In recent years, the accurate detection of Alzheimer's disease (AD) at its early stage, using various biomarkers through machine learning techniques, has been given paramount importance in the medical field. However, in reality, the input datasets contain lots of missing values due to several factors such as increasing mortality rate, avoiding invasive procedures, and dropping out from the study. In this work, after analyzing the pattern of structural and clinical data from tadpole study in Alzheimer's disease neuroimaging initiative (ADNI) database, it has been found that the unobserved data are not missing completely at random. In view of this fact, with the assumption that the missing data patterns are in blocks, we propose a novel stacked sparse autoencoder based method to assign a value in the missing places and to select the significant structural and clinical features in order to discriminate the patients having AD, mild cognitive impairment (MCI), and cognitively normal (CN) clinical status. Through experimental results, it is shown that the proposed imputation algorithm achieves better performance for semi-supervised AD classification in terms of accuracy, sensitivity, and specificity in 5-fold cross validation when compared to the state-of-the-art methods.