Two reductions in competitive learning founded on distortion standards are discussed from the viewpoint of generating necessary and appropriate reference vectors under the condition of their predetermined number. The first approach is termed the segmental reduction and competitive learning algorithm. The algorithm is presented as follows: First, numerous reference vectors are prepared and the algorithm is processed under competitive learning. Next, reference vectors are sequentially eliminated to reach their prespecified number based on the partition error criterion. The second approach is termed the general reduction and competitive learning algorithm. The algorithm is presented as follows: First, numerous reference vectors are prepared and the algorithm is processed under competitive learning. Next, reference vectors are sequentially erased based on the average distortion criterion. Experimental results demonstrate the effectiveness of our approaches compared to conventional techniques in average distortion. The two approaches are applied to image coding to determine their feasibility in quality and computation time.