MATLAB Implementation of Gaussian Kernel Function - A Commonly Used Kernel in Machine Learning

In machine learning and data mining, kernel functions serve as essential tools that map original data into higher-dimensional spaces, making data more separable for classification tasks. Among various kernel functions, the Gaussian kernel (also known as Radial Basis Function kernel) is particularly popular due to its ability to handle non-linear relationships through adjustable bandwidth parameters. The MATLAB implementation below calculates the Gaussian kernel similarity between two vectors: function K = gaussianKernel(x1, x2, sigma) % x1 and x2 are n-dimensional vectors % sigma represents the kernel bandwidth parameter controlling the influence radius sim = x1 - x2; K = exp(-(sim' * sim) / (2 * sigma^2)); end Key implementation details: - The function computes the squared Euclidean distance between vectors using (sim' * sim) - The exponential term transforms the distance measure into a similarity score - The sigma parameter regulates the kernel's sensitivity to distance variations Beyond the Gaussian kernel, other common kernel functions include linear kernels and polynomial kernels, each possessing distinct characteristics and applications. The linear kernel performs simple dot products suitable for linearly separable data, while polynomial kernels can capture more complex relationships through degree parameters. Therefore, kernel selection requires careful analysis based on specific problem domains and data characteristics, considering factors such as data distribution, computational complexity, and expected relationship patterns.