The immune repertoire is a collection of immune recep-tors that has emerged as an important biomarker for both diagnostic and therapeutic of cancer patients. In terms of deep learning, analyzing immune repertoire is a challeng-ing multiple-instance learning problem in which the im-mune repertoire of an individual is a bag, and the immune receptor is an instance. Although several deep learning methods for immune repertoire analysis are introduced, they consider the immune repertoire as a set-like struc-ture that doesn’t take account of the nature of the im-mune response. When the immune response occurs, mu-tations are introduced to the immune receptor sequence sequentially to optimize the immune response against the pathogens that enter our body. As a result, immune receptors for the specific pathogen have the lineage of evolution; thus, immune repertoire is better represented as a graph-like structure. In this work, we present our novel method graph representation of immune repertoire (GRIP), which analyzes the immune repertoire as a hier-archical graph structure and utilize the collection of graph neural network followed by graph pooling and transformer to efficiently represents the immune reper-toire as an embedding vector. We show that GRIP predict the survival probability of cancer patients better than the set-based methods and graph-based structure is critical for performance. Also, GRIP provides interpretable re-sults, which prove that GRIP adequately use the progno-sis-related immune receptor and give further possibility to use the GRIP as the novel biomarker searching tool

Clustering is unsupervised and exploratory in nature. Yet, it can be performed through penalized regression with grouping pursuit, as demonstrated in Pan et al. (2013). In this paper, we develop a more efficient algorithm for scalable computation and a new theory of clustering consistency for the method. This algorithm, called DC-ADMM, combines difference of convex (DC) programming with the alternating direction method of multipliers (ADMM). This algorithm is shown to be more computationally efficient than the quadratic penalty based algorithm of Pan et al. (2013) because of the former's closed-form updating formulas. Numerically, we compare the DC- ADMM algorithm with the quadratic penalty algorithm to demonstrate its utility and scalability. Theoretically, we establish a finite-sample mis- clustering error bound for penalized regression based clustering with the $L_0$ constrained regularization in a general setting. On this ground, we provide conditions for clustering consistency of the penalized clustering method. As an end product, we put R package prclust implementing PRclust with various loss and grouping penalty functions available on GitHub and CRAN.