Chronic obstructive pulmonary disease (COPD) is a heterogeneous disease and the traditional variables extracted from computed tomography (CT) images may not be sufficient to describe all the topological features of lung tissues in COPD patients. We employed an unsupervised three-dimensional (3D) convolutional autoencoder (CAE)-feature constructor (FC) deep learning network to learn from CT data and derive tissue pattern-clusters jointly. We then applied exploratory factor analysis (EFA) to discover the unobserved latent traits (factors) among pattern-clusters. CT images at total lung capacity (TLC) and residual volume (RV) of 541 former smokers and 59 healthy non-smokers from the cohort of the SubPopulations and Intermediate Outcome Measures in the COPD Study (SPIROMICS) were analyzed. TLC and RV images were registered to calculate the Jacobian (determinant) values for all the voxels in TLC images. 3D Regions of interest (ROIs) with two data channels of CT intensity and Jacobian value were randomly extracted from training images and were fed to the 3D CAE-FC model. 80 pattern-clusters and 7 factors were identified. Factor scores computed for individual subjects were able to predict spirometry-measured pulmonary functions. Two factors which correlated with various emphysema subtypes, parametric response mapping (PRM) metrics, airway variants, and airway tree to lung volume ratio were discriminants of patients across all severity stages. Our findings suggest the potential of developing factor-based surrogate markers for new COPD phenotypes.