Tensor decomposition for time-resolved immune cell sequencing in cancer

Abstract

The immune system plays a crucial role in the detection and elimination of cancer cells, with T cell receptors (TCRs) enabling antigen recognition. γδ T cells are a less common and relatively understudied subset of T cells compared to their αβ counterparts. Although they have been shown to play important roles in cancer immunity, especially due to their ability to act independently of MHC (Major Histocompatibility Complex) presentation, much less is known about their behavior over time. This makes them a promising but challenging target for immune repertoire analysis. This thesis applies different tensor decomposition methods to time-resolved γδ TCR sequencing data from sarcoma patients to uncover interpretable immune dynamics. After preprocessing, data from 13 of 16 patients were retained, and multiple tensors of varying temporal lengths (70, 100, 200, and 300 days) were constructed to balance patient availability with time resolution. Three decomposition models (CP, Tucker, and PARAFAC2) were applied to both simulated and real data to evaluate their ability to capture latent patterns across sequences, time, and patients. Furthermore, a clustering pipeline was applied to extract the patient outcomes and was compared to ground-truth data. Our results with the simulated data validate that tensor decomposition can be an effective tool for finding relevant patterns and subgroups in the data. In particular, by clustering the patient factor matrices of the Tucker decomposition, we observed groupings that showed partial agreement with known clinical labels, suggesting that the model captures some meaningful variation in immune response. In addition to unsupervised pattern discovery, we evaluated classical immunological metrics, including richness, evenness, and clonality, over time to further characterize immune repertoire dynamics. Therefore, this work confirms that tensor decomposition can extract informative, low-dimensional representations from complex immune repertoire data and may support future efforts in stratifying patients or monitoring treatment responses.