Alzheimer’s disease (AD) is a degenerative disease with insidious onset and chronic nervous system, which can be roughly classified into three stages: preclinical AD, mild cognitive impairment (MCI), and clinical AD. Given that timely treatment of MCI can delay the course of AD, identifying what stage of the disease is at the time of early diagnosis is critical in clinical practice. Based on the survey data of elderly residents in Changsha community, this paper constructs the cognitive impairment data set and explores the application of the emerging classification algorithm Convolutional Support Vector Machine(CSVM) in identifying elderly cognitive impairment, a small data classification problem. CSVM is an improved Support Vector Machine classification(SVC) algorithm, which uses the convolution filtering idea of the Convolutional Neural Networks(CNN) algorithm to preprocess the nonlinearly separable sample set to improve the classification ability of SVM. In addition, the optimal convolution filter (solution) is found by the Simplified Swarm Optimization(SSO) algorithm and orthogonal array experimental design. A variable update amplitude method is also proposed to optimize the SSO update strategy further. Aiming at the problem of an unbalanced sample set, a stratified sampling method is used to divide and cross-validate the sample data, and a variety of evaluation indicators are used to evaluate the performance of the model. Experimental results show that the data set processed by a specific convolution filter can significantly improve the classification performance of linear SVM. The accurate differentiation of normal cognition(NC), MCI, and AD helps intervene in adjuvant treatment for potential patients timely.