The self-organizing map (SOM) is an unsupervised learning algorithm which has been successfully applied to various applications. In the last several decades, there have been variants of SOM used in many application domains. In this work, two new SOM algorithms are developed for image quantization and compression. The first algorithm is a sample-size adaptive SOM algorithm that can be used for color quantization of images to adapt to the variations of network parameters and training sample size. Based on the sample-size adaptive self-organizing map, we use the sampling ratio of training data, rather than the conventional weight change between adjacent sweeps, as a stop criterion. As a result, it can significantly speed up the learning process. The second algorithm is a novel classified SOM method for edge preserving quantization of images using an adaptive subcodebook and weighted learning rate. The subcodebook sizes of two classes are automatically adjusted in training iterations that can be estimated incrementally. The proposed weighted learning rate updates the neuron efficiently no matter how large the weighting factor is.