数学模型建立常用方法

目标:
美赛不当拖油瓶~~
数建最基本得建模方法

插值拟合

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:aab0373f-c8cc-4d19-9af4-ce46822b2d2f

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:15db3e44-e795-4908-a9f0-5b23835ceccb

小波分析,聚类分析(高斯混合聚类,K-均值聚类等)

用于插值之前
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:848c64fe-8291-4be2-93f5-ff25ee4c8275

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:0cc8e6c6-6e0c-4493-b6ab-888c918b81a0

主成分分析,线性判别分析、局部保留投影

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:95889bf0-48db-4dc8-8c9a-2a366f527d1c

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:3a4747c3-b18c-465a-9de9-3843284b8f41

均值、方差分析、协方差分析等统计方法

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:b40ae1d4-82d4-429c-9163-9e3333429f54

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:556fdd11-33f4-4f75-9c51-2dc0dde1e99f

指内部具有的关系

灰色关联分析

用于样本点个数较少

典型相关分析

适合两组指标之间的关系

Superman或kendall等级相关分析

Pearson相关或Copula相关

建立指标进行判别

距离聚类(系统聚类)

有坐标 常用

关联性聚类

常用 与指标有关

层次聚类

密度聚类

其他聚类

贝叶斯判别

统计判别方法

费舍尔判别

用于训练样本少

模糊识别

分好类的数据点比较少

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:262f7334-060c-4cef-891e-33cb4f2afd52

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:c1f08ded-24a8-49c2-8b66-bcce6c0185cd

模糊综合评价

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:1ed9b656-c9ae-44f0-a591-9f893d30b242

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:d6806402-1371-4be0-8afb-4f67c7978a5a

主成分分析

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:fd489e06-ecc3-4ec4-8e10-34b67ec17e9c

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:bc28fa2d-6141-4f4f-949e-07e2881b3117

指标间关联性很强

层次分析法

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:ad45d618-66f9-4ec1-a7cd-4ede3622df48

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:a98f4196-a898-453f-aad6-28864492c4e3

数据包络(DEA)分析法

优化问题
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:040432f9-4ff4-4455-9236-1268d0d91d97

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:7edc7602-db37-4d3e-b8fb-ac443ad85212

秩和比综合评价法

排序,指标间关联性不强

神经网络评价

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:5a8106b7-4a07-4d88-9ebf-e09e4a6e9f96

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:0f2e3a95-cc51-4ead-a2b5-cbbd435c718a

样本大才行

优劣解距离法(TOPSIS)

与层次分析法差不多

投影寻踪综合评价法

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:6e37dd42-d5c1-4356-8d60-4ead7c5a2d98

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:084b470a-13b8-4419-969b-c2624d621ae3

方差分析、协方差分析

比较基本

200可能是大小的界限
分五类

  • 小样本的内部预测
  • 大样本的内部预测
  • 小样本的未来预测
    [TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:1da807f3-90ce-42a2-b47d-895247ad3a39
    [En]

    [TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:cd63d538-f5cb-4097-b6d3-614edd33d3f4

  • 大样本的未来预测

灰色预测模型

数据样本点个数少,0-50个
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:ca089a15-7ae1-4abd-8ef1-c7ce711a4a1b

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:bf136a9a-d9e8-4084-a057-3467d7fa8b75

微分方程预测

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:645461a5-2dc1-4979-a28f-b3f7156dec28

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:04bdfa3c-a684-44ee-b275-ed59f3e91155

点数不少。50-100

插值拟合预测

小样本未来预测

回归分析预测

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:7550ec9b-8720-4495-b688-32d5ecc2391b

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:27553601-f983-4fe0-99c9-7d17eb8f7228

样本点个数n>3*自变量+1
因变量要符合正态分布

马尔科夫预测

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:c870fb74-70e5-4d09-b062-1ffaa72e93a3

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:5acfd0e3-9b15-4cd2-b11a-deb044b1f22e

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:38dda5ed-e123-427e-8e49-7a6a272249d6

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:8cc5675f-c320-446e-af70-9c4fb4107247

时间序列预测

大样本
[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:9961d897-524f-4c27-96cf-97beaec42089

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:0c179dff-fdd8-44d1-9554-9a5ef8932af3

ARMA模型,周期模型,季节模型

小波分析预测

神经网络预测

混沌序列预测

设计最优解
组合得最优解

线性规划,整数规划,0-1规划

简单的问题(物料、车间
有约束,有明确的目标

非线性规划与智能优化算法

复杂优化问题

多目标规划和目标规划

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:920498a3-9199-4caf-9d63-7f73ceace39b

[En]

[TencentCloudSDKException] code:FailedOperation.ServiceIsolate message:service is stopped due to arrears, please recharge your account in Tencent Cloud requestId:465c5348-6d5f-4781-8cc4-69917d5c4aa1

动态规划

图论、网络优化

多因素交错复杂

排队论与计算机仿真

模糊规划

范围约束

灰色规划

Original: https://blog.csdn.net/jiangti_ng/article/details/122630307
Author: 大数据界Olu
Title: 数学模型建立常用方法

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