Fluorodeoxyglucose (FDG) positron emission tomography (PET) measures the decline in the regional cerebral metabolic rate for glucose, offering a reliable metabolic biomarker even on presymptomatic Alzheimer's disease (AD) patients. PET scans provide functional information that is unique and unavailable using other types of imaging. However, the computational efficacy of FDG-PET data alone, for the classification of various Alzheimers Diagnostic categories, has not been well studied. This motivates us to correctly discriminate various AD Diagnostic categories using FDG-PET data. Deep learning has improved state-of-the-art classification accuracies in the areas of speech, signal, image, video, text mining and recognition. We propose novel methods that involve probabilistic principal component analysis on max-pooled data and mean-pooled data for dimensionality reduction, and multilayer feed forward neural network which performs binary classification. Our experimental dataset consists of baseline data of subjects including 186 cognitively unimpaired (CU) subjects, 336 mild cognitive impairment (MCI) subjects with 158 Late MCI and 178 Early MCI, and 146 AD patients from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset. We measured F1-measure, precision, recall, negative and positive predictive values with a 10-fold cross validation scheme. Our results indicate that our designed classifiers achieve competitive results while max pooling achieves better classification performance compared to mean-pooled features. Our deep model based research may advance FDG-PET analysis by demonstrating their potential as an effective imaging biomarker of AD.