Geometric structures guided learning model and algorithms for bulk RNAseq data analysis

许多疾病的潜在药物和治疗方法的发现在很大程度上取决于鉴别 在单个细胞类型内的疾病条件下表达的(DE)基因。虽然有可能 通过实验筛选出用于DE分析的单个细胞类型的细胞，通过计算利用大块组织 数据具有更高的可用性、更低的成本和更少的人工处理。关键的一步 这项研究的目的是(完全)解开特定细胞类型中的基因表达 异质的块状组织。完全反卷积可以看作是一种非负矩阵分解 (NMF)问题，然而，NMF是强不适定的，其不可分的解给出了巨大的挑战 在数据可解释性方面。这些挑战在不同的应用中是不同的，所以如果不采取特殊处理， 基因表达数据的完全去卷积结果将使DE分析几乎准确 不可能。在这项提议中，数学模型和相关的计算算法将是 为散体组织RNAseq分析的基础研究而建立的，为了更好的数据可解释性， 可靠性和效率。为了应对这一挑战，给定的批量组织数据集的几何结构 将首先进行探索，以确定组成细胞类型的标记基因。然后，建立了该模型 通过(1)强制NMF的弱可解性条件(由于噪声)和(2)执行几何 对已知数据空间的约束。这项工作的动机是许多 生物数据，在这些数据中，样本组织的表达水平显示出某些 基因。对于海量的生物数据，将发展随机快速计算算法。 在经过验证和基准测试后，该模型将应用于各种数据集的DE分析。 这一新提出的模型对于破译许多疾病中的细胞转录变化很重要。在……里面 建模策略，本研究提供了观察拓扑/几何的新视角 数据结构，实施相应的约束以增强问题的可解性和数据 可解释性。在计算上，本研究发展了非线性图的拉普拉斯正则化优化 结合随机压缩算法，能够以较低的存储空间处理海量数据。 要求高、复杂度低、适应现代计算机硬件结构。 AS

Discovering potential drugs and treatments of many diseases heavily depends on identifying differentially expressed (DE) genes in disease conditions within individual cell types. While it is possible to experimentally sort out cells of individual cell types for DE analysis, computationally leveraging bulk tissue data has the advantage of greater availability, lower expenses, and less human handling. A critical step toward this research is to (completely) deconvolute gene expressions in specific cell types from the heterogeneous bulk tissues. Complete deconvolution can be viewed as a nonnegative matrix factorization (NMF) problem, however, NMF is strongly ill-posed, and its non-separable solutions give great challenges in data interpretability. These challenges vary in different applications, so if no special treatment is taken, results from complete deconvolution of gene expression data will make accurate DE analysis almost impossible. In this proposal, a mathematical model and associated computational algorithms will be established for the fundamental research of bulk tissue RNAseq analysis, for better data interpretability, reliability, and efficiency. To tackle this challenge, the geometric structure of the given bulk tissue data set will be explored first to identify marker genes for the constituent cell types. Then the model is established by (1) enforcing the weak solvability condition (because of noises) of NMF and (2) performing geometrical constraints on the data space of knowns. This work is motivated by the common characteristics of many biological data, in which expression levels across sample tissues exhibit strong correlations among certain genes. For massive amount of biological data, stochastic fast computational algorithms will be developed. After validation and benchmarking, the proposed model will be applied to DE analysis for various datasets. This proposed new model is important to decipher cellular transcriptional alterations in many diseases. In modeling strategies, this research provides a new perspective of observing topological/geometric structures of data, enforcing the corresponding constraints to enhance problem solvability and data interpretability. In computation, this research develops nonlinear graph Laplacian regularized optimization associated with stochastic compression algorithms, which can process massive data with low storage. requirement, low complexity, and adapt to modern structure of computer hardware. As