高维复杂数据网络与节点属性的统计推断

发布时间：2018-03-06 06:22

本文选题：矩阵奇异值分解　切入点：Wilks　出处：《青岛大学》2017年硕士论文　论文类型：学位论文

【摘要】：本文首先研究两个相关关系矩阵(对称矩阵或非对称矩阵)之间的相关关系,给出预测并解决如下问题:网络间相关性检验以及高维网络中包含不可观测的潜变量结构问题。对网络(相关系数矩阵)进行矩阵奇异值分解(SVD)获取低秩因子(潜变量),对低秩因子构建Wilks’Lambda统计量以检验网络间的相关性。若检验显示存在显著线性关系,则对低秩因子构建线性回归模型。若检验结果显示非线性关系,采用非线性模型,并使用极大似然估计法对模型参数进行估计。获取待估低秩因子(潜变量)后,可使用矩阵奇异值分解等方法对低秩因子进行还原,进而可以对网络中缺失地相关关系进行填补,对潜在相关关系进行预测。其次,受正态分布下的精度矩阵相关性质对缺失值识别的启发,对一般连续型分布的样本通过高斯Copula模型转换至正态分布中以识别该分布下缺失值。通过该步预测,为之后的缺失值填补提供合理有效的判断和解释。并针对高维复杂数据的稀疏性、混合数据等特性分别引入逆回归模型,混合数据的潜变量高斯Copula模型等方法以解决相应的问题,为模型推广至高维复杂数据中提供理论支持。最后,通过数值模拟小样本下模型结构,通过对对称网络回归系数、缺失值填补、未知节点关系、以及非对称网络缺失值填补预测等四个实验模拟,发现各评价指标显示相较于对比方法,模型效果较好,且随着数据维度增加,模型效果更佳。在实证分析章节,对四个包括药物结构相似性、靶点蛋白序列相似性和药物与靶点相互作用的数据集进行分析,一致发现在相似性检验以及模型预测过程中均优于对比方法,尤其在降维过程中,降维效果显著。
[Abstract]:In this paper, we first study the correlation between two correlation matrices (symmetric matrix or asymmetric matrix). The following problems are given to predict and solve the following problems: the correlation test between networks and the structure of non-observable latent variables in high-dimensional networks. The low rank factors are obtained by matrix singular value decomposition (SVD) for the network (correlation coefficient matrix). For low rank factors, Wilks'Lambda statistics are constructed to test the correlation between networks. If the test shows a significant linear relationship, Then a linear regression model is constructed for low rank factors. If the test results show a nonlinear relationship, the nonlinear model is used and the parameters of the model are estimated by using the maximum likelihood estimation method. After obtaining the low rank factors (latent variables) to be estimated, The method of matrix singular value decomposition can be used to restore the low rank factor, and then the missing correlation can be filled, and the potential correlation can be predicted. Inspired by the correlation property of precision matrix under normal distribution, the samples of general continuous distribution are transformed to normal distribution by Gao Si Copula model to recognize the missing value under this distribution. It provides reasonable and effective judgment and explanation for filling the missing value, and introduces inverse regression model for the characteristics of high dimensional complex data such as sparsity, mixed data and so on. Gao Si Copula model of mixed data is used to solve the corresponding problems, which provides theoretical support for extending the model to high dimensional complex data. Finally, through numerical simulation of the model structure under small samples, the regression coefficient of symmetric network is obtained. Four experimental simulations, including missing value filling, unknown node relationship and asymmetric network missing value filling prediction, show that each evaluation index shows a better effect than the contrast method, and with the increase of data dimension, the model has a better effect. The model works better. In the empirical analysis chapter, four data sets including drug structural similarity, target protein sequence similarity and drug / target interaction are analyzed. It is found that the method is better than the contrast method in the process of similarity test and model prediction, especially in the process of dimensionality reduction.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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