Recently, the outbreak of Coronavirus Disease 2019 (COVID-19) has spread rapidly across the world. Due to the large number of infected patients and heavy labor for doctors, computer-aided diagnosis with machine learning algorithm is urgently needed, and could largely reduce the efforts of clinicians and accelerate the diagnosis process. Chest computed tomography (CT) has been recognized as an informative tool for diagnosis of the disease. In this study, we propose to conduct the diagnosis of COVID-19 with a series of features extracted from CT images. To fully explore multiple features describing CT images from different views, a unified latent representation is learned which can completely encode information from different aspects of features and is endowed with promising class structure for separability. Specifically, the completeness is guaranteed with a group of backward neural networks (each for one type of features), while by using class labels the representation is enforced to be compact within COVID-19/community-acquired pneumonia (CAP) and also a large margin is guaranteed between different types of pneumonia. In this way, our model can well avoid overfitting compared to the case of directly projecting high-dimensional features into classes. Extensive experimental results show that the proposed method outperforms all comparison methods, and rather stable performances are observed when varying the number of training data.