Function Normalization Implementation Using MATLAB

Implementing function normalization in MATLAB is a common preprocessing step, particularly useful for scaling data to uniform dimensions. The core objective of normalization is to adjust data distribution so that it has a mean of 0 and standard deviation of 1, a process also known as standardization (Z-score normalization). The implementation approach follows these key algorithmic steps: 1. Compute Mean and Standard Deviation: Calculate the mean (using MATLAB's `mean()` function) and standard deviation (using `std()`) of input data. These statistical measures determine the linear transformation parameters for normalization. 2. Centralization Processing: Subtract the mean from original data using vectorized operations (e.g., `data - mean_value`) to shift the data distribution center to zero. 3. Variance Scaling: Divide the centralized data by the standard deviation (e.g., `centered_data ./ std_value`) to standardize the dispersion of new data to unity. This normalization method preserves the original data distribution pattern while eliminating dimensional differences. In machine learning applications, normalization accelerates gradient descent convergence; in signal processing, it prevents scale discrepancies between different sensor data. MATLAB's built-in `zscore` function can directly perform this operation, but understanding its underlying logic enables custom extensions (such as handling missing values or performing dimension-specific normalization through axis parameter adjustments in custom functions).