Example Illustrating the LBG Algorithm with Implementation Insights

The LBG algorithm is a classic vector quantization method widely used in image compression and data dimensionality reduction. Its core principle involves iteratively clustering data into subsets and generating representative codewords for each subset, achieving compression or feature extraction objectives.

Consider an image grayscale compression scenario: Assume the original image contains millions of pixels, each with a grayscale value ranging from 0-255. The LBG algorithm begins by randomly initializing N codewords (e.g., N=16), representing candidate grayscale values for compression. The iterative optimization proceeds through the following steps, which can be implemented using functions like `kmeans` in MATLAB or custom distance-calculation loops:

Partitioning Phase: Calculate the Euclidean distance between all pixels and current codewords (using vectorized operations for efficiency), assigning each pixel to the cluster of its nearest codeword. Update Phase: Recompute the mean of all pixels within each cluster (e.g., with `mean()` function applied per cluster) and set this mean as the new codeword. Termination Condition: The iteration stops when codeword changes fall below a threshold or the maximum iteration count is reached, typically monitored via a while-loop with convergence checks.

Ultimately, each pixel in the image only requires storage of its cluster index (just 4 bits for 16 codewords) instead of the original 8-bit grayscale value, achieving a 50% compression rate. This process highlights the LBG algorithm's strong similarity to K-Means clustering but emphasizes optimization for vector space quantization, where code implementation focuses on efficient distance calculations and centroid updates.