本文研究课题源于国家自然科学基金项目“经验知识推理理论研究” (No.60273087)和西北工业大学基础研究基金“智能科学的逻辑基础研究” (No.W018101)。 功能核磁共振成像(functional Magnetic Resonance Imaging，fMRI)是在核磁共振原理的基础上根据人脑功能区被信号激活时产生局部磁共振信号的改变而工作的。通常，fMRI体现为不同时刻的一系列MRI所构成的影像集合，因为它有较高的空间和时间分辨率，并能重复实现无损伤活体探测，所以常被用于分析认知过程的脑信号响应。 从数据挖掘的角度来看，fMRI数据具有海量的特征属性(体元)，但相对来说数据记录(影像帧数量)很少；信噪比很低；学习模型推广较难。本研究的目的是发现受试主体所经历的认知活动同所检测到的fMRI信号间的内在关系，具体的实施需先进行特征的提取，并在提取结果的基础上重建特征以消除噪声，之后进行回归分析，最后对回归分析可能出现的多种结果进行融合，形成最终推断。 PBAIC2006、2007这两届基于脑科学与机器学习的国际竞赛为本文提供了原始数据来源，我们也得以在这两次竞赛的基础上系统地、进一步地对fMRI脑图分析作出深入地研究，所取得的创新性成果如下： (1)提出了基于Vorouoi分区的概率密度估计(Voronoi Partition based Probability Density Estimation，VPDE)的一致收敛条件 数据概率密度的估计是本文特征提取的先决条件。原有的基于直方图的密度估计方法灵活性差，本文提出了基于Voronoi分区的概率密度估计方法，给出本方法一致收敛于未知密度的条件(充分条件)并给出了证明，这种方法能够自适应地随数据密度改变分区大小，从而较好适应fMRI数据局部性、瞬时变化的特性。 (2)提出基于Voronoi分区核密度估计(Voronoi Region Based Kernel Density Estimation，VKDE)的互信息估计算法 fMRI数据属性多、规模大，其组合更为天文数字，因此很难进行提取。本文提出的基于VKDE互信息估计的特征提取算法，通过对比输入属性与输出特征间互信息来进行特征提取。同其他方法相比，这种算法在数据处理中取得了较好的结果，特别是在较难估计的某些事件相关推断上(如PBAIC2006中的sadness任务)，使所推断结果同参照结果相比相关性提高了8%。 (3)提出了基于分层快速混合聚类(Hybrid Fast Hierarchical Clustering Method，HFHC)的特征重建算法 在利用所得到的筛选属性进行特征重建问题上，本文提出了分层快速混合聚类的HFHC分析方法，同已有k-均值聚类方法相比，在保证聚类有效性有所提高的前提下，使得聚类所节省的时间在62%以上(采用主频为1.83MHz的英特尔单核心中央处理器，物理存储空间为1G)。 (4)提出了回归过程训练的非同质验证(Non-homogeneity Validation Method，NHVM)方法 我们在通过训练-验证模式自适应地生成回归模型时，提出了针对训练和验证阶段分别采用不相同的误差代价准则的方法来得到模型的超参数的非同质验证方法，其中，在训练时使用均方误差准则，并且在验证时采用相关性准则，使得在信噪比较低的数据集上取得了较好的推广能力。 (5)提出基于泛组合运算的多推断融合算法(Universal Combination based Multiple Predictions Emsemble，UCMPE)，并用于多分类器和多推断融合 在泛逻辑的理论基础上，提出了基于泛组合运算的多推断融合策略，并将其应用于多分类器的融合，在UCI的spam数据集上的测试结果表明，在分类精度高于Bayes策略的Max、Sum、Product等组合规则的前提下召回率提高了12%以上，本策略在应用于多回归估计子的融合上也取得了较好的结果。通过上述算法及策略的使用，在PBAIC2006数据集上总的推断成绩达到了0.529并超过目前最好的已公开资料0.521。 近年来脑神经图像序列研究领域、以及统计学习、机器学习领域正处于深入发展的阶段。本文对此也作出了积极的研究并取得了一定的成果。尽管本研究的对象是fMRI脑图序列分析，但其应用却不仅局限在这个领域，比如变核宽的密度估计、互信息估计、分层聚类以及基于泛组合运算的多推断融合这些方法在领域上并没有特别的限制。同时也发现了一些值得深入探讨的理论问题，如泛组合运算簇的选取、以及其中的S决策函数同具体问题的关联等。 关键词：多推断融合，分层快速聚类，交叉验证，互信息，核磁共振成像，核方法，泛逻辑学，泛组合运算

 This thesis comes from the National Nature Science Foundation - Research on Theories of Experience Knowledge Reasoning (No.60273087) and Northwest Polytechnical University Basic Research Foundation- Research on Logical Foundation of Intelligent Science (No.W018101). Magnetic Resonance Imaging (MRI) that uses a powerful magnetic field to align the nuclear magnetization of (usually) hydrogen atoms in water in the body, is primarily a medical imaging technique most commonly used in radiology to visualize the structure and function of the body. The lack of harmful effects on the patient and the operator make MRI well-suited for "interventional radiology". Functional MRI (fMRI) measures signal changes in the brain that are due to changing neural activity. The brain is scanned at low resolution but at a rapid rate (typically once every 2-3 seconds). Increases in neural activity cause changes in the MR signal via T2 changes; this mechanism is referred to as the BOLD (blood-oxygen-level dependent) effect. From the view of data mining, fMRI data are charactered by mass of features but less record number, low signal-noise-ratio (SNR) and hard to be generalized. The motivation of this thesis is to find the inherent relationship between the cognitive activities of the brain and the BOLD signals detected by scanner. The implementation include firstly picking up valuable feature attributes from the whole voxels of the fMRI data, secondly reconstructing the features in order to eliminate the noise, and then proceeding the regression analysis to find the relationship between the cognitive activities and the BOLD signals, finally fusing the diverse predicts of different regression methods into one acceptable. PBAIC2006 and 2007, two international competitions which based on brain science and machine learning, supply the data of precious raw fMRI and feature ratings for this thesis. Also the two competitions give this thesis a foundation for process the research of fMRI brain images systematically and thoroughly. The main research results and innovations are listed as follows: (1)The conditions for uniform convergence voronoi partition based probability density estimation (VPDE) are proposed. The precondition of feature extraction in the thesis is probability density estimation of data. The original histogram-based Probability density estimation method is poor of flexibility. In this thesis, The conditions for uniform convergence voronoi partition based probability density estimation (VPDE) are proposed and proved. In a learning system, this density estimation method can change the size of partition area adaptively according to the density of the training data. Consequently, this method is more suit to the character of fMRI data for their localized and transient changing attribution. (2)A new method of mutual information estimation based on voronoi region based kernel density estimation (VKDE) is proposed. Because the fMRI data are characteristic of huge number of voxels, extraction valuable features from them is very difficult. To solve this problem, a new method of mutual information estimation based on voronoi region based kernel density estimation (VKDE) is proposed. Comparing with other methods, this method achieves better results especially on some hard mission prediction of event relevant analysis. For examble, the relative achievement of mission ‘sadness' is improved at least 8% more than other methods. (3)A feature reconstruction method based on hybrid Fast hierarchical clustering method (HFHC) is proposed. To solve problem of reconstructing features from extracted voxels, hybrid Fast hierarchical clustering method (HFHC) is proposed in this thesis. Comparing with the existing k-means clustering methods, this method saves more than 62% running time on condition of ensuring validity of clustering. (4)A Non-homogeneity Validation Method (NHVM) for regression procession training is proposed. When generating regression model according to training-validation schema, a non-homogeneity validation method (NHVM) of using different error cost criteria in different process of training and process of validation is proposed. During the period of training, the mean square error criterion is used; during the period of validating, the relevance criterion is used. This made the learning system better generalization ability when processing low SNR data. (5)A method of universal combination based multiple predictions emsemble (UCMPE) is proposed, and is used on fusing of multiple classifiers or multiple regressers. On the theoretical foundation of universal logic, a method of universal combination based multiple predictions emsemble (UCMPE) is proposed, and is used on fusing of multiple classifiers or multiple regressers. The test results on UCI dataset ‘spam' show that while keeping classification accuracy not lower than ‘Max', ‘Sum' and ‘Product' combination rule of Bayes methods, UCMPE can improve recall rate by at least 12% over other methods. This method also achieves better result on application of multi regressors' fusion. By using the above-mentioned methods, the final result of relativity prediction of PBAIC2006 is 0.529 and better than the best result 0.521 that have been published. Although the research object of this thesis is fMRI brain images analysis, the application is not limited to this field. For example, these methods like density estimation based on adaptive kernel width, mutual information estimation, HFHC and multi-prediction fusion based on universal combination operation can be easily generalized to other research fields in the follow-up works. Key words: Multi-predictions emsemble, Hybrid Fast hierarchical clustering, Cross validation, Mutual information, functional magnetic resonance imaging, Kernel method, Universal logics, Universal combination operation