2021年美赛C题：亚洲大黄蜂扩散模型与图像识别策略

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"Solution.pdf"文档提供了2021年美国大学生数学建模竞赛C题的解决方案，该题关注的主题是亚洲大黄蜂在加拿大不列颠哥伦比亚省温哥华岛的扩散情况及其影响。参赛团队采用综合评估模型，结合传播预测模型、图像分类模型以及数据描述准确度，以优化公共资源的利用，进行深入调查。第一部分，团队对报告中提供的阳性ID传播距离进行了时间序列分析。通过对数据的平稳性检验和差异分析，确认了该系列具有可预测性。他们采用了自回归移动平均模型（ARIMA），来拟合这些数据，以便对未来黄蜂扩散趋势进行预测。同时，他们还研究了纬度季节变化和经度变化的影响，这有助于理解可能影响扩散的关键地理因素。在第二部分，针对图像识别的要求，团队采取了策略性方法。他们通过过采样技术增强训练数据集，以解决类别不平衡问题，同时着重于特征权重，提高了模型的代表性。此外，团队还引入了L2正则化和Dropout技术，以防止过拟合，确保模型在泛化能力上的提升。他们构建了一个分类模型，这个模型旨在精确识别与亚洲大黄蜂相关的图像，为追踪和控制提供关键依据。整个解决方案展示了参赛者如何运用统计学、机器学习和数据科学的方法来解决实际环境中的问题，强调了模型的实用性和有效性。通过这种综合运用，团队不仅解决了比赛中的挑战，也为实际工作中处理类似问题提供了有价值的参考框架。"

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2.Date and latitude and longitude of all positive reports, calculate the distance between these

locations and the source of propagation. If the distance image is drawn at intervals of one day,

then the derivative of the line between two adjacent valid data points should be always greater

than zero or always less than zero.

3.According to the available data, for all positive reports, the location corresponding to the

earliest date is determined to be the source of transmission, and there should be no positive

reports earlier than this report.

4.The positive identification result model analysis of all unverified samples found that almost no

samples in this part will be re-identified as positive. Therefore, the positive data that may exist in

the unverified samples are ignored. We only based on the existing known samples of Asian The

giant hornet makes propagation predictions.

1.4.2 Hypothesis of classification model based on convolutional neural network (CNN)

In the file 2021MCM ProblemC Images by GlobalID.xlsx and the file 2021 MCM ProblemC

DataSet.xlsx, we found that only reports containing image information can give Lab comments.

That is to say, although some witnesses have submitted reports to the laboratory, which do not

contain image information, the laboratory is unable to judge whether these reports describe the

Asian giant hornets or not. Therefore, in this model, we only consider reports that contain image

information that can be judged, and consider that reports that do not contain image information

are invalid data. Since the report provided by the witnesses to the laboratory

contains .jpg, .png, .mp4, and. video files, the .jpg file occupies the vast majority and only

contains one .mp4 and. video file, so this model is only for. jpg file, other files can be ignored

due to too few.

2 Problem analysis

2.1 Task1

Problem one requires us to analyze the spread of Asian giant hornets over time. From the

information in the task, we can observe that the distribution of hornets varies with time, and the

position information this time is relative to the position information next time. Therefore, Time-

Series Analysis can be used properly. After judgment, the data is stable, so the ARIMA model

can be used to solve the problem.

2.2 Task2

Problem two requires us to build a model of the likelihood of classification errors. In order to

achieve the purpose, we use Python to match the positive ID and negative ID in the data set file

one by one to construct the training set and the test set. At the same time, the data is filtered to

remove unprocessed corresponding pictures and other non-picture files. What’s more, we use the

training set to construct and train the h5 model, after that, we can draw conclusions easily.

2.3 Task3

Problem three requires us to build a model to solve the problem of how to determine the report as

a positive identification. As a result, we introduced the AHP model to combine quantitative

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