MATLAB Source Code for Curve Fitting Using Gaussian Mixture Models

The MATLAB source code for Gaussian mixture model curve fitting employs probability distributions to model complex data patterns. The core algorithm utilizes a weighted combination of multiple Gaussian distributions, where each component has distinct mean (μ) and variance (σ²) parameters. Through iterative expectation-maximization (EM) algorithm, the code automatically optimizes the weights, means, and covariances to form a composite distribution that best represents the underlying data structure. Key implementation aspects include: - Initialization of Gaussian components using k-means clustering - Expectation step computing posterior probabilities via Bayes' theorem - Maximization step updating parameters using maximum likelihood estimation - Convergence checking through log-likelihood improvement thresholds To effectively utilize this source code, users should possess fundamental knowledge of probability theory and MATLAB programming. The code provides modular functions for data preprocessing, model initialization, and parameter customization, allowing adaptation to specific dataset characteristics and modeling requirements. Data quality considerations are critical for successful implementation. The code incorporates data validation routines and supports common preprocessing techniques like outlier removal and normalization. Users must verify whether their datasets satisfy GMM assumptions, including sample independence and adequate component separation, to ensure model validity. The implementation includes diagnostic tools for assessing model fit through residual analysis and goodness-of-fit metrics.