【Advanced】Data Classification based on SVDD Algorithm with Matlab Simulation

# [Advanced篇] Data Classification Based on SVDD Algorithm in MATLAB Simulation

### 2.1 Data Preprocessing and Feature Extraction

#### 2.1.1 Data Standardization and Normalization

Data standardization and normalization are important steps in data preprocessing, as they can eliminate the influence of data units, enhance the robustness and convergence speed of the algorithm.

**Standardization**: Transforms data into a distribution with a mean of 0 and a standard deviation of 1. The commonly used standardization method is z-score standardization, with the formula:

x_std = (x - mean(x)) / std(x)

**Normalization**: Maps data to the range of [0, 1] or [-1, 1]. The commonly used normalization method is min-max normalization, with the formula:

x_norm = (x - min(x)) / (max(x) - min(x))

### 2.1.2 Feature Selection and Dimension Reduction

Feature selection and dimension reduction can reduce the dimensionality of the data, remove redundant and irrelevant features, and improve the efficiency and accuracy of the algorithm.

**Feature Selection**: ***mon feature selection methods include:

- **Filter Methods**: Evaluate feature importance based on statistical measures (e.g., information gain, chi-square test).
- **Wrapper Methods**: Embed the feature selection process into model training to select features that enhance model performance.

**Dimension Reduction**: ***mon dimension reduction methods include:

- **Principal Component Analysis (PCA)**: Projects data onto the direction of maximum variance.
- **Singular Value Decomposition (SVD)**: Decomposes data into a product of singular values and orthogonal matrices.

# 2. Implementation of SVDD Algorithm in MATLAB

### 2.1 Data Preprocessing and Feature Extraction

#### 2.1.1 Data Standardization and Normalization

In the SVDD algorithm, data standardization and normalization are crucial preprocessing steps. Standardization transforms data into a distribution with a mean of 0 and a standard deviation of 1, while normalization maps data to the range of [0, 1] or [-1, 1]. These operations help enhance the robustness and convergence speed of the algorithm.

The following MATLAB functions can be used for data standardization and normalization:

% Data Standardization
data_std = zscore(data);

% Data Normalization to [0, 1]
data_normalized = normalize(data, 'range');

% Data Normalization to [-1, 1]
data_normalized = normalize(data, 'range', [-1, 1]);

#### 2.1.2 Feature Selection and Dimension Reduction

Feature selection and dimension reduction are common techniques to reduce data dimensions and improve algorithm efficiency. Feature selection reduces the number of features by choosing those with discriminatory power, whereas dimension reduction reduces data complexity by projecting high-dimensional data into lower-dimensional spaces.

The following MATLAB functions can be used for feature selection and dimension reduction:

% Feature Selection (based on variance)
[selected_features, ~] = featureSelect(data, 'variance');

% Principal Component Analysis (PCA)
[coeff, score, latent] = pca(data);

% Linear Discriminant Analysis (LDA)
[coeff, score, latent] = lda(data, labels);

### 2.2 SVDD Model Construction and Parameter Optimization

#### 2.2.1 Selection of Kernel Function and Parameter Setting

The kernel function is a key component of the SVDD algorithm, ***monly used kernel functions include linear, polynomial, radial basis function (RBF), and sigmoid kernels.

The following MATLAB functions can be used to select and set kernel function parameters:

% Linear Kernel
kernel = 'linear';

% Polynomial Kernel
kernel = 'polynomial';
kernel_degree = 3; % Polynomial order

% Radial Basis Function (RBF) Kernel
kernel = 'rbf';
kernel_sigma = 0.5; % Width parameter for RBF kernel

% Sigmoid Kernel
kernel = 'sigmoid';
kernel_gamma = 1; % Slope parameter for sigmoid kernel

#### 2.2.2 Model Training and Hyperparameter Optimization

Training the SVDD model involves selecting a kernel function, setting hyperparameters (such as the penalty parameter C and kernel function parameters), and solving an optimization problem. The following MATLAB function can be used to train the SVDD model:

% Train SVDD Model
model = fitcsvm(data, labels, 'KernelFunction', kernel, ...
     'BoxConstraint', C, 'KernelScale', kernel_sigma);

Hyperparameter optimization can be improved using techniques such as grid search or Bayesian optimization. The following MATLAB functions can be used for hyperparameter optimization:

% Grid Search
[best_C, best_sigma] = gridSearch(@fitcsvm, data, labels, ...
     'KernelFunction', kernel, 'BoxConstraint', [0.1, 1, 10], ...
     'KernelScale', [0.1, 0.5, 1]);

% Bayesian Optimization
[best_C, best_sigma] = bayesopt(@fitcsvm, data, labels, ...
     'KernelFunction', kernel, 'BoxConstraint', [0.1, 10], ...