Speech intelligibility is an important assessment criterion of the communicative performance of pathological speakers. To assist clinicians in their assessment, time- and cost-efficient automatic intelligibility measures offering a repeatable and reliable assessment are desired. In this paper, we propose to automatically assess pathological speech intelligibility based on a distance measure between the subspaces of spectral patterns of the pathological speech signal and of a fully intelligible (healthy) speech signal. To extract the subspace of spectral patterns we investigate two linear decomposition methods, i.e., Principal Component Analysis and Approximate Joint Diagonalization. Pathological speech intelligibility is then derived using a Grassman distance measure which quantifies the difference between the extracted subspaces of pathological and healthy speech. Experiments on an English database of Cerebral Palsy patients show that the proposed intelligibility measure is significantly correlated with subjective intelligibility ratings. In addition, comparisons to state-of-the-art measures show that the proposed subspace-based measure achieves a high performance with a significantly lower computational cost and without imposing any constraints on the speech material of the speakers.