High-throughput analysis of animal behavior is increasingly common following the advances of recording technology, leading to large high-dimensional data sets. This dimensionality can sometimes be reduced while still retaining relevant information. In the case of the nematode worm Caenorhabditis elegans, more than 90% of the shape variance can be captured using just four principal components. However, it remains unclear if other methods can achieve a more compact representation or contribute further biological insight to worm locomotion. Here we take a data-driven approach to worm shape analysis using independent component analysis (ICA), non-negative matrix factorization (NMF), a cosine series, and jPCA (a dynamic variant of principal component analysis [PCA]) and confirm that the dimensionality of worm shape space is close to four. Projecting worm shapes onto the bases derived using each method gives interpretable features ranging from head movements to tail oscillation. We use these as a comparison method to find differences between the wild type N2 worms and various mutants. For example, we find that the neuropeptide mutant nlp-1(ok1469) has an exaggerated head movement suggesting a mode of action for the previously described increased turning rate. The different bases provide complementary views of worm behavior and we expect that closer examination of the time series of projected amplitudes will lead to new results in the future.