Accurate identification of Alzheimer's disease (AD) and mild cognitive impairment (MCI) is crucial so as to improve diagnosis techniques and to better understand the neurodegenerative process. In this work, we aim to apply the machine learning method to individual identification and identify the discriminate features associated with AD and MCI. Diffusion tensor imaging scans of 48 patients with AD, 39 patients with late MCI, 75 patients with early MCI, and 51 age-matched healthy controls (HCs) are acquired from the Alzheimer's Disease Neuroimaging Initiative database. In addition to the common fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity metrics, there are two novel metrics, named local diffusion homogeneity that used Spearman's rank correlation coefficient and Kendall's coefficient concordance, which are taken as classification metrics. The recursive feature elimination method for support vector machine (SVM) and logistic regression (LR) combined with leave-one-out cross validation are applied to determine the optimal feature dimensions. Then the SVM and LR methods perform the classification process and compare the classification performance. The results show that not only can the multi-type combined metrics obtain higher accuracy than the single metric, but also the SVM classifier with multi-type combined metrics has better classification performance than the LR classifier. Statistically, the average accuracy of the combined metric is more than 92% for all between-group comparisons of SVM classifier. In addition to the high recognition rate, significant differences are found in the statistical analysis of cognitive scores between groups. We further execute the permutation test, receiver operating characteristic curves, and area under the curve to validate the robustness of the classifiers, and indicate that the SVM classifier is more stable and efficient than the LR classifier. Finally, the uncinated fasciculus, cingulum, corpus callosum, corona radiate, external capsule, and internal capsule have been regarded as the most important white matter tracts to identify AD, MCI, and HC. Our findings reveal a guidance role for machine-learning based image analysis on clinical diagnosis.