随着信息技术的发展，多变量模式分析方法越来越成为认知神经科学领域的研究热点。其中，脑状态分类是基于神经影像数据的有监督模式分析方法，具有很高的理论价值和应用潜力。功能磁共振成像（functional magnetic resonance imaging, fMRI）是无创的和高空间分辨率的现代神经影像技术，在认知神经科学领域中被广泛用于揭示认知加工过程的神经机制。多体素模式分析（Multi-voxel pattern analysis, MVPA）是广泛使用的基于fMRI数据的脑状态分类分析框架。使用MVPA能够通过脑状态分类分析的手段，达到深入探索神经机制的目的。 fMRI数据的特点是信噪比低、噪声复杂、具有分类能力的体素数量少且分布复杂，这些特点使得传统的特征选择方法和分类模型无法直接应用于MVPA。因此，适用于fMRI数据的特征选择方法和分类器模型是MVPA研究的关键。研究表明，通过使用正则化约束条件，可以大大提高MVPA特征选择的有效性和分类模型的鲁棒性。因此，对基于正则化约束的MVPA进行研究，可以有效推动脑状态分类研究的发展，具有较大的研究价值。 进一步研究表明，fMRI数据中具有分类能力的体素分布具有稀疏特性和空间聚集特性，如何有效利用这些特性是基于正则化约束的MVPA方法研究要解决的关键问题。目前使用较多的约束条件是考察稀疏特性的稀疏正则化约束。虽然稀疏正则化约束可以提高MVPA特征选择和分类的能力，但现有的稀疏正则化约束算法计算效率低且无法考察fMRI数据的空间结构。近年来，有研究表明在MVPA分类模型中使用全变异（Total Variation, TV）正则化约束可以考察空间聚集特性，从而提高其分类能力。与TV正则化约束类似，欧拉弹性（Euler’s Elastica, EE）正则化约束也被有效地用于图像处理中，但EE正则化约束还可以有效克服TV正则化约束易出现的“物体边缘不连续”的现象，抗噪性也强于后者。而在针对fMRI数据的MVPA分析中，使用EE正则化约束能否更加有效地考察fMRI数据的空间聚集特性，能否进一步提升脑状态分类的准确性和鲁棒性尚不清楚。 因此，本研究将针对基于正则化约束的MVPA特征选择方法和分类模型开展以下三个方面的研究： 1. 针对稀疏正则化约束求解计算效率低的问题，我们提出拉普拉斯平滑0-范数稀疏正则化约束（Laplacian smoothed L0 norm, LSL0）快速特征选择方法。该方法在平滑0范数稀疏表征方法（Smoothed L0 norm, SL0）的基础上，使用拉普拉斯核函数对0范数稀疏表征问题进行求解，再根据求得的稀疏解进行特征选择。模拟数据结果表明，LSL0算法在稀疏向量的估计准确性上优于原始的SL0方法。模拟和真实fMRI数据结果表明LSL0算法在提取分类特征方面优于SL0和独立成分分析、T检验等传统算法，其优势表现在使用LSL0方法选择出的分类体素数量更少而且得到的分类准确率更高。 2. 将EE正则化约束与线性回归问题相结合，为了考察fMRI数据的空间聚集特性，构造EE正则化约束回归模型，进而提出基于EE正则化约束的fMRI特征选择方法。模拟三维数据结果表明，EE正则化回归在空间源向量的估计准确性方面强于TV正则化约束回归。模拟和真实fMRI数据的特征选择结果表明，基于EE约束的特征选择方法优于TV约束方法，LSL0及广义线性模型方法（generalized linear model, GLM）。EE方法的优势主要表现在：与另外三种方法相比 ，EE方法的抗噪性更强，任务激活脑区的检测更加准确，选择出的分类体素的分类准确率更高。 3. 将EE正则化约束引入分类模型，提出基于EE正则化约束的多元逻辑回归（Eulser’s Elastica Multinominal Logistical Regression, EELR）分类方法。模拟和真实fMRI数据实验结果表明，在抗噪性和检测具有分类能力的脑区方面，EELR方法强于TV正则化约束多元逻辑回归方法（TVLR）方法；在分类准确率方面，EELR方法强于TVLR和稀疏正则化约束多元逻辑回归方法（SLR）；此外，本研究还通过激活模式分析表明，在检测任务激活脑区方面，EELR方法强于TVLR和GLM方法。 综上，本研究进一步证明了稀疏正则化约束在MVPA特征选择中的有效性，并且提升了计算效率。LSL0特征选择方法在计算速度和分类体素的分类准确率方面均优于优于SL0方法，独立成分分析方法和T检验方法。本研究还证明了EE正则化约束在MVPA中的有效性，即使用EE正则化约束可以有效提升MVPA抗噪性、特征选择的准确性、分类模型的分类准确率。EE特征选择方法在抗噪性和选择分类体素的准确性方面强于LSL0方法、TV特征选择方法和GLM方法。EELR分类方法在抗噪性和分类准确率方面强于TVLR方法，并且在检测分类脑区和任务激活脑区方面强于TVLR和GLM方法。这说明基于EE正则化约束的MVPA方法在脑状态分类和检测有意义脑区两个方面都具有优势。

Multivariate pattern analysis methods are attracting more and more attention in neuroscience research. Among various multivariate pattern analysis methids, supervised learning methods have been widely used to classify brain states from brain acitivites. Functional magnetic resonance imaging (fMRI) technology is a modern non-invasive neuroimaging technology. Because of its high spatial-resolution, fMRI has been widely used in uncoverring neural mechanism of cognitive process. Multi-voxel pattern analysis (MVPA) has become a powerful method of fMRI data to classify brain states classification data and reveal neural machanism. It is well known that fMRI data contain complicated noises and have low signal-noise ratio and sparse discriminative voxels. It is hard for the traditional feature selection methods and classification model to be applied in MVPA. Thus, efficient feature selection methods and robust classification models are necessary to MVPA based on fMRI. Recently, it has been found that regularization methods can largely benefit MVPA feature selection and classification model. Thus, it is essential to further investigate regularized MVPA feature selection methods and classification models in brain classficiation based on fMRI. Specifically, the discriminative voxels of fMRI data are distributed in spatially sparse and clustering manners, which are informative for regularized MVPA methods. Sparse regularization has been widely applied in MVPA feature selection and classification by considering the sparse character of fMRI data. Although the sparse regularization can improve MVPA methods, existing sparser regularized methods have low computational efficiency and do not consider spatially clustering character of fMRI data. Recently, it has been demonstrated that total variation (TV) regularization can increase MVPA classification accurices by considering clustering character of fMRI data. Euler’s Elastica (EE) considering the spatial information of image has been succefully used in image processing. In contrast to TV regularization, EE regularization can overcome the ‘discontinuity on edges’ of TV regularization and is more robust against noises. However, it is still unknow whether EE regularization can fit for the clustering character of fMRI data and increase accuracy and robustness of MVPA methods. We performed the following three studies to improve MVPA feature selection and classification model using sparse and EE regularization. 1. We proposed the Laplacian smoothed L0 norm (LSL0) approach for feature selection of fMRI data. Based on the fast sparse decomposition using smoothed L0 norm (SL0) (Mohimani, 2007), the LSL0 method used the Laplacian function to approximate the L0 norm of sources. Results of the simulated and real fMRI data demonstrated the feasibility and robustness of LSL0 for the sparse source estimation and feature selection. Simulated results indicated that LSL0 produced more accurate source estimation than SL0 at high noise levels. The classification accuracy using voxels that were selected by LSL0 was higher than that by SL0 in both simulated and real fMRI experiment. Moreover, both LSL0 and SL0 showed higher classification accuracy and required less time than ICA and ttest for the fMRI decoding. LSL0 outperformed SL0 in sparse source estimation at high noise level and in feature selection. Moreover, LSL0 and SL0 showed better performance than ICA and t-test feature selection. 2. We developed a multivariate regression model using EE in 3-D space as constraint for voxel selection. We performed experimental tests on both simulated data and real fMRI data to investigate the feasibility and robustness of EE regression. The performance of EE regression was compared with TV regression and generalized linear model (GLM) in brain activity detection and compared with TV regression, GLM and LSL0 in feature selection for brain state decoding. The results indicated that EE regression possessed better sensitivity to detect brain regions specific to a task than did GLM. Moreover, the features selected by EE regression showed significantly higher classification accuracy than those by TV regression, GLM and LSL0. 3. We introduced EE to fMRI-based decoding for the first time and proposed the EE regularized multinomial logistic regression (EELR) algorithm for multi-class classification. We performed experimental tests on both simulated and real fMRI data to investigate the feasibility and robustness of EELR. The performance of EELR was compared with sparse logistic regression (SLR) and TV regularized LR (TVLR). The results showed that EELR was more robustness to noises and showed significantly higher classification performance than TVLR and SLR. Moreover, we transferred the discriminative pattern into the activation pattern of forward model. The forward models and weights patterns revealed that EELR detected larger brain regions that were discriminative to each task and activated by each task than TVLR. The results suggest that EELR not only performs well in brain decoding but also reveals meaningful discriminative and activation patterns. In conclusion, the present study investigated sparse and EE regularized MVPA feature selection and classification methods in fMRI-based brain state classfication. LSL0 feature selection method shows higher computational efficiency and higher classification accuracy than SL0, ICA and T-test methods. Moreover, we proposed EE regularizied feature selection method and EELR classification method. It was demonstrated that EE feature selection method outperformed LSL0, TV feature selection and GLM methods in robustness and feature selection. Furthermore, EELR was better than TVLR in robustness and classification accuracy, and EELR was better than TVLR and GLM in detecting discrimative and activition brain areas. The results suggest that EE regularized MVPA methods are useful in both improving brain state classification accuracy and detecting meaningful brain areas, which may imply that EE regularizaed MVPA methods would become a powerful tool to decode brain states from fMRI data and uncover neural machinism.