Melanoma is the most deadly skin cancer. Early diagnosis is a current challenge for clinicians. Current algorithms for skin lesions classification focus mostly on segmentation and feature extraction. This paper instead puts the emphasis on the learning process, proposing two kernel-based classifiers: support vector machines, and spin glass-Markov random fields. We benchmarked these algorithms against a state-of-the-art method on melanoma recognition. We show with extensive experiments that the support vector machine approach outperforms the other methods, proving to be an effective classification algorithm for computer assisted diagnosis of melanoma.