Alzheimer's disease is a chronic degenerative disease of the central nervous system. Clinically early detection of Alzheimer's disease is helpful in taking care of the patients. The nuclear imaging method, single-photon emission computed tomography (SPECT), is a useful tool in analyzing the cerebral blood flow. Most common regional abnormalities for Alzheimer's disease are symmetric or asymmetric bilateral temporal or parietal hypoperfusion, or frontal hypoperfusion. Statistical Parametric Mapping (SPM) is employed to do pre-processing of SPECT volumes. Due to its effectiveness, easiness and fastness, SPM has been widely applied to the diagnosis and function research of brain diseases. The proposed system can provide a quantitatively automatic analysis of the SPECT volumes. The selection of three variables based on the statistical parametric t maps between Alzheimer's and normal volumes are proposed. Then an optimal linear classifier is applied to discriminate between these two group of volumes. In statistical pattern recognition, the Bayes error, the overlap among different class densities, is the smallest possible error in the current measurement space. Due to the effectiveness of the variable selection, the simple optimal linear classifier achieves a near-Bayes error ratio. The sensitivity and specificity of the proposed method are 88% and 90%, respectively. With the high sensitivity and specificity performance, the proposed automatic analysis of brain SPECT volumes can assist in the clinical practice of radiologists.