Imaging mass spectrometry (IMS) is a promising technology which allows for detailed analysis of spatial distributions of (bio)molecules in organic samples. In many current applications, IMS relies heavily on (semi)automated exploratory data analysis procedures to decompose the data into characteristic component spectra and corresponding abundance maps, visualizing spectral and spatial structure. The most commonly used techniques are principal component analysis (PCA) and independent component analysis (ICA). Both methods operate in an unsupervised manner. However, their decomposition estimates usually feature negative counts and are not amenable to direct physical interpretation. We propose probabilistic latent semantic analysis (pLSA) for non-negative decomposition and the elucidation of interpretable component spectra and abundance maps. We compare this algorithm to PCA, ICA, and non-negative PARAFAC (parallel factors analysis) and show on simulated and real-world data that pLSA and non-negative PARAFAC are superior to PCA or ICA in terms of complementarity of the resulting components and reconstruction accuracy. We further combine pLSA decomposition with a statistical complexity estimation scheme based on the Akaike information criterion (AIC) to automatically estimate the number of components present in a tissue sample data set and show that this results in sensible complexity estimates.