基于图和网络的学习算法及其在系统生物学中的一些应用
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摘要
随着社会和科学技术的不断发展,人们正在积累越来越多的各个层次的数据和信息,但是这并没有从根本上解决许多具有挑战性的问题。最典型的例子是,二十世纪分子生物学的迅速发展只是获得了细胞各个组分的知识,而并没有攻克很多复杂的疾病,比如癌症等。这意味着我们需要从系统的水平整合不同的知识和数据,研究它们内部的相互关系和作用,从而才能最终掌握复杂系统的规律,对它们进行控制和优化。同时由于海量数据的复杂性,我们需要机器学习和数据挖掘技术对信息进行自动加工。图和网络是表达复杂系统内部不同尺度、不同组分之间相互作用和关联的最直观的方式。因此,我们迫切需要结合实际应用领域,例如系统生物学,发展基于图和网络的学习算法对系统进行研究。
本文针对基于图和网络的学习算法,以实际分类问题和系统生物学中的一些应用为驱动背景,以图论、统计、优化方法为基本工具,以数据整合为核心,以结点分类、链接预测、子网发现和图匹配问题为对象和目标,对基于图和网络的学习算法进行了深入的研究。本文的主要研究内容和创新点包括以下几个方面:
1.本文综述了基于图和网络的学习算法,介绍了系统生物学的定义和当前的发展,阐述了图和网络在当前系统生物学中的核心作用,指出了图和网络的方法在以系统生物学为代表的实际应用中的巨大潜力。
2.考虑基于链接的半监督结点分类问题,以图的拉普拉斯矩阵的谱变换来构造半监督核为目标,本文提出了一种基于图的同时学习最优非参数谱变换和构建分类器的半监督学习方法。该算法的基本思想是以最大化特征空间的Fisher判别率作为谱变换图核学习和分类器构建的共同准则,并转化为一个半定规划的凸优化问题来求解。与利用核配准进行半监督核学习的算法比较,该算法不需要再进行分类器训练,因为分类器的学习和最优核的构造是同时完成的。在7个分类数据集上,该算法性能均优于或相当于当前基于核校准准则的半监督学习算法。
3.考虑药物-蛋白相互作用网络的预测问题,本文以最大化集成网络中结点属性、链接信息以及未标记样本的信息为目标,提出应用流形正则化的半监督学习算法,并利用核方法整合药物化学分子结构信息、蛋白质序列信息和药物-蛋白网络拓扑结构信息来对未知的药物-蛋白相互作用进行预测,从而提高了预测的精度。用我们提出的方法预测的一些药物-蛋白相互作用已经被最新的药物数据库证实。
4.从系统生物学的角度出发,考虑把蛋白质-DNA和蛋白质-蛋白质相互作用网络整合到基因微阵列数据的分析中。为了辨识与疾病相关的基因功能模块,本文提出了一个新的基于相互作用网络的正则化项来鼓励系数的绝对值在网络上的平滑,结合(?)_1范数的稀疏特性,得到一种基于图的弹性网算法,并从理论上分析了新的正则化项的数学特性,开发了一种新的求解算法,该算法具有全路径计算的优点。理论分析和仿真结果表明,基于图的弹性网算法能得到更小的预测误差。最后,将我们的算法应用到一个阿尔茨海默病的微阵列基因表达数据集上,辨识出了四个与阿尔茨海默病相关的基因功能模块。
5.为了融合不同尺度和模态的信息,考虑把反映分子功能信息的三维荧光分子断层扫描(FMT)图像和反映解剖结构的CT图像进行配准,从而在一幅图像上同时表达多方面的信息。但是直接配准最大直径只有几个毫米的肿瘤的三维FMT图像和体长有近十厘米的整个小鼠的三维CT图像是非常困难的。由于我们可以得到二维平面图像跟FMT图像的坐标关系。因此本文提出一个新的思路,即先对FMT成像过程中得到的二维平面图像与三维的CT图像进行预配准,预配准的结果再作为下一步FMT和CT三维配准的初始值,这样就减小了最终三维配准时两个对象的大小差异所导致的配准难度。在配准过程中,对两个对象分别进行分割得到点集,将问题转化为点集图匹配,使配准完全不同模态的图像成为可能。对于匹配的优化算法,结合全局和局部优化的思想,提出了两种优化方法:结合最小二乘进行局部搜索的序贯蒙特卡罗采样算法;结合差分进化和把最小二乘作为另一种搜索方式的单纯形法。大量的仿真实验结果验证了结合全局搜索和局部搜索优化算法在减少迭代次数和寻优能力上的优越性。最后,在两个实际小鼠数据上的运行结果显示这种预配准的方法为下一步三维FMT和CT图像的配准提供了很好的初始值。
With the on-going development of human society and technology, more and more data and information from different scales are accumulated. However, many problems are still unsolved and unclear to us. For example, the dramatic development of molecular biology just provided much knowledge of different parts of cells and does not conquer any complex disease such as cancer. We can not understand complex systems and handle them without integrating so many data and knowledge from the system view and investigating their internal correlation. We also need machine learning and data mining techniques to help us process the huge data automatically. Graph and network are natural ways to describe the correlation between different components from different scale of a complex system. So it is emergent to develop graph and network based learning algorithms to analyze systems from real application such as systems biology.
The dissertation targets graph and network based learning algorithms motivated from real classification and systems biology. From the data integration view, it presents in-depth study of link based node classification, link prediction, subnetwork searching and graph match problems employing graph theory, statistics and optimization tools. The main contributions of the dissertation are as follows:
1. We surveyed the graph and network based learning algorithms and introduced the definition and current development of systems biology. It was shown that graph and network is the core of systems biology and has huge potential applications in systems biology.
2. Link based node classification on the graph is a semi-supervised learning method. In order to construct a semi-supervised kernel by spectral transform on a graph Laplacian matrix, we proposed an graph based algorithm to learn the optimal non-parametric spectral transform and construct a classifier simultaneously. The main ideal is to use the Fisher discriminate ration in the feature space as the common criterion of spectral transform graph kernel learning and classifier construction which can be maximized by a convex semidefinite programming. Compared with kernel alignment method, our algorithm integrated optimal kernel construction and classifiers learning rather than separating into two steps. We compared our method with the kernel alignment method on 7 data sets and find our method is competitive with kernel alignment,and outperforms its competitor in some data sets.
3. We considered the drug-protein interaction prediction. Aiming at extracting information from node properties, link and unlabeled samples, we applied a manifold regularized semi-supervised learning method as well as constructing a new kernel which integrated the chemical structure of drugs, sequence information of proteins and the topology information of drug-protein interaction network. The proposed method improved the prediction accuracy on 4 data sets. Furthermore, some predicted drug-protein interactions by our method are confirmed by latest drug bank data set.
4. From the view of systems biology, it is important to integrate protein-DNA and protein-protein interaction into the microarray data analysis. To identify the disease related gene functional module, we put forward a new network based regularization term to encourage the smoothness of the absolute values of the coefficients on the network. This new term was combined with (\ norm term which imposed sparsity to form a graph-based elastic network method. The group effect of the new method is analyzed mathematically. A new whole path optimization algorithm is also proposed to solve the proposed graph-based elastic network. The simulation results and theoretical analysis demonstrated our method can get better prediction accuracy. Finally we applied the new method to a gene expression data set of Alzheimer's disease and identified 4 gene functional modules which are related with the progress of Alzheimer's disease.
5. Systems biology intrinsically required the integration of data from different scale. We considered the registration of three dimensional fluorescent molecular tomography revealing molecular functions and the three dimensional CT images containing anatomical structure information to get more information. However it is difficult to directly co-register the 3D FMT (Fluorescence Molecular Tomography, FMT) image of a small tumor in a mouse whose maximal diameter is only a few mm with a larger CT image of the entire animal that spans about ten cm. The exact coordinates of 3D FMT in the 2D flat images is known. So we proposed to co-register the two dimensional flat image and 3D CT images as the initial position for the final 3D registration between FMT and CT. which bridged the gap between the 3D FMT image and 3D CT image of the animal. During registration, two data points were obtained from the segmentation of the two objects. So the problem was casted as a data points matching which made the registration of images from totally different modalities feasible. We proposed two matching optimization methods by combining the global and local searching methods. One improved sequential monter carlo sampling method by incorporating least squares as a local search. Another combined differential evolution and improved simplex method endowed with least squares as a new local searching. A number of simulation results verified the advantages of combining local search and global search in reducing iteration number and finding better solutions. The visualization of the alignments of the 3D FMT and CT images through 2D pre-registration on two mice data shows promising results.
本文针对基于图和网络的学习算法,以实际分类问题和系统生物学中的一些应用为驱动背景,以图论、统计、优化方法为基本工具,以数据整合为核心,以结点分类、链接预测、子网发现和图匹配问题为对象和目标,对基于图和网络的学习算法进行了深入的研究。本文的主要研究内容和创新点包括以下几个方面:
1.本文综述了基于图和网络的学习算法,介绍了系统生物学的定义和当前的发展,阐述了图和网络在当前系统生物学中的核心作用,指出了图和网络的方法在以系统生物学为代表的实际应用中的巨大潜力。
2.考虑基于链接的半监督结点分类问题,以图的拉普拉斯矩阵的谱变换来构造半监督核为目标,本文提出了一种基于图的同时学习最优非参数谱变换和构建分类器的半监督学习方法。该算法的基本思想是以最大化特征空间的Fisher判别率作为谱变换图核学习和分类器构建的共同准则,并转化为一个半定规划的凸优化问题来求解。与利用核配准进行半监督核学习的算法比较,该算法不需要再进行分类器训练,因为分类器的学习和最优核的构造是同时完成的。在7个分类数据集上,该算法性能均优于或相当于当前基于核校准准则的半监督学习算法。
3.考虑药物-蛋白相互作用网络的预测问题,本文以最大化集成网络中结点属性、链接信息以及未标记样本的信息为目标,提出应用流形正则化的半监督学习算法,并利用核方法整合药物化学分子结构信息、蛋白质序列信息和药物-蛋白网络拓扑结构信息来对未知的药物-蛋白相互作用进行预测,从而提高了预测的精度。用我们提出的方法预测的一些药物-蛋白相互作用已经被最新的药物数据库证实。
4.从系统生物学的角度出发,考虑把蛋白质-DNA和蛋白质-蛋白质相互作用网络整合到基因微阵列数据的分析中。为了辨识与疾病相关的基因功能模块,本文提出了一个新的基于相互作用网络的正则化项来鼓励系数的绝对值在网络上的平滑,结合(?)_1范数的稀疏特性,得到一种基于图的弹性网算法,并从理论上分析了新的正则化项的数学特性,开发了一种新的求解算法,该算法具有全路径计算的优点。理论分析和仿真结果表明,基于图的弹性网算法能得到更小的预测误差。最后,将我们的算法应用到一个阿尔茨海默病的微阵列基因表达数据集上,辨识出了四个与阿尔茨海默病相关的基因功能模块。
5.为了融合不同尺度和模态的信息,考虑把反映分子功能信息的三维荧光分子断层扫描(FMT)图像和反映解剖结构的CT图像进行配准,从而在一幅图像上同时表达多方面的信息。但是直接配准最大直径只有几个毫米的肿瘤的三维FMT图像和体长有近十厘米的整个小鼠的三维CT图像是非常困难的。由于我们可以得到二维平面图像跟FMT图像的坐标关系。因此本文提出一个新的思路,即先对FMT成像过程中得到的二维平面图像与三维的CT图像进行预配准,预配准的结果再作为下一步FMT和CT三维配准的初始值,这样就减小了最终三维配准时两个对象的大小差异所导致的配准难度。在配准过程中,对两个对象分别进行分割得到点集,将问题转化为点集图匹配,使配准完全不同模态的图像成为可能。对于匹配的优化算法,结合全局和局部优化的思想,提出了两种优化方法:结合最小二乘进行局部搜索的序贯蒙特卡罗采样算法;结合差分进化和把最小二乘作为另一种搜索方式的单纯形法。大量的仿真实验结果验证了结合全局搜索和局部搜索优化算法在减少迭代次数和寻优能力上的优越性。最后,在两个实际小鼠数据上的运行结果显示这种预配准的方法为下一步三维FMT和CT图像的配准提供了很好的初始值。
With the on-going development of human society and technology, more and more data and information from different scales are accumulated. However, many problems are still unsolved and unclear to us. For example, the dramatic development of molecular biology just provided much knowledge of different parts of cells and does not conquer any complex disease such as cancer. We can not understand complex systems and handle them without integrating so many data and knowledge from the system view and investigating their internal correlation. We also need machine learning and data mining techniques to help us process the huge data automatically. Graph and network are natural ways to describe the correlation between different components from different scale of a complex system. So it is emergent to develop graph and network based learning algorithms to analyze systems from real application such as systems biology.
The dissertation targets graph and network based learning algorithms motivated from real classification and systems biology. From the data integration view, it presents in-depth study of link based node classification, link prediction, subnetwork searching and graph match problems employing graph theory, statistics and optimization tools. The main contributions of the dissertation are as follows:
1. We surveyed the graph and network based learning algorithms and introduced the definition and current development of systems biology. It was shown that graph and network is the core of systems biology and has huge potential applications in systems biology.
2. Link based node classification on the graph is a semi-supervised learning method. In order to construct a semi-supervised kernel by spectral transform on a graph Laplacian matrix, we proposed an graph based algorithm to learn the optimal non-parametric spectral transform and construct a classifier simultaneously. The main ideal is to use the Fisher discriminate ration in the feature space as the common criterion of spectral transform graph kernel learning and classifier construction which can be maximized by a convex semidefinite programming. Compared with kernel alignment method, our algorithm integrated optimal kernel construction and classifiers learning rather than separating into two steps. We compared our method with the kernel alignment method on 7 data sets and find our method is competitive with kernel alignment,and outperforms its competitor in some data sets.
3. We considered the drug-protein interaction prediction. Aiming at extracting information from node properties, link and unlabeled samples, we applied a manifold regularized semi-supervised learning method as well as constructing a new kernel which integrated the chemical structure of drugs, sequence information of proteins and the topology information of drug-protein interaction network. The proposed method improved the prediction accuracy on 4 data sets. Furthermore, some predicted drug-protein interactions by our method are confirmed by latest drug bank data set.
4. From the view of systems biology, it is important to integrate protein-DNA and protein-protein interaction into the microarray data analysis. To identify the disease related gene functional module, we put forward a new network based regularization term to encourage the smoothness of the absolute values of the coefficients on the network. This new term was combined with (\ norm term which imposed sparsity to form a graph-based elastic network method. The group effect of the new method is analyzed mathematically. A new whole path optimization algorithm is also proposed to solve the proposed graph-based elastic network. The simulation results and theoretical analysis demonstrated our method can get better prediction accuracy. Finally we applied the new method to a gene expression data set of Alzheimer's disease and identified 4 gene functional modules which are related with the progress of Alzheimer's disease.
5. Systems biology intrinsically required the integration of data from different scale. We considered the registration of three dimensional fluorescent molecular tomography revealing molecular functions and the three dimensional CT images containing anatomical structure information to get more information. However it is difficult to directly co-register the 3D FMT (Fluorescence Molecular Tomography, FMT) image of a small tumor in a mouse whose maximal diameter is only a few mm with a larger CT image of the entire animal that spans about ten cm. The exact coordinates of 3D FMT in the 2D flat images is known. So we proposed to co-register the two dimensional flat image and 3D CT images as the initial position for the final 3D registration between FMT and CT. which bridged the gap between the 3D FMT image and 3D CT image of the animal. During registration, two data points were obtained from the segmentation of the two objects. So the problem was casted as a data points matching which made the registration of images from totally different modalities feasible. We proposed two matching optimization methods by combining the global and local searching methods. One improved sequential monter carlo sampling method by incorporating least squares as a local search. Another combined differential evolution and improved simplex method endowed with least squares as a new local searching. A number of simulation results verified the advantages of combining local search and global search in reducing iteration number and finding better solutions. The visualization of the alignments of the 3D FMT and CT images through 2D pre-registration on two mice data shows promising results.
引文
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