Vector Quantization Using LBG Method with Center Splitting Technique

Vector quantization serves as a fundamental technique in data compression and signal processing applications, effectively reducing the dimensionality of complex high-dimensional data. The Linde-Buzo-Gray (LBG) algorithm stands as a widely adopted method for generating optimal codebooks that accurately represent input data vectors. A critical component of this algorithm is the center splitting approach, which systematically refines the codebook through iterative optimization. The LBG algorithm implementation typically begins with initializing a codebook containing a single centroid representing the entire dataset's mean. The center splitting mechanism then enhances the codebook through these computational stages: Initialization – Starting with a single centroid computed as the global mean of all input vectors Splitting – Each existing centroid undergoes perturbation by generating two new vectors: centroid + ε and centroid - ε, where ε represents a small distortion vector, effectively doubling the codebook size Clustering – Assignment of all input vectors to their nearest codewords using distance calculations (commonly Euclidean distance: d(x,y) = √Σ(x_i-y_i)²) Centroid Update – Recalculation of each codeword as the arithmetic mean of all vectors in its corresponding cluster Iteration – Repeated execution of splitting, clustering, and centroid updates until achieving the target codebook size or meeting distortion threshold criteria This methodology ensures the final codebook closely approximates the original data distribution while minimizing quantization error. The center splitting technique proves particularly effective in speech coding and image compression applications where maintaining information integrity during dimensionality reduction is paramount. The algorithm's robustness stems from its straightforward implementation and guaranteed convergence properties. However, practical implementations often incorporate optimizations like tree-structured vector quantization (TSVQ) to enhance computational efficiency when handling large-scale datasets. Key implementation considerations include appropriate distance metric selection, convergence threshold setting, and efficient nearest-neighbor search algorithms.