【Basic】Data Regression Prediction Based on Support Vector Machine (SVM) in Matlab

## 2.1 Establishment of SVM Regression Model

### 2.1.1 Selection of Kernel Function

The kernel function is a crucial component of the SVM regression model, ***mon kernel functions include:

- **Linear Kernel Function:** `K(x, y) = x^T y`, suitable for scenarios where data is linearly separable.
- **Polynomial Kernel Function:** `K(x, y) = (x^T y + c)^d`, where 'd' is the order of the polynomial and 'c' is a constant, suitable for non-linearly separable data.
- **Radial Basis Function (RBF):** `K(x, y) = exp(-γ ||x - y||^2)`, with 'γ' being the kernel width parameter, suitable for complex data distributions.

Choosing the appropriate kernel function requires experimentation and comparison based on the specific characteristics of the data to achieve optimal model performance.

### 2.1.2 Parameter Optimization and Model Evaluation

Parameters of the SVM regression model include the type of kernel function, kernel function parameters, and regularization parameters. Parameter optimization can be performed using methods such as cross-validation or grid search to find the optimal combination of parameters.

Model evaluation metrics include Mean Squared Error (MSE), Mean Absolute Error (MAE), and Coefficient of Determination (R^2). These metrics can be used to assess the predictive accuracy and generalization ability of the model.

# 2. Application of SVM in Data Regression

### 2.1 Establishment of SVM Regression Model

#### 2.1.1 Selection of Kernel Function

The kernel function is a key component of the SVM regression model, mapping the input space to a high-dimensional feature space, ***monly used kernel functions include:

- **Linear Kernel Function:** `k(x, y) = x^T y`
- **Polynomial Kernel Function:** `k(x, y) = (x^T y + c)^d`
- **Gaussian Kernel Function:** `k(x, y) = exp(-γ||x - y||^2)`
- **Sigmoid Kernel Function:** `k(x, y) = tanh(αx^T y + c)`

The choice of kernel function depends on the nature of the data and the complexity of the regression task. Generally, the Gaussian and polynomial kernel functions are suitable for non-linear data, while the linear kernel function is suitable for linear data.

#### 2.1.2 Parameter Optimization and Model Evaluation

Parameters of the SVM regression model include the type of kernel function, kernel function parameters (such as γ and c), regularization parameter C, and loss function parameter ε. These parameters need to be optimized through cross-validation or grid search.

Cross-validation is a technique to assess the generalization ability of a model, dividing the dataset into a training set and a test set, and evaluating the model's performance on the test set multiple times. Grid search is a parameter optimization technique that searches for the optimal combination of parameters within a given range.

Model evaluation metrics include Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R-squared value. RMSE and MAE measure the error between predicted values and actual values, while the R-squared value measures the goodness of fit of the model.

### 2.2 Performance Analysis of SVM Regression Model

#### 2.2.1 Evaluation Metrics and Model Comparison

The performance of the SVM regression model can be evaluated by comparing it with other regression models, such as linear regression, decision tree regression, and neural network regression. Evaluation metrics include RMSE, MAE, and R-squared value.

#### 2.2.2 Model Robustness and Generalization Ability

The robustness of the SVM regression model refers to its resistance to outliers and noise. Generalization ability refers to the model's predictive performance on unseen data. Robustness and generalization ability can be assessed through cross-validation and dataset splitting.

# Import necessary libraries
import numpy as np
import pandas as pd
from sklearn.svm import SVR
from sklearn.model_selection import train_test_split, cross_val_score

# Load data
data = pd.read_csv('data.csv')

# Split dataset into training set and test set
X_train, X_test, y_train, y_test = train_test_split(data.drop('target', axis=1), data['target'], test_size=0.2)

# Establish SVM regression model using Gaussian kernel function
model = SVR(kernel='rbf')

# O