Recent advances in data acquisition and sharing have made available large quantities of complex data in which features may have complex interrelationships or may not be scalar. For such datasets, the traditional matrix model is no longer appropriate and may fail to capture relationships between features or fail to discover the underlying concepts that features represent. These datasets are better modeled using tensors, which are high-order generalizations of matrices. However, naive tensor algorithms suffer from poor efficiency and may fail to consider spatiotemporal neighborhood relationships in analysis. To surmount these difficulties, we propose TWave, a wavelet and tensor-based methodology for automatic summarization, classification, concept discovery, clustering, and compression of complex datasets. We also derive TWaveCluster, a novel high-order clustering approach based on WaveCluster, and compare our approach against WaveCluster and k-means. The efficiency of our method is competitive with WaveCluster and significantly outperforms k-means. TWave consistently outperformed competitors in both speed and accuracy on a 9.3 GB medical imaging dataset. Our results suggest that a combined wavelet and tensor approach such as TWave may be successfully employed in the analysis of complex high-order datasets.