Many classical machine learning techniques have been used to explore Alzheimer's disease (AD), evolving from image decomposition techniques such as principal component analysis toward higher complexity, non-linear decomposition algorithms. With the arrival of the deep learning paradigm, it has become possible to extract high-level abstract features directly from MRI images that internally describe the distribution of data in low-dimensional manifolds. In this work, we try a new exploratory data analysis of AD based on deep convolutional autoencoders. We aim at finding links between cognitive symptoms and the underlying neurodegeneration process by fusing the information of neuropsychological test outcomes, diagnoses, and other clinical data with the imaging features extracted solely via a data-driven decomposition of MRI. The distribution of the extracted features in different combinations is then analyzed and visualized using regression and classification analysis, and the influence of each coordinate of the autoencoder manifold over the brain is estimated. The imaging-derived markers could then predict clinical variables with correlations above 0.6 in the case of neuropsychological evaluation variables such as the MMSE or the ADAS11 scores, achieving a classification accuracy over 80% for the diagnosis of AD.