Longitudinal’omics analytical methods are extensively used in the field of evolving precision medicine, by enabling ‘big data’ recording and high-resolution interpretation of complex datasets, driven by individual variations in response to perturbations such as disease pathogenesis, medical treatment or changes in lifestyle. However, inherent technical limitations in biomedical studies often result in the generation of feature-rich and sample-limited datasets. Analyzing such data using conventional modalities often proves to be challenging since the repeated, high-dimensional measurements overload the outlook with inconsequential variations that must be filtered from the data in order to find the true, biologically relevant signal. Tensor methods for the analysis and meaningful representation of multi-way data may prove useful to the biological research community by their advertised ability to tackle this challenge. In this study, we present TCAM—a new unsupervised tensor factorization method for the analysis of multi-way data. Building on top of cutting-edge developments in the field of tensor-tensor algebra, we characterize the unique mathematical properties of our method, namely, 1) preservation of geometric and statistical traits of the data, which enables uncovering information beyond the inter-individual variation that often takes-over the focus, especially in human studies. 2) Natural and straightforward out-of-sample extension, making TCAM amenable for integration in machine learning workflows. A series of re-analyses of real-world, human experimental datasets showcase these theoretical properties, while providing empirical confirmation of TCAM’s utility in the analysis of longitudinal’omics data.