2023 Asia-Pacific Mathematical Modeling A question ideas: Updated as soon as possible after the competition starts, get the business card at the end of the article
2023 Asia-Pacific Mathematical Modeling Question B Question Ideas: Updated as soon as possible after the competition starts, get the business card at the end of the article
2023 Asia-Pacific Mathematical Modeling C Question Ideas: Updated as soon as possible after the competition starts, get the business card at the end of the article
Important note: Interpretation of excellent papers is very important! ! !
This is my first contact with mathematical modeling, so in the process of studying the paper, in addition to learning the thinking methods and mathematical knowledge they used to solve problems, and analyzing their advantages and disadvantages, we also paid more attention to learning how to write An excellent mathematical modeling paper to convey your research ideas and results. After studying this excellent paper, we have gained the following points:
1. We have a general understanding of what parts a mathematical modeling paper should include;
2. What should be written in each part, and how to write to better attract others’ attention;
3. Learn from the success of this excellent paper in writing and handling problems. 4. Summarize the shortcomings of this paper and remind us not to make similar mistakes in the future.
2. Writing content and skills
2.1 Abstract
The abstract is the key to whether a paper can stand out among many papers. A good abstract must Clearly describe the approach to solving the problem and prominently express the most important conclusions of the paper. The abstract of this paper succinctly points out the method of dealing with the problem and gives the answer, which plays a better role in summarizing the full text and clarifying the organization. Let readers have an overall impression of the following discussion. The shortcoming is that he mentioned using two methods to analyze the two methods of predicting rainfall, but in fact from the main part at the end, we can see that he only focused on the two aspects mentioned in the title - accuracy and public feelings - to analyze, there are no two methods.
2.2 Restatement of the problem
Once again clarify the practical significance of the problem studied in the paper, and clearly put forward the problem to be solved.
2.3 Analysis of the problem
Analyze the problem and briefly describe the conditions and general solutions required to solve the problem
Advantages: The organization is relatively clear. The discussion is logical and clearly expressed. And a Matlab graph is given to convert longitude and latitude into coordinates
, which intuitively reflects the data in the question on the graph.
Disadvantages: Regarding the section that considers public feelings, the narrative is a bit brief.
2.4 Assumptions and symbols of the model
Whether a model is well built depends largely on whether its assumptions are well made. Oversimplified assumptions are close to reality, but are inappropriate or impossible to solve, and oversimplified assumptions are not of sufficient practical significance. This requires us to use our imagination, insight and judgment, be good at distinguishing priorities, and try to make the problem as simple and uniform as possible in order to simplify the processing method.
The variables and constants that will appear in the article are explained here first to facilitate the reader's reading. The symbols in this paper are very clear and detailed.
2.5 Establishment and solution of the model,
1. Problem (1) and its solution
First clarify the algorithm, give or derive the required The calculation formula is obtained; then Matlab programming can be used to calculate the corresponding results; the obtained answers are analyzed and corresponding conclusions are given.
Advantages: The model established in this article is very simple, so the algorithm given is also very refined. He mainly uses the forecast data at grid points to predict the data at the observation site, and then compares it with the actual measured data, and uses the forecast deviation rate to determine the inferiority of the two methods. When the data is very complex, Matlab is used well.
2. Problem (2) and its solution
Please refer to the above
2.6 Error and analysis of the model
The error and analysis of the model help to improve the model and make the model applicable in more situations.
Advantages: Seeing the main possible problems and disputes, which is equivalent to re-explaining the desirability of your own method;
Disadvantages: For Other errors were not analyzed. Not thought through enough.
2.7 Model evaluation and promotion
Point out why your model is desirable and its advantages. The evaluation of this argument does a good job of summarizing its advantages, noting the high accuracy of its method and mentioning its use of good mathematical tools.
The main purpose of mathematical models is to solve practical problems. After a model is made and solved, it will not be successful if it is not applied to practice. Therefore, model promotion or model application is essential in modeling papers.
2.8 References
The source of the cited information must be indicated, which is stated here.
#coding=utf-8
#Author:Dodo
#Date:2018-11-15
#Email:[email protected]
'''
数据集：Mnist
训练集数量：60000
测试集数量：10000
------------------------------
运行结果：
正确率：81.72%（二分类）
运行时长：78.6s
'''
import numpy as np
import time
def loadData(fileName):
'''
加载Mnist数据集
:param fileName:要加载的数据集路径
:return: list形式的数据集及标记
'''
print('start to read data')
# 存放数据及标记的list
dataArr = []; labelArr = []
# 打开文件
fr = open(fileName, 'r')
# 将文件按行读取
for line in fr.readlines():
# 对每一行数据按切割福','进行切割，返回字段列表
curLine = line.strip().split(',')
# Mnsit有0-9是个标记，由于是二分类任务，所以将>=5的作为1，<5为-1
if int(curLine[0]) >= 5:
labelArr.append(1)
else:
labelArr.append(-1)
#存放标记
#[int(num) for num in curLine[1:]] -> 遍历每一行中除了以第一哥元素（标记）外将所有元素转换成int类型
#[int(num)/255 for num in curLine[1:]] -> 将所有数据除255归一化(非必须步骤，可以不归一化)
dataArr.append([int(num)/255 for num in curLine[1:]])
#返回data和label
return dataArr, labelArr
def perceptron(dataArr, labelArr, iter=50):
'''
感知器训练过程
:param dataArr:训练集的数据 (list)
:param labelArr: 训练集的标签(list)
:param iter: 迭代次数，默认50
:return: 训练好的w和b
'''
print('start to trans')
#将数据转换成矩阵形式（在机器学习中因为通常都是向量的运算，转换称矩阵形式方便运算）
#转换后的数据中每一个样本的向量都是横向的
dataMat = np.mat(dataArr)
#将标签转换成矩阵，之后转置(.T为转置)。
#转置是因为在运算中需要单独取label中的某一个元素，如果是1xN的矩阵的话，无法用label[i]的方式读取
#对于只有1xN的label可以不转换成矩阵，直接label[i]即可，这里转换是为了格式上的统一
labelMat = np.mat(labelArr).T
#获取数据矩阵的大小，为m*n
m, n = np.shape(dataMat)
#创建初始权重w，初始值全为0。
#np.shape(dataMat)的返回值为m，n -> np.shape(dataMat)[1])的值即为n，与
#样本长度保持一致
w = np.zeros((1, np.shape(dataMat)[1]))
#初始化偏置b为0
b = 0
#初始化步长，也就是梯度下降过程中的n，控制梯度下降速率
h = 0.0001
#进行iter次迭代计算
for k in range(iter):
#对于每一个样本进行梯度下降
#李航书中在2.3.1开头部分使用的梯度下降，是全部样本都算一遍以后，统一
#进行一次梯度下降
#在2.3.1的后半部分可以看到（例如公式2.6 2.7），求和符号没有了，此时用
#的是随机梯度下降，即计算一个样本就针对该样本进行一次梯度下降。
#两者的差异各有千秋，但较为常用的是随机梯度下降。
for i in range(m):
#获取当前样本的向量
xi = dataMat[i]
#获取当前样本所对应的标签
yi = labelMat[i]
#判断是否是误分类样本
#误分类样本特诊为： -yi(w*xi+b)>=0，详细可参考书中2.2.2小节
#在书的公式中写的是>0，实际上如果=0，说明改点在超平面上，也是不正确的
if -1 * yi * (w * xi.T + b) >= 0:
#对于误分类样本，进行梯度下降，更新w和b
w = w + h * yi * xi
b = b + h * yi
#打印训练进度
print('Round %d:%d training' % (k, iter))
#返回训练完的w、b
return w, b
def test(dataArr, labelArr, w, b):
'''
测试准确率
:param dataArr:测试集
:param labelArr: 测试集标签
:param w: 训练获得的权重w
:param b: 训练获得的偏置b
:return: 正确率
'''
print('start to test')
#将数据集转换为矩阵形式方便运算
dataMat = np.mat(dataArr)
#将label转换为矩阵并转置，详细信息参考上文perceptron中
#对于这部分的解说
labelMat = np.mat(labelArr).T
#获取测试数据集矩阵的大小
m, n = np.shape(dataMat)
#错误样本数计数
errorCnt = 0
#遍历所有测试样本
for i in range(m):
#获得单个样本向量
xi = dataMat[i]
#获得该样本标记
yi = labelMat[i]
#获得运算结果
result = -1 * yi * (w * xi.T + b)
#如果-yi(w*xi+b)>=0，说明该样本被误分类，错误样本数加一
if result >= 0: errorCnt += 1
#正确率 = 1 - （样本分类错误数 / 样本总数）
accruRate = 1 - (errorCnt / m)
#返回正确率
return accruRate
if __name__ == '__main__':
#获取当前时间
#在文末同样获取当前时间，两时间差即为程序运行时间
start = time.time()
#获取训练集及标签
trainData, trainLabel = loadData('../Mnist/mnist_train.csv')
#获取测试集及标签
testData, testLabel = loadData('../Mnist/mnist_test.csv')
#训练获得权重
w, b = perceptron(trainData, trainLabel, iter = 30)
#进行测试，获得正确率
accruRate = test(testData, testLabel, w, b)
#获取当前时间，作为结束时间
end = time.time()
#显示正确率
print('accuracy rate is:', accruRate)
#显示用时时长
print('time span:', end - start)