Vector Quantization Using LBG Method with Center Splitting Algorithm

Vector quantization is a fundamental process for converting continuous or analog signals into digital representations through discrete coding. The LBG algorithm, developed by Linde, Buzo, and Gray, serves as a widely adopted approach for vector quantization codebook design. This algorithm operates through iterative clustering of input data vectors into a set of representative codewords that form the quantization codebook. The implementation begins with a single codeword (typically the centroid of the entire dataset) and employs a center splitting mechanism where each codeword is iteratively divided into two new codewords. This splitting process involves adding small perturbation vectors to the original codeword, followed by Lloyd's algorithm iterations that alternate between nearest-neighbor partitioning and centroid recalculation. The algorithm continues this splitting and optimization cycle until achieving the target codebook size, ensuring each codeword represents a Voronoi region in the vector space. Key implementation considerations include: initial distortion calculation, splitting factor determination, convergence threshold setting, and mean squared error minimization during centroid updates. The LBG method with center splitting has demonstrated effectiveness in various applications including image compression (codebook design for VQ-based compression), speech coding (vector quantization of LPC parameters), pattern recognition (feature vector quantization), and data mining (high-dimensional data clustering). The algorithm typically requires careful parameter tuning for splitting epsilon values and iteration limits to balance computational efficiency and quantization accuracy.