 8.5],
[8.0, 8.2], [8.7, 7.2],
[8.8, 7.0], [8.2, 8.3], [7.7, 7.6], [8.3, 8.1], [8.3, 7.7], [8.0, 7.7], [6.7, 6.2], [8.4, 7.8],
[7.6, 7.3], [6.4, 8.3],
[8.0, 6.6], [7.0, 6.1], [8.2, 6.5], [6.7, 6.4], [7.1, 8.4], [6.6, 7.6], [7.9, 7.6], [8.0, 8.0],
[7.3, 8.6], [8.7, 7.5],
[7.8, 9.2], [7.3, 6.1], [7.7, 7.4], [8.0, 7.3], [8.2, 7.3], [6.5, 8.4], [6.7, 7.0], [7.9, 8.2],
[6.0, 7.1], [7.9, 7.6],
[7.1, 7.8], [9.0, 7.4], [7.2, 8.5], [9.1, 6.5], [7.3, 8.6], [7.2, 7.7], [8.8, 7.3], [7.0, 6.5],
[6.7, 8.4], [7.4, 8.3],
[9.2, 6.3], [7.8, 8.0], [9.4, 7.3], [8.0, 6.5], [6.8, 7.3], [8.5, 7.4], [6.6, 7.4], [8.6, 8.4],
[9.8, 6.9], [6.7, 9.5],
[6.5, 8.0], [8.1, 7.6], [7.4, 8.0], [8.8, 6.1], [7.1, 9.3], [7.3, 7.7], [7.9, 6.7], [7.2, 9.8],
[8.7, 7.8], [7.8, 9.0],
[7.2, 7.3], [9.2, 8.9], [7.3, 7.3], [8.3, 6.7], [7.2, 8.2], [8.1, 7.6], [7.5, 9.7], [6.8, 6.9],
[8.8, 7.5], [7.6, 7.0],
[7.9, 8.7], [8.8, 7.8], [7.5, 7.0], [8.2, 8.2], [6.9, 6.7], [8.1, 7.8], [8.9, 7.4], [9.4, 7.1],
[5.8, 7.9], [7.2, 8.0],
[8.0, 7.2], [7.2, 9.0], [7.3, 7.4], [7.3, 7.9], [9.0, 7.0], [7.9, 7.8], [7.2, 6.9], [8.4, 6.7],
[8.4, 6.2], [8.4, 7.9],
[7.6, 6.5], [6.3, 7.0], [8.1, 7.2], [7.2, 7.9], [7.9, 7.0], [7.7, 7.0], [7.1, 7.4], [8.9, 7.7],
[7.5, 6.3], [7.3, 7.4],
[8.1, 6.9], [5.4, 8.1], [7.7, 7.1], [7.8, 7.8], [7.3, 8.1], [9.1, 7.5], [7.4, 7.1], [6.6, 7.2],
[7.7, 7.8], [7.7, 8.8],
[6.5, 8.4], [8.5, 8.0], [5.9, 8.3], [6.9, 6.4], [7.7, 6.8], [8.5, 6.5], [8.6, 6.5], [8.4, 7.2],
[8.0, 7.9], [8.3, 8.4],
[9.2, 7.7], [8.6, 8.0], [7.2, 8.3], [7.6, 8.7], [6.7, 7.5], [6.6, 7.1], [8.7, 8.0], [7.0, 7.8],
[8.4, 8.9], [6.6, 7.8],
[8.3, 6.7], [6.7, 7.8], [6.6, 7.1], [8.3, 7.2], [8.9, 8.0], [6.8, 6.6], [8.0, 7.7], [6.3, 7.4],
[7.2, 8.8], [7.7, 7.4]])模型训练效果
2.2、圆环分类
圆环分类任务涉及在特征空间中识别环形结构的数据分布。
数据点围绕某个中心形成多个同心圆，每个环对应不同的类别。
图像分类、手写数字识别、模式识别等。
圆环分类数据
class1_points = np.array(
[[1.7, 4.6], [5.4, 7.7], [3.8, 1.9], [3.5, 2.2], [2.2, 2.5], [4.1, 8.1], [3.7, 7.3], [1.8, 4.2],
[6.8, 2.7], [6.9, 3.1],
[7.9, 6.9], [8.1, 5.0], [7.2, 7.0], [7.9, 3.8], [6.3, 2.2], [5.0, 2.6], [4.9, 7.6], [6.1, 1.6],
[3.0, 6.6], [3.3, 6.7],
[1.8, 4.9], [3.2, 7.5], [7.8, 3.7], [7.3, 2.5], [7.1, 6.7], [1.6, 6.0], [2.6, 2.8], [1.9, 4.3],
[2.5, 2.8], [7.3, 3.3],
[7.7, 5.1], [2.7, 7.4], [6.2, 7.7], [5.6, 7.6], [6.4, 7.2], [7.1, 6.6], [3.8, 8.1], [2.4, 6.3],
[7.5, 3.7], [1.6, 2.9],
[3.9, 7.8], [7.2, 6.9], [7.4, 4.8], [7.5, 4.4], [2.0, 5.2], [2.0, 4.0], [7.3, 3.8], [5.5, 7.6],
[7.5, 5.9], [4.0, 2.4],
[6.9, 7.1], [5.3, 2.0], [3.3, 7.0], [4.0, 2.3], [2.7, 2.7], [5.9, 7.8], [5.7, 2.1], [7.8, 5.9],
[2.6, 7.0], [5.4, 2.1],
[7.0, 2.7], [5.4, 7.4], [7.0, 6.4], [7.5, 5.3], [4.2, 2.1], [3.7, 7.7], [7.7, 5.3], [6.1, 7.3],
[1.6, 4.3], [3.3, 2.4],
[1.9, 6.4], [1.9, 6.2], [7.7, 6.0], [4.2, 8.4], [4.7, 1.6], [3.0, 3.3], [2.1, 3.6], [1.8, 6.7],
[4.8, 7.7], [6.8, 2.7],
[3.3, 2.5], [5.6, 7.5], [5.9, 7.9], [2.3, 4.6], [2.2, 6.2], [4.8, 1.7], [1.9, 4.2], [1.4, 4.1],
[3.5, 7.1], [5.9, 7.8],
[6.6, 6.8], [2.3, 5.3], [4.0, 7.6], [3.9, 7.2], [4.6, 2.4], [3.0, 2.2], [7.3, 2.7], [1.6, 5.3],
[2.8, 2.8], [2.5, 5.7],
[7.7, 5.6], [4.6, 1.3], [3.1, 7.3], [2.0, 3.1], [7.1, 3.7], [6.1, 7.7], [3.1, 1.9], [6.5, 6.3],
[2.1, 3.6], [7.3, 5.2],
[1.7, 6.0], [2.2, 5.0], [7.4, 2.7], [2.2, 6.4], [5.0, 8.2], [2.6, 2.8], [2.6, 2.5], [7.5, 4.0],
[1.7, 3.7], [3.8, 7.7],
[2.9, 6.2], [4.9, 1.8], [1.9, 5.3], [6.8, 6.7], [5.2, 1.6], [5.7, 2.3], [3.8, 8.1], [6.7, 3.0],
[2.3, 3.1], [8.3, 5.8],
[2.1, 4.5], [5.3, 1.7], [3.2, 1.9], [7.0, 3.1], [6.3, 2.0], [4.2, 7.2], [6.1, 7.4], [2.3, 6.5],
[5.4, 1.5], [5.7, 7.2],
[4.5, 7.5], [2.4, 6.8], [7.6, 4.5], [3.3, 2.0], [1.8, 3.6], [1.8, 4.3], [7.5, 4.9], [4.6, 8.3],
[6.9, 6.8], [7.4, 3.4],
[3.6, 7.9], [7.6, 4.4], [7.8, 6.1], [6.0, 2.2], [6.4, 2.7], [4.9, 7.6], [1.7, 6.4], [7.7, 5.7],
[6.8, 6.8], [3.1, 2.9],
[2.0, 2.5], [4.5, 2.3], [6.7, 7.2], [7.5, 7.1], [1.9, 5.5], [5.5, 1.7], [6.6, 2.2], [6.1, 7.2],
[3.9, 2.1], [2.5, 6.6],
[7.7, 3.9], [7.4, 5.5], [7.6, 3.8], [3.7, 2.2], [2.3, 7.3], [5.0, 2.2], [5.5, 1.4], [2.9, 7.0],
[6.7, 2.4], [2.0, 5.6],
[6.4, 2.6], [7.3, 4.9], [4.0, 1.6], [3.3, 2.3], [7.6, 5.1], [3.5, 1.5], [4.7, 7.9], [6.1, 7.4],
[2.2, 6.2], [6.9, 2.6],
[2.2, 2.7], [4.1, 7.5], [8.2, 4.4], [3.5, 7.8], [2.4, 6.5], [2.1, 3.8], [1.8, 5.1], [2.3, 2.6],
[6.4, 2.7], [7.0, 2.6],
[7.4, 3.6], [5.9, 1.7], [8.3, 5.8], [7.8, 3.6], [7.7, 5.1], [8.0, 3.9], [1.3, 5.3], [3.4, 7.1],
[4.7, 7.8], [2.1, 3.8],
[7.1, 6.0], [7.5, 4.1], [7.1, 3.5], [7.3, 6.9], [6.6, 2.3], [7.5, 3.3], [7.1, 6.5], [8.0, 5.8],
[8.0, 4.2], [3.6, 7.7],
[1.9, 5.0], [2.6, 2.8], [5.1, 7.0], [6.9, 7.2], [2.0, 6.0], [7.5, 2.5], [4.0, 2.1], [2.9, 7.0],
[4.2, 7.2], [5.3, 1.8],
[2.6, 6.8], [3.1, 2.3], [3.6, 2.3], [5.5, 1.3], [1.3, 4.2], [6.2, 1.9], [2.5, 3.1], [1.8, 4.5],
[1.7, 5.5], [5.7, 7.8],
[8.2, 4.8], [2.0, 3.4], [1.4, 4.4], [5.5, 7.9], [4.0, 1.7], [7.8, 4.7], [6.3, 7.2], [2.5, 2.3],
[7.4, 4.4], [5.1, 7.9]])
class2_points = np.array(
[[5.7, 4.8], [4.8, 5.0], [4.7, 4.6], [4.6, 5.3], [5.0, 5.5], [4.3, 4.9], [4.2, 5.9], [6.0, 5.0],
[4.1, 5.2], [5.4, 5.0],
[4.9, 5.4], [4.5, 6.2], [5.3, 5.5], [4.2, 5.0], [4.0, 4.9], [5.9, 4.9], [4.3, 6.1], [4.5, 4.3],
[5.1, 5.8], [5.6, 4.5],
[4.9, 4.3], [5.5, 5.7], [5.4, 5.0], [4.7, 4.9], [5.6, 5.3], [5.8, 4.8], [4.8, 5.6], [5.3, 5.3],
[5.1, 4.7], [5.0, 5.3],
[4.0, 4.4], [5.9, 5.2], [5.7, 4.7], [5.8, 5.2], [5.1, 4.0], [5.8, 5.9], [5.3, 6.0], [5.5, 4.8],
[5.1, 4.7], [4.7, 4.3],
[5.7, 5.0], [4.3, 4.7], [5.7, 4.9], [4.7, 4.0], [4.9, 4.9], [5.2, 4.6], [4.6, 5.6], [5.2, 5.3],
[4.8, 5.9], [4.5, 4.7],
[5.3, 5.2], [4.7, 4.3], [4.7, 5.7], [4.7, 4.2], [4.7, 5.3], [5.3, 5.4], [5.4, 5.9], [4.6, 4.1],
[4.1, 5.8], [5.6, 5.1],
[5.2, 4.5], [5.6, 4.7], [5.0, 4.8], [5.7, 4.3], [4.5, 5.7], [4.4, 5.7], [5.5, 5.3], [4.7, 5.4],
[5.1, 5.7], [5.2, 4.3],
[4.6, 4.9], [4.7, 5.5], [4.5, 4.2], [5.2, 4.5], [5.4, 3.9], [4.0, 5.0], [4.4, 4.0], [5.0, 4.2],
[5.8, 5.6], [5.8, 5.2],
[4.7, 4.6], [4.7, 5.8], [5.6, 4.5], [5.8, 4.9], [4.6, 5.5], [5.6, 4.5], [5.1, 4.5], [4.2, 4.8],
[4.9, 5.3], [5.0, 5.2],
[4.0, 4.8], [5.5, 4.8], [6.0, 4.7], [4.4, 5.1], [4.3, 4.9], [5.1, 5.6], [4.7, 5.6], [5.1, 4.9],
[4.2, 5.4], [4.4, 4.6],
[5.5, 5.9], [4.1, 4.8], [5.0, 4.6], [5.2, 5.0], [4.1, 5.5], [4.6, 5.1], [5.2, 5.5], [5.1, 4.0],
[4.4, 4.5], [5.3, 5.3],
[4.8, 5.3], [5.2, 4.6], [5.7, 4.4], [4.3, 5.0], [5.1, 4.9], [4.6, 5.0], [5.4, 5.6], [5.3, 4.4],
[4.6, 4.3], [5.2, 5.6],
[5.0, 4.3], [4.4, 4.4], [5.5, 4.9], [4.3, 5.5], [5.0, 5.3], [4.8, 4.9], [5.3, 5.6], [4.1, 4.7],
[4.6, 5.2], [5.5, 4.6],
[4.6, 4.6], [4.5, 5.4], [4.6, 4.2], [5.1, 4.3], [5.2, 4.3], [5.1, 5.6], [5.5, 4.5], [5.1, 4.0],
[4.5, 5.1], [4.8, 3.7],
[4.3, 5.1], [4.6, 5.4], [5.2, 3.9], [4.6, 5.1], [4.2, 5.1], [4.5, 5.2], [5.6, 5.3], [5.6, 5.1],
[5.9, 5.2], [5.0, 4.1],
[5.1, 4.3], [4.8, 6.0], [5.3, 5.5], [5.3, 4.4], [4.4, 5.1], [5.2, 5.0], [4.9, 4.4], [5.3, 5.2],
[5.2, 6.1], [5.6, 5.9],
[4.7, 4.2], [6.1, 5.6], [4.6, 5.7], [5.5, 5.0], [4.5, 5.1], [4.8, 6.0], [4.8, 5.0], [5.5, 4.3],
[4.1, 4.9], [3.9, 4.6],
[4.9, 5.3], [4.4, 4.1], [4.6, 5.3], [5.0, 4.7], [5.3, 5.9], [5.1, 5.4], [5.3, 5.3], [4.9, 4.5],
[5.6, 5.1], [5.2, 4.5],
[5.3, 4.6], [5.5, 5.6], [5.0, 6.1], [4.5, 5.3], [4.8, 5.6], [4.7, 4.9], [4.7, 5.6], [4.6, 4.3],
[5.8, 5.0], [4.9, 4.8],
[5.6, 5.3], [5.5, 5.2], [4.8, 5.3], [4.6, 4.5], [5.2, 4.9], [5.5, 5.6], [6.2, 4.1], [5.6, 5.3],
[5.3, 5.4], [5.4, 5.0],
[5.5, 4.8], [5.1, 4.6], [4.8, 5.4], [4.8, 5.3], [5.8, 4.8], [4.5, 4.8], [4.6, 4.9], [4.3, 3.9],
[4.6, 5.3], [5.1, 5.3],
[5.4, 5.7], [4.3, 5.2], [4.8, 4.9], [5.6, 4.7], [4.2, 5.0], [5.3, 5.6], [4.9, 4.0], [5.1, 4.7],
[5.0, 5.4], [6.0, 5.5],
[5.5, 4.6], [5.7, 5.3], [4.5, 4.7], [5.5, 5.0], [5.9, 4.9], [5.5, 4.6], [4.9, 5.6], [5.4, 5.3],
[5.2, 4.4], [4.3, 4.5],
[5.1, 4.2], [4.3, 5.1], [5.6, 5.7], [4.8, 5.0], [5.1, 5.5], [5.7, 5.2], [5.9, 4.9], [5.1, 4.3],
[5.3, 5.2], [4.4, 4.7],
[5.2, 5.8], [6.3, 5.1], [4.0, 5.4], [5.4, 4.7], [4.2, 5.3], [5.7, 4.9], [5.4, 5.5], [4.8, 5.2],
[5.4, 5.8], [4.6, 5.0]])模型训练效果
2.3、月牙分类
月牙分类任务要求识别流形或不规则的形状，数据分布呈现出像月牙形状的特征。
数据集中的点通常呈现出一种弯曲的形态，具有独特的边界。
生物医学影像分析、信号处理、推荐系统等。
月牙分类数据
class1_points = np.array(
[[6.5, 4.3], [4.5, 6.4], [1.3, 5.1], [1.7, 4.4], [4.8, 5.7], [5.4, 5.6], [1.8, 4.9], [1.2, 3.8],
[2.8, 5.7], [6.4, 3.8],
[4.5, 5.9], [5.3, 6.0], [5.9, 5.0], [1.7, 4.6], [2.3, 5.7], [3.4, 6.1], [5.9, 4.4], [5.4, 5.1],
[5.2, 5.2], [5.6, 5.4],
[4.2, 6.2], [1.4, 3.7], [3.6, 6.3], [4.8, 6.0], [4.8, 6.0], [5.0, 6.1], [5.8, 5.1], [1.6, 4.5],
[1.5, 5.1], [2.2, 6.0],
[5.1, 5.8], [3.8, 6.3], [2.0, 5.7], [2.1, 5.6], [2.0, 5.1], [1.0, 4.9], [3.0, 6.3], [6.0, 4.2],
[2.3, 6.3], [4.8, 6.1],
[1.8, 5.1], [2.2, 5.7], [6.3, 4.3], [5.7, 5.3], [5.6, 5.5], [3.0, 6.1], [6.1, 3.7], [6.3, 4.7],
[3.4, 6.1], [5.2, 5.7],
[5.8, 3.7], [0.7, 4.6], [4.9, 6.2], [1.8, 5.1], [4.6, 5.9], [1.5, 5.0], [1.4, 4.4], [4.0, 6.4],
[5.3, 5.8], [4.6, 6.1],
[3.5, 6.0], [6.2, 4.6], [4.5, 6.0], [2.6, 6.1], [5.9, 5.0], [2.8, 6.4], [2.4, 6.0], [5.3, 6.0],
[2.0, 5.7], [1.2, 3.7],
[2.8, 5.9], [2.5, 5.5], [6.3, 4.6], [1.2, 3.7], [6.3, 4.4], [6.0, 4.8], [1.5, 4.2], [6.4, 4.2],
[1.3, 4.6], [2.0, 5.2],
[1.9, 5.2], [1.6, 5.4], [5.5, 5.7], [3.5, 6.6], [1.7, 5.0], [6.2, 4.6], [6.1, 4.5], [4.1, 5.9],
[6.1, 4.9], [1.7, 5.2],
[3.5, 6.2], [2.9, 6.4], [5.0, 5.8], [2.5, 5.8], [3.1, 6.0], [2.0, 5.1], [2.6, 5.7], [6.1, 4.0],
[6.5, 4.4], [5.4, 6.1],
[5.9, 4.1], [4.7, 5.9], [2.4, 6.5], [4.5, 6.4], [5.9, 4.6], [0.9, 3.9], [3.6, 6.3], [3.7, 6.3],
[1.6, 4.3], [6.0, 5.7],
[4.2, 6.3], [1.8, 5.2], [2.7, 5.9], [2.4, 5.5], [6.4, 3.8], [5.2, 6.1], [6.2, 4.7], [4.2, 6.5],
[5.7, 3.6], [3.9, 6.1],
[1.1, 4.6], [5.5, 5.3], [2.0, 5.9], [5.2, 5.4], [5.7, 5.2], [5.3, 5.0], [1.4, 4.1], [2.8, 6.6],
[3.6, 6.3], [1.1, 4.3],
[5.5, 5.2], [3.9, 6.9], [6.2, 4.2], [5.5, 5.5], [1.6, 4.1], [1.1, 3.9], [1.4, 4.9], [4.5, 6.1],
[1.7, 5.0], [1.9, 4.7],
[5.8, 5.7], [4.8, 5.6], [3.2, 5.7], [6.3, 4.0], [1.6, 4.2], [1.8, 5.1], [1.9, 5.5], [2.9, 5.6],
[1.0, 3.8], [5.9, 5.5],
[2.6, 5.6], [5.3, 5.4], [1.5, 5.0], [3.2, 6.1], [1.0, 4.1], [1.9, 5.8], [3.3, 6.2], [6.1, 3.9],
[2.9, 5.8], [4.8, 5.9],
[6.0, 4.4], [3.6, 6.2], [1.6, 5.1], [5.6, 5.0], [4.0, 6.2], [6.2, 4.3], [4.2, 6.4], [4.0, 6.1],
[5.5, 5.1], [4.3, 6.1],
[4.5, 5.8], [3.7, 6.7], [1.6, 5.6], [5.7, 4.6], [1.6, 4.9], [6.2, 5.7], [2.8, 6.2], [2.1, 5.7],
[5.8, 6.2], [1.5, 5.0],
[5.6, 5.6], [4.1, 5.7], [1.8, 4.6], [6.4, 4.1], [1.2, 3.8], [2.4, 6.0], [1.5, 5.2], [6.0, 3.9],
[5.9, 4.7], [1.9, 5.5],
[2.3, 5.5], [6.1, 4.4], [2.0, 5.2], [1.8, 5.5], [4.6, 6.3], [3.4, 6.2], [4.7, 6.3], [3.1, 6.1],
[3.8, 6.3], [5.7, 5.5],
[1.9, 5.4], [4.7, 5.9], [6.0, 4.2], [4.5, 6.5], [1.3, 4.2], [5.1, 6.0], [1.8, 5.2], [4.0, 6.4],
[5.8, 5.6], [1.2, 3.9],
[6.1, 5.4], [1.7, 4.9], [6.3, 5.0], [5.2, 5.0], [3.0, 6.4], [1.6, 4.8], [1.5, 5.2], [4.7, 6.3],
[1.5, 4.8], [5.3, 5.8],
[4.3, 5.9], [3.2, 6.3], [2.4, 5.5], [2.6, 5.4], [1.2, 3.9], [4.8, 6.3], [6.2, 4.6], [1.3, 5.3],
[6.6, 4.1], [2.9, 6.3],
[3.3, 6.1], [6.0, 5.3], [1.5, 4.9], [5.6, 5.7], [5.9, 4.5], [4.9, 6.1], [6.0, 4.6], [5.0, 5.4],
[3.4, 6.1], [5.9, 4.9],
[2.8, 5.4], [1.9, 5.3], [3.2, 5.8], [1.2, 4.7], [3.1, 6.3], [1.2, 4.0], [6.0, 5.7], [2.7, 6.0],
[3.4, 6.0], [5.9, 5.4]])
class2_points = np.array(
[[6.5, 2.5], [6.4, 2.3], [6.6, 2.8], [7.0, 2.6], [4.3, 2.9], [4.1, 3.7], [3.9, 3.3], [7.2, 2.7],
[3.8, 4.5], [4.0, 4.7],
[4.0, 3.9], [8.3, 3.8], [6.5, 3.1], [8.0, 3.6], [7.9, 3.4], [6.8, 2.5], [4.0, 4.4], [7.0, 2.6],
[7.7, 3.1], [6.0, 2.1],
[6.7, 2.7], [8.7, 4.2], [4.0, 3.9], [5.9, 2.2], [6.3, 2.7], [7.3, 2.9], [5.0, 2.6], [8.1, 3.9],
[4.2, 4.0], [5.1, 2.5],
[8.2, 3.3], [7.1, 2.9], [5.0, 3.0], [7.1, 2.3], [4.8, 3.1], [3.5, 4.4], [8.3, 3.3], [5.2, 3.0],
[6.1, 2.2], [6.8, 2.2],
[3.9, 4.9], [8.6, 3.6], [6.0, 2.3], [4.1, 4.0], [5.2, 2.8], [8.2, 3.5], [8.1, 3.4], [8.7, 4.9],
[5.0, 2.4], [5.0, 2.6],
[8.0, 3.0], [8.4, 4.3], [5.3, 2.7], [8.7, 5.1], [5.6, 2.5], [5.4, 2.7], [3.8, 4.5], [9.1, 4.3],
[8.8, 4.1], [4.7, 3.3],
[8.4, 4.6], [8.3, 4.5], [7.0, 2.7], [6.4, 2.3], [5.2, 2.5], [7.0, 2.2], [8.6, 3.3], [7.5, 3.0],
[4.0, 3.9], [7.6, 3.0],
[7.0, 2.7], [4.3, 3.1], [5.7, 2.8], [3.8, 4.3], [4.9, 3.1], [4.1, 3.3], [7.0, 2.3], [5.1, 2.9],
[8.9, 4.5], [6.0, 2.7],
[7.4, 2.6], [8.7, 4.7], [8.6, 4.5], [7.7, 3.0], [8.9, 5.0], [4.1, 4.0], [3.9, 4.8], [3.7, 3.8],
[5.5, 2.3], [7.5, 3.4],
[4.2, 3.3], [4.1, 3.5], [7.8, 3.1], [3.8, 4.7], [5.2, 3.3], [3.5, 4.7], [3.5, 4.8], [3.9, 4.2],
[6.7, 3.1], [7.9, 3.0],
[8.6, 4.1], [8.5, 4.4], [7.3, 2.6], [3.4, 4.7], [8.7, 3.9], [7.6, 3.0], [4.6, 3.1], [4.8, 2.7],
[4.5, 2.5], [7.4, 2.9],
[5.1, 2.7], [6.9, 2.7], [7.6, 2.6], [9.0, 5.0], [7.1, 2.2], [5.0, 2.7], [5.6, 2.4], [3.6, 4.8],
[6.0, 2.4], [6.9, 2.9],
[8.3, 4.9], [3.9, 4.0], [4.9, 3.1], [8.7, 3.9], [6.3, 2.4], [6.8, 2.5], [5.8, 2.1], [4.5, 4.1],
[4.7, 3.2], [6.3, 2.6],
[8.8, 4.8], [8.6, 4.1], [4.5, 3.8], [3.6, 4.3], [8.8, 5.0], [4.2, 3.9], [8.6, 4.4], [8.8, 4.0],
[5.0, 3.4], [6.4, 2.5],
[4.6, 2.6], [6.0, 2.6], [8.1, 3.5], [8.7, 4.5], [4.8, 2.8], [5.9, 2.7], [6.8, 2.6], [8.9, 4.6],
[6.4, 2.6], [6.9, 2.5],
[8.8, 3.3], [3.7, 4.0], [8.3, 4.0], [3.6, 4.3], [7.2, 2.2], [8.8, 4.4], [8.7, 4.7], [3.8, 4.4],
[8.1, 3.4], [3.5, 4.7],
[8.7, 4.1], [4.3, 3.8], [3.6, 4.0], [5.0, 2.7], [7.7, 3.2], [8.4, 3.2], [4.3, 3.7], [8.6, 4.3],
[7.5, 3.2], [8.3, 3.8],
[4.9, 2.9], [5.4, 2.4], [3.9, 4.9], [8.9, 3.6], [8.3, 3.4], [8.2, 3.3], [7.8, 2.8], [8.2, 3.2],
[8.9, 4.8], [8.6, 3.8],
[3.9, 5.3], [4.4, 4.6], [7.8, 3.0], [6.9, 2.7], [7.7, 3.0], [3.7, 3.7], [6.6, 3.0], [5.3, 2.6],
[4.4, 4.1], [8.1, 3.6],
[8.5, 3.4], [8.0, 3.7], [5.2, 2.7], [7.3, 2.8], [4.1, 4.0], [8.5, 3.6], [7.5, 2.4], [3.9, 3.8],
[5.9, 2.5], [6.6, 2.9],
[4.4, 3.4], [4.8, 3.3], [4.4, 3.1], [8.7, 4.8], [6.2, 2.7], [5.0, 3.2], [5.6, 2.7], [8.5, 4.2],
[4.2, 3.5], [4.0, 3.1],
[3.8, 4.1], [5.3, 2.2], [4.9, 3.3], [5.7, 3.1], [4.4, 3.5], [5.3, 2.8], [4.2, 3.3], [8.4, 3.6],
[8.1, 3.5], [3.8, 4.4],
[3.6, 4.3], [4.3, 4.6], [7.9, 3.1], [8.9, 4.9], [7.8, 3.2], [4.1, 3.7], [4.8, 3.1], [3.7, 4.3],
[8.5, 3.8], [5.2, 2.7],
[7.3, 2.8], [6.5, 2.6], [8.4, 4.3], [8.2, 4.0], [7.2, 2.9], [3.7, 4.2], [7.6, 2.6], [4.3, 4.7],
[4.5, 3.5], [4.0, 4.2],
[6.4, 2.7], [6.3, 2.6], [8.9, 3.9], [5.8, 2.3], [6.1, 2.6], [4.1, 3.7], [8.2, 3.1], [9.1, 4.5],
[3.7, 4.1], [6.3, 2.7]])模型训练效果
三、PyTorch实现
以月牙分类为例
划分数据集
# 将 point1 分割为训练集和测试集
np.random.shuffle(class1_points) # 随机打乱数据
split_index = int(0.1 * len(class1_points)) # 取前 10% 的数据作为测试集
class1_train_points = class1_points[split_index:]
class2_train_points = class2_points[split_index:]
class1_test_points = class1_points[:split_index]
class2_test_points = class2_points[:split_index]
# 合并两类点
train_points = np.concatenate((class1_train_points, class2_train_points))
# 标签 0表示类别1，1表示类别2
train_labels1 = np.zeros(len(class1_train_points))
train_labels2 = np.ones(len(class2_train_points))
train_labels = np.concatenate((train_labels1, train_labels2))
# 合并两类点
test_points = np.concatenate((class1_test_points, class2_test_points))
# 标签 0表示类别1，1表示类别2
test_labels1 = np.zeros(len(class1_test_points))
test_labels2 = np.ones(len(class2_test_points))
test_labels = np.concatenate((test_labels1, test_labels2))构建模型
class ModelClass(nn.Module):
def __init__(self):
super().__init__()
self.layer1 = nn.Linear(2, 8)
self.layer2 = nn.Linear(8, 16)
self.layer3 = nn.Linear(16, 32)
self.layer4 = nn.Linear(32, 16)
self.layer5 = nn.Linear(16, 8)
self.layer6 = nn.Linear(8, 2)
def forward(self, x):
x = torch.tanh(self.layer1(x))
x = torch.tanh(self.layer2(x))
x = torch.tanh(self.layer3(x))
x = torch.tanh(self.layer4(x))
x = torch.tanh(self.layer5(x))
x = torch.softmax(self.layer6(x),dim=1)
return x
model = ModelClass()创建损失函数和优化器
criterion = nn.CrossEntropyLoss()
optimizer = optim.Adam(model.parameters(), lr=0.01, weight_decay=0.005)模型训练
for n in range(1,2001):
# 将numpy数据转换为torch tensor
inputs = torch.tensor(train_points, dtype=torch.float32)
train_labels = torch.tensor(train_labels, dtype=torch.long)
# 前向传播
outputs = model(inputs)
loss = criterion(outputs, train_labels)
# 反向传播和优化
optimizer.zero_grad()
loss.backward()
optimizer.step()
if n % 100== 0 or n == 1:
print(n,loss.item())可视化
# 创建等高线绘图的网格点
x_min, x_max = 0, 10
y_min, y_max = 0, 10
step_size = 0.2
xx, yy = np.meshgrid(np.arange(x_min, x_max, step_size),
np.arange(y_min, y_max, step_size))
grid_points = np.c_[xx.ravel(), yy.ravel()]
# 创建三维图形和右侧的二维子图
fig = plt.figure(figsize=(10, 5))
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)
step_list = []
loss_list = []
test_step_list = []
test_loss_list = []
# 开始迭代
for n in range(1,2001):
# 将numpy数据转换为torch tensor
inputs = torch.tensor(train_points, dtype=torch.float32)
train_labels = torch.tensor(train_labels, dtype=torch.long)
# 前向传播
outputs = model(inputs)
loss = criterion(outputs, train_labels)
# 反向传播和优化
optimizer.zero_grad()
loss.backward()
optimizer.step()
# 更新右侧的损失图数据并绘制
step_list.append(n)
loss_list.append(loss.detach())
# 显示频率设置
frequency_display = 50
# 显示与输出
if n % 100== 0 or n == 1:
# 使用训练好的模型预测网格点的标签
grid_points_tensor = torch.tensor(grid_points, dtype=torch.float32)
Z = model(grid_points_tensor).detach().numpy()
Z = Z[:, 1] # 取正类的概率值
Z = Z.reshape(xx.shape)
# 绘制2D图
ax1 = plt.subplot(121)
ax1.clear()
ax1.scatter(class1_train_points[:, 0], class1_train_points[:, 1], c='blue', label='label1')
ax1.scatter(class2_train_points[:, 0], class2_train_points[:, 1], c='red', label='label2')
ax1.contour(xx, yy, Z, levels=[0.5], colors='black')
# 计算测试集损失
test_inputs = torch.tensor(test_points, dtype=torch.float32)
y_pred_test = model(test_inputs)
test_labels = torch.tensor(test_labels, dtype=torch.long)
loss_test = criterion(y_pred_test, test_labels)
test_step_list.append(n)
test_loss_list.append(loss_test.detach())
ax2 = plt.subplot(122)
ax2.clear()
ax2.plot(step_list, loss_list, 'r-', label='Train Loss')
ax2.plot(test_step_list, test_loss_list, 'b-', label='Test Loss') # 绘制测试集损失
ax2.set_xlabel("Step")
ax2.set_ylabel("Loss")
ax2.legend()
plt.show()完整代码
import numpy as np
import torch
import random
import torch.nn as nn
import torch.optim as optim
import matplotlib.pyplot as plt
import torch.nn.init as init
# 创造数据，数据集
class1_points = np.array(
[[6.5, 4.3], [4.5, 6.4], [1.3, 5.1], [1.7, 4.4], [4.8, 5.7], [5.4, 5.6], [1.8, 4.9], [1.2, 3.8],
[2.8, 5.7], [6.4, 3.8],
[4.5, 5.9], [5.3, 6.0], [5.9, 5.0], [1.7, 4.6], [2.3, 5.7], [3.4, 6.1], [5.9, 4.4], [5.4, 5.1],
[5.2, 5.2], [5.6, 5.4],
[4.2, 6.2], [1.4, 3.7], [3.6, 6.3], [4.8, 6.0], [4.8, 6.0], [5.0, 6.1], [5.8, 5.1], [1.6, 4.5],
[1.5, 5.1], [2.2, 6.0],
[5.1, 5.8], [3.8, 6.3], [2.0, 5.7], [2.1, 5.6], [2.0, 5.1], [1.0, 4.9], [3.0, 6.3], [6.0, 4.2],
[2.3, 6.3], [4.8, 6.1],
[1.8, 5.1], [2.2, 5.7], [6.3, 4.3], [5.7, 5.3], [5.6, 5.5], [3.0, 6.1], [6.1, 3.7], [6.3, 4.7],
[3.4, 6.1], [5.2, 5.7],
[5.8, 3.7], [0.7, 4.6], [4.9, 6.2], [1.8, 5.1], [4.6, 5.9], [1.5, 5.0], [1.4, 4.4], [4.0, 6.4],
[5.3, 5.8], [4.6, 6.1],
[3.5, 6.0], [6.2, 4.6], [4.5, 6.0], [2.6, 6.1], [5.9, 5.0], [2.8, 6.4], [2.4, 6.0], [5.3, 6.0],
[2.0, 5.7], [1.2, 3.7],
[2.8, 5.9], [2.5, 5.5], [6.3, 4.6], [1.2, 3.7], [6.3, 4.4], [6.0, 4.8], [1.5, 4.2], [6.4, 4.2],
[1.3, 4.6], [2.0, 5.2],
[1.9, 5.2], [1.6, 5.4], [5.5, 5.7], [3.5, 6.6], [1.7, 5.0], [6.2, 4.6], [6.1, 4.5], [4.1, 5.9],
[6.1, 4.9], [1.7, 5.2],
[3.5, 6.2], [2.9, 6.4], [5.0, 5.8], [2.5, 5.8], [3.1, 6.0], [2.0, 5.1], [2.6, 5.7], [6.1, 4.0],
[6.5, 4.4], [5.4, 6.1],
[5.9, 4.1], [4.7, 5.9], [2.4, 6.5], [4.5, 6.4], [5.9, 4.6], [0.9, 3.9], [3.6, 6.3], [3.7, 6.3],
[1.6, 4.3], [6.0, 5.7],
[4.2, 6.3], [1.8, 5.2], [2.7, 5.9], [2.4, 5.5], [6.4, 3.8], [5.2, 6.1], [6.2, 4.7], [4.2, 6.5],
[5.7, 3.6], [3.9, 6.1],
[1.1, 4.6], [5.5, 5.3], [2.0, 5.9], [5.2, 5.4], [5.7, 5.2], [5.3, 5.0], [1.4, 4.1], [2.8, 6.6],
[3.6, 6.3], [1.1, 4.3],
[5.5, 5.2], [3.9, 6.9], [6.2, 4.2], [5.5, 5.5], [1.6, 4.1], [1.1, 3.9], [1.4, 4.9], [4.5, 6.1],
[1.7, 5.0], [1.9, 4.7],
[5.8, 5.7], [4.8, 5.6], [3.2, 5.7], [6.3, 4.0], [1.6, 4.2], [1.8, 5.1], [1.9, 5.5], [2.9, 5.6],
[1.0, 3.8], [5.9, 5.5],
[2.6, 5.6], [5.3, 5.4], [1.5, 5.0], [3.2, 6.1], [1.0, 4.1], [1.9, 5.8], [3.3, 6.2], [6.1, 3.9],
[2.9, 5.8], [4.8, 5.9],
[6.0, 4.4], [3.6, 6.2], [1.6, 5.1], [5.6, 5.0], [4.0, 6.2], [6.2, 4.3], [4.2, 6.4], [4.0, 6.1],
[5.5, 5.1], [4.3, 6.1],
[4.5, 5.8], [3.7, 6.7], [1.6, 5.6], [5.7, 4.6], [1.6, 4.9], [6.2, 5.7], [2.8, 6.2], [2.1, 5.7],
[5.8, 6.2], [1.5, 5.0],
[5.6, 5.6], [4.1, 5.7], [1.8, 4.6], [6.4, 4.1], [1.2, 3.8], [2.4, 6.0], [1.5, 5.2], [6.0, 3.9],
[5.9, 4.7], [1.9, 5.5],
[2.3, 5.5], [6.1, 4.4], [2.0, 5.2], [1.8, 5.5], [4.6, 6.3], [3.4, 6.2], [4.7, 6.3], [3.1, 6.1],
[3.8, 6.3], [5.7, 5.5],
[1.9, 5.4], [4.7, 5.9], [6.0, 4.2], [4.5, 6.5], [1.3, 4.2], [5.1, 6.0], [1.8, 5.2], [4.0, 6.4],
[5.8, 5.6], [1.2, 3.9],
[6.1, 5.4], [1.7, 4.9], [6.3, 5.0], [5.2, 5.0], [3.0, 6.4], [1.6, 4.8], [1.5, 5.2], [4.7, 6.3],
[1.5, 4.8], [5.3, 5.8],
[4.3, 5.9], [3.2, 6.3], [2.4, 5.5], [2.6, 5.4], [1.2, 3.9], [4.8, 6.3], [6.2, 4.6], [1.3, 5.3],
[6.6, 4.1], [2.9, 6.3],
[3.3, 6.1], [6.0, 5.3], [1.5, 4.9], [5.6, 5.7], [5.9, 4.5], [4.9, 6.1], [6.0, 4.6], [5.0, 5.4],
[3.4, 6.1], [5.9, 4.9],
[2.8, 5.4], [1.9, 5.3], [3.2, 5.8], [1.2, 4.7], [3.1, 6.3], [1.2, 4.0], [6.0, 5.7], [2.7, 6.0],
[3.4, 6.0], [5.9, 5.4]])
class2_points = np.array(
[[6.5, 2.5], [6.4, 2.3], [6.6, 2.8], [7.0, 2.6], [4.3, 2.9], [4.1, 3.7], [3.9, 3.3], [7.2, 2.7],
[3.8, 4.5], [4.0, 4.7],
[4.0, 3.9], [8.3, 3.8], [6.5, 3.1], [8.0, 3.6], [7.9, 3.4], [6.8, 2.5], [4.0, 4.4], [7.0, 2.6],
[7.7, 3.1], [6.0, 2.1],
[6.7, 2.7], [8.7, 4.2], [4.0, 3.9], [5.9, 2.2], [6.3, 2.7], [7.3, 2.9], [5.0, 2.6], [8.1, 3.9],
[4.2, 4.0], [5.1, 2.5],
[8.2, 3.3], [7.1, 2.9], [5.0, 3.0], [7.1, 2.3], [4.8, 3.1], [3.5, 4.4], [8.3, 3.3], [5.2, 3.0],
[6.1, 2.2], [6.8, 2.2],
[3.9, 4.9], [8.6, 3.6], [6.0, 2.3], [4.1, 4.0], [5.2, 2.8], [8.2, 3.5], [8.1, 3.4], [8.7, 4.9],
[5.0, 2.4], [5.0, 2.6],
[8.0, 3.0], [8.4, 4.3], [5.3, 2.7], [8.7, 5.1], [5.6, 2.5], [5.4, 2.7], [3.8, 4.5], [9.1, 4.3],
[8.8, 4.1], [4.7, 3.3],
[8.4, 4.6], [8.3, 4.5], [7.0, 2.7], [6.4, 2.3], [5.2, 2.5], [7.0, 2.2], [8.6, 3.3], [7.5, 3.0],
[4.0, 3.9], [7.6, 3.0],
[7.0, 2.7], [4.3, 3.1], [5.7, 2.8], [3.8, 4.3], [4.9, 3.1], [4.1, 3.3], [7.0, 2.3], [5.1, 2.9],
[8.9, 4.5], [6.0, 2.7],
[7.4, 2.6], [8.7, 4.7], [8.6, 4.5], [7.7, 3.0], [8.9, 5.0], [4.1, 4.0], [3.9, 4.8], [3.7, 3.8],
[5.5, 2.3], [7.5, 3.4],
[4.2, 3.3], [4.1, 3.5], [7.8, 3.1], [3.8, 4.7], [5.2, 3.3], [3.5, 4.7], [3.5, 4.8], [3.9, 4.2],
[6.7, 3.1], [7.9, 3.0],
[8.6, 4.1], [8.5, 4.4], [7.3, 2.6], [3.4, 4.7], [8.7, 3.9], [7.6, 3.0], [4.6, 3.1], [4.8, 2.7],
[4.5, 2.5], [7.4, 2.9],
[5.1, 2.7], [6.9, 2.7], [7.6, 2.6], [9.0, 5.0], [7.1, 2.2], [5.0, 2.7], [5.6, 2.4], [3.6, 4.8],
[6.0, 2.4], [6.9, 2.9],
[8.3, 4.9], [3.9, 4.0], [4.9, 3.1], [8.7, 3.9], [6.3, 2.4], [6.8, 2.5], [5.8, 2.1], [4.5, 4.1],
[4.7, 3.2], [6.3, 2.6],
[8.8, 4.8], [8.6, 4.1], [4.5, 3.8], [3.6, 4.3], [8.8, 5.0], [4.2, 3.9], [8.6, 4.4], [8.8, 4.0],
[5.0, 3.4], [6.4, 2.5],
[4.6, 2.6], [6.0, 2.6], [8.1, 3.5], [8.7, 4.5], [4.8, 2.8], [5.9, 2.7], [6.8, 2.6], [8.9, 4.6],
[6.4, 2.6], [6.9, 2.5],
[8.8, 3.3], [3.7, 4.0], [8.3, 4.0], [3.6, 4.3], [7.2, 2.2], [8.8, 4.4], [8.7, 4.7], [3.8, 4.4],
[8.1, 3.4], [3.5, 4.7],
[8.7, 4.1], [4.3, 3.8], [3.6, 4.0], [5.0, 2.7], [7.7, 3.2], [8.4, 3.2], [4.3, 3.7], [8.6, 4.3],
[7.5, 3.2], [8.3, 3.8],
[4.9, 2.9], [5.4, 2.4], [3.9, 4.9], [8.9, 3.6], [8.3, 3.4], [8.2, 3.3], [7.8, 2.8], [8.2, 3.2],
[8.9, 4.8], [8.6, 3.8],
[3.9, 5.3], [4.4, 4.6], [7.8, 3.0], [6.9, 2.7], [7.7, 3.0], [3.7, 3.7], [6.6, 3.0], [5.3, 2.6],
[4.4, 4.1], [8.1, 3.6],
[8.5, 3.4], [8.0, 3.7], [5.2, 2.7], [7.3, 2.8], [4.1, 4.0], [8.5, 3.6], [7.5, 2.4], [3.9, 3.8],
[5.9, 2.5], [6.6, 2.9],
[4.4, 3.4], [4.8, 3.3], [4.4, 3.1], [8.7, 4.8], [6.2, 2.7], [5.0, 3.2], [5.6, 2.7], [8.5, 4.2],
[4.2, 3.5], [4.0, 3.1],
[3.8, 4.1], [5.3, 2.2], [4.9, 3.3], [5.7, 3.1], [4.4, 3.5], [5.3, 2.8], [4.2, 3.3], [8.4, 3.6],
[8.1, 3.5], [3.8, 4.4],
[3.6, 4.3], [4.3, 4.6], [7.9, 3.1], [8.9, 4.9], [7.8, 3.2], [4.1, 3.7], [4.8, 3.1], [3.7, 4.3],
[8.5, 3.8], [5.2, 2.7],
[7.3, 2.8], [6.5, 2.6], [8.4, 4.3], [8.2, 4.0], [7.2, 2.9], [3.7, 4.2], [7.6, 2.6], [4.3, 4.7],
[4.5, 3.5], [4.0, 4.2],
[6.4, 2.7], [6.3, 2.6], [8.9, 3.9], [5.8, 2.3], [6.1, 2.6], [4.1, 3.7], [8.2, 3.1], [9.1, 4.5],
[3.7, 4.1], [6.3, 2.7]])
# 将 class1_points 分割为训练集和测试集
np.random.shuffle(class1_points) # 随机打乱数据
split_index = int(0.1 * len(class1_points)) # 取前10%的数据作为测试集
# 将 class1 和 class2 中的数据分为训练和测试集
class1_train_points = class1_points[split_index:] # 90%的 class1 数据作为训练集
class2_train_points = class2_points[split_index:] # 90%的 class2 数据作为训练集
class1_test_points = class1_points[:split_index] # 10%的 class1 数据作为测试集
class2_test_points = class2_points[:split_index] # 10%的 class2 数据作为测试集
# 合并训练集
train_points = np.concatenate((class1_train_points, class2_train_points)) # 合并两个类别的训练点
# 创建训练标签，类别1用0表示，类别2用1表示
train_labels1 = np.zeros(len(class1_train_points)) # 类别1的标签
train_labels2 = np.ones(len(class2_train_points)) # 类别2的标签
train_labels = np.concatenate((train_labels1, train_labels2)) # 合并所有训练标签
# 合并测试集
test_points = np.concatenate((class1_test_points, class2_test_points)) # 合并两个类别的测试点
# 创建测试标签
test_labels1 = np.zeros(len(class1_test_points)) # 类别1的标签
test_labels2 = np.ones(len(class2_test_points)) # 类别2的标签
test_labels = np.concatenate((test_labels1, test_labels2)) # 合并所有测试标签
# 2. 定义前向模型
class YourModelClass(nn.Module):
def __init__(self):
super(YourModelClass, self).__init__()
# 定义六层的全连接神经网络结构
self.layer1 = nn.Linear(2, 8) # 输入层到第一隐藏层
self.layer2 = nn.Linear(8, 16) # 第一隐藏层到第二隐藏层
self.layer3 = nn.Linear(16, 32) # 第二隐藏层到第三隐藏层
self.layer4 = nn.Linear(32, 16) # 第三隐藏层到第四隐藏层
self.layer5 = nn.Linear(16, 8) # 第四隐藏层到第五隐藏层
self.layer6 = nn.Linear(8, 2) # 第五隐藏层到输出层
def forward(self, x):
# 前向传播函数
x = torch.tanh(self.layer1(x)) # 使用tanh激活函数
x = torch.tanh(self.layer2(x))
x = torch.tanh(self.layer3(x))
x = torch.tanh(self.layer4(x))
x = torch.tanh(self.layer5(x))
x = torch.softmax(self.layer6(x), dim=1) # 使用softmax激活函数进行分类
return x
# 实例化模型
model = YourModelClass()
# 3. 定义损失函数和优化器
criterion = nn.CrossEntropyLoss() # 交叉熵损失用于多分类问题
optimizer = optim.Adam(model.parameters(), lr=0.01, weight_decay=0.005) # Adam优化器，学习率和权重衰减
# 创建等高线绘图的网格点
x_min, x_max = 0, 10
y_min, y_max = 0, 10
step_size = 0.2
xx, yy = np.meshgrid(np.arange(x_min, x_max, step_size), np.arange(y_min, y_max, step_size)) # 生成网格点
grid_points = np.c_[xx.ravel(), yy.ravel()] # 将网格点展平为二维数组
# 创建图形和子图
fig = plt.figure(figsize=(10, 5))
ax1 = fig.add_subplot(121) # 左侧图
ax2 = fig.add_subplot(122) # 右侧图
step_list = [] # 存储训练步数
loss_list = [] # 存储训练损失
test_step_list = [] # 存储测试步数
test_loss_list = [] # 存储测试损失
# 4. 开始迭代
num_iterations = 2000
for n in range(num_iterations + 1):
# 将numpy数据转换为torch tensor
inputs = torch.tensor(train_points, dtype=torch.float32) # 将训练点转换为张量
train_labels = torch.tensor(train_labels, dtype=torch.long) # 将训练标签转换为张量
# 前向传播
outputs = model(inputs) # 得到模型输出
loss = criterion(outputs, train_labels) # 计算损失
# 反向传播和优化
optimizer.zero_grad() # 清除梯度
loss.backward() # 反向传播计算梯度
optimizer.step() # 更新参数
# 更新损失图数据
step_list.append(n) # 记录当前步数
loss_list.append(loss.detach()) # 记录当前损失值
# 5. 显示频率设置
frequency_display = 50 # 每50步输出一次信息
# 6. 显示与输出
if n % frequency_display == 0 or n == 1:
# 使用训练好的模型预测网格点的标签
grid_points_tensor = torch.tensor(grid_points, dtype=torch.float32) # 将网格点转换为张量
Z = model(grid_points_tensor).detach().numpy() # 得到予测输出
Z = Z[:, 1] # 取类别2的概率值（1的列）
Z = Z.reshape(xx.shape) # 调整Z的形状以适应网格
# 绘制2D图形
ax1.clear() # 清除当前图
ax1.scatter(class1_train_points[:, 0], class1_train_points[:, 1], c='blue', label='label1') # 类别1的点
ax1.scatter(class2_train_points[:, 0], class2_train_points[:, 1], c='red', label='label2') # 类别2的点
ax1.contour(xx, yy, Z, levels=[0.5], colors='black') # 绘制等高线
# 计算测试集损失
test_inputs = torch.tensor(test_points, dtype=torch.float32) # 将测试点转换为张量
y_pred_test = model(test_inputs) # 得到模型输出
test_labels = torch.tensor(test_labels, dtype=torch.long) # 将测试标签转换为张量
loss_test = criterion(y_pred_test, test_labels) # 计算测试集损失
test_step_list.append(n) # 记录测试步数
test_loss_list.append(loss_test.detach()) # 记录测试损失
ax2.clear() # 清除当前损失图
ax2.plot(step_list, loss_list, 'r-', label='Train Loss') # 绘制训练损失
ax2.plot(test_step_list, test_loss_list, 'b-', label='Test Loss') # 绘制测试损失
ax2.set_xlabel("Step") # x轴标签
ax2.set_ylabel("Loss") # y轴标签
ax2.legend() # 显示图例
plt.show() # 展示图形 作者：蹦蹦跳跳真可爱589
