MATLAB Code Implementation for SOM Algorithm

Self-Organizing Map (SOM) is an unsupervised learning neural network model commonly used for data dimensionality reduction and visualization. MATLAB provides convenient toolbox functions to implement the SOM algorithm, with the following core concepts explained: SOM algorithm maps high-dimensional data to a low-dimensional (typically 2D) grid through competitive learning mechanisms. MATLAB implementation generally involves these key steps: Network Initialization: First define the network topology (such as rectangular or hexagonal grid) and randomly initialize weight vectors. The dimensionality of weight vectors matches the feature dimension of input data. In code, this involves setting grid dimensions using parameters like `dimensions = [10 10]` for a 10x10 grid. Competitive Process: For each input sample, calculate distances (e.g., Euclidean distance) to all neuronal weight vectors, identifying the closest neuron as the Best Matching Unit (BMU). This can be implemented using vectorized operations like `distances = sum((weights - input_vector).^2, 2)`. Weight Update: Adjust weights of the BMU and its neighboring neurons using a neighborhood function (e.g., Gaussian function), moving them closer to the current input sample. The neighborhood radius typically decreases gradually with increasing iterations. The update formula follows: `weights = weights + learning_rate * neighborhood * (input - weights)`. Iterative Training: Repeat the above process until reaching preset iteration limits or convergence conditions. During training, both learning rate and neighborhood radius dynamically decay to stabilize the network. MATLAB's training parameters include `trainParam.epochs` for iteration control. MATLAB's `selforgmap` function simplifies SOM implementation, allowing users to quickly build models by specifying grid dimensions and training parameters. After training, data distribution can be visualized using `plotsomhits`, while topological relationships between neurons can be displayed with `plotsomnd`. The SOM algorithm is particularly suitable for exploring intrinsic data structures, such as customer segmentation or image feature extraction. By adjusting grid size and training parameters, users can balance model granularity with generalization capability. Key tunable parameters include map size, learning rate schedules, and neighborhood radius decay functions.