This paper first explains how the relations between Japanese Alzheimer's disease (AD) patients and their mitochondrial SNP frequencies at individual mtDNA positions examined using the radial basis function (RBF) network and a method based on RBF network predictions and that Japanese AD patients are associated with the haplogroups G2a and N9b1. It then describes a method for the initial diagnosis of Alzheimer's disease that is based on the mtSNP haplogroups of the AD patients. The method examines the relations between someone's mtDNA mutations and the mtSNPs of AD patients. As the mtSNP haplogroups thus obtained indicate which nucleotides of mtDNA loci are changed in the Alzheimer's patients, a person's probability of becoming an AD patient can be predicted by comparing those mtDNA mutations with that person's mtDNA mutations. The proposed method can also be used to diagnose diseases such as Parkinson's disease and type 2 diabetes and to identify people likely to become centenarians.