doublez0108 / mathematic-model

Basic Mathematic Model | Study Notes & Demos

数学模型 | Mathematic Model

关于作者 | About the Auther

姓名 | Name:bust_in_silhouette:	张喆 | doubleZ
学校 | University:school:	同济大学 | Tongji Univ.
联系方式 | Email:email:	[email protected]

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开发环境 | Development Environment

• 操作系统 | Operating System: macOS Catalina 10.15.2
• IDE:
  • Jupiter notebook 6.0.1
  • PyCharm 2019.3.2
• 语言 | Language: python
• 主要依赖 | Dependances: sklearn, keras, scipy, numpy, matploblib, Axes3D, PIL

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基础数学模型 | Basic Mathematical Model

• 方程 | Euqation

  • 夹逼法求解一元高次方程 | Squeeze Theorem

• 矩阵 | Matrix

  • 基础运算 | Basic Operation
  • 奇艺值分解 | SVD

• 遗传算法 | Genetic Algorithm

  • 数值遗传算法寻优 | NGA for Optimization

    🌰刹车距离与车速关系 | The relationship between braking distance and speed

  • 数值遗传算法 | NGA

• 回归分析 Regression Analysis

  • 线性回归 | Linear Regression
    • 一元线性回归 | Unitary Linear Regression
    • 多元线性回归 | Multiple Linear Regression
  • 降维回归 | Dimension Reduction
    • 主成分分析 | PCA
    • 主成分回归 | PCR
  • 偏最小二乘法 | PLSR
  • 交叉验证 | Cross Validation

• 数据可视化 | Data Visualization

  • 常见图表 | Basic Chart

  • 三维图像 | 3D Fingure

  • 聚类分析 | Clustering Analysis

    • 无监督 | Unsupervised
    • 有监督 | PLSDA
    • 概率等高线模拟 | Probability Contour Simulation

    🌰鸢尾花数据可视化 | Iris data visualization

    🌰小麦优、劣颗粒分类聚类可视化 | Visualization of classification and clustering of superior and inferior grains in wheat

• 神经网络 | Neural Network

  • 神经网络 | Neural Network

  • 非线性分类 | Nonlinear Classification

  • MLPClassifier神经网络 | MLPC

  • MLPRegressor神经网络回归 | MLPR

    🌰手写数字图像识别 | Handwritten Digit Recognition

• 最优化建模 | Optimization

  • 线性规划 | Linear Programming

• 深度学习 | Deep Learning

  • Keras深度学习模型 | Keras

    🌰手写数字图像识别 | Handwritten Digit Recognition

    🌰小麦分类 | Classification of wheat

• 概率建模 | Probability

  • 朴素贝叶斯概率建模 | NBM

    🌰身高体重等与性别的关系 | The relationship between height, weight and gender

    🌰鸢尾花数据分类 | Iris data classification

    🌰网络文本分析 | Network text analysis

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项目结构 | Project Structure

.
├── DataVisualization
│   ├── Examples
│   │   ├── Iris
│   │   │   ├── IrisClassifyDV.ipynb
│   │   │   ├── IrisContourDV.ipynb
│   │   │   └── IrisDV_3D.ipynb
│   │   ├── README.md
│   │   └── WheatGrainClassification
│   │       ├── WheatGrainClassificationDV.py
│   │       ├── wheat_train_PCA_X.txt
│   │       └── wheat_train_PCA_Y.txt
│   ├── Plot
│   │   ├── plot.py
│   │   ├── plot3d.py
│   │   └── subplot.py
│   └── README.md
├── DeepLearning
│   └── Keras
│       ├── Examples
│       │   ├── HandwrittenDigitRecongnition_DL.ipynb
│       │   └── Wheat
│       │       ├── wheat.ipynb
│       │       ├── wheat_train_PCA_X.txt
│       │       └── wheat_train_PCA_Y.txt
│       ├── Keras.ipynb
│       └── README.md
├── GeneticAlgorithm
│   ├── Examples
│   │   └── Braking Distance Speed
│   │       ├── BrakingDistance_Speed.py
│   │       └── data.txt
│   ├── Individual.py
│   ├── NumericGeneticAlgorithm.py
│   └── README.md
├── Matrix
│   └── README.md
├── NeuralNetwork
│   ├── HandwrittenDigitRecongnition
│   │   ├── HandwrittenDigitRecongnition.ipynb
│   │   ├── HandwrittenDigitRecongnition.py
│   │   ├── README.md
│   │   ├── Sklearn.ipynb
│   │   └── handwritting.png
│   ├── MLPClassifier.ipynb
│   ├── MLPRegressor.ipynb
│   ├── NeuralNetwork.py
│   ├── NeurallNetwork.ipynb
│   ├── README.md
│   └── data
│       ├── 1x0.txt
│       └── 1y0.txt
├── Optimization
│   └── LinearProgramming
│       ├── Examples
│       │   └── example.py
│       └── README.md
├── Probability
│   └── NaiveBayesianModel
│       ├── Examples
│       │   ├── Gender
│       │   │   ├── GenderExample.ipynb
│       │   │   └── genderData.txt
│       │   ├── Iris
│       │   │   └── IrisExample.ipynb
│       │   └── NetworkTextAnalysis
│       │       ├── NetworkTextAnalysis.ipynb
│       │       └── text.txt
│       └── README.md
├── README.md
├── RegressionAnalysis
│   ├── CrossValidation
│   │   ├── CrossValidation.py
│   │   └── README.md
│   ├── DimensionReduction
│   │   ├── PrincipleComponentAnalysis
│   │   │   └── PCA.py
│   │   ├── PrincipleComponentRegression
│   │   │   └── PCR.py
│   │   └── README.md
│   ├── PartialLeastSquaresRegression
│   │   ├── PLSR.py
│   │   └── README.md
│   ├── README.md
│   └── UnaryLinearRegression
│       ├── ULR.py
│       └── data.txt
└── SolveEquations
    └── SqueezeTheorem
        ├── OneVarHighOrder.py
        └── README.md

34 directories, 56 files