Golay X, Kollias S, Stoll G, Meier D, Valavanis A, Boesiger P
Institute of Biomedical Engineering and Medical Informatics, University of Zurich, Switzerland.
Magn Reson Med. 1998 Aug;40(2):249-60. doi: 10.1002/mrm.1910400211.
Fuzzy logic clustering algorithms are a new class of processing strategies for functional MRI (fMRI). In this study, the ability of such methods to detect brain activation on application of a stimulus task is demonstrated. An optimization of the selected algorithm with regard to different parameters is proposed. These parameters include (a) those defining the pre-processing procedure of the data set; (b) the definition of the distance between two time courses, considered as p-dimensional vectors, where p is the number of sequential images in the fMRI data set; and (c) the number of clusters to be considered. Based on the assumption that such a clustering algorithm should cluster the pixel time courses according to their similarity and not their proximity (in terms of distance), cross-correlation-based distances are defined. A clear mathematical description of the algorithm is proposed, and its convergence is proven when similarity measures are used instead of conventional Euclidean distance. The differences between the membership function given by the algorithm and the probability are clearly exposed. The algorithm was tested on artificial data sets, as well as on data sets from six volunteers undergoing stimulation of the primary visual cortex. The fMRI maps provided by the fuzzy logic algorithm are compared to those achieved by the well established cross-correlation technique.
模糊逻辑聚类算法是功能磁共振成像（fMRI）的一类新型处理策略。在本研究中，展示了此类方法在应用刺激任务时检测大脑激活的能力。提出了针对不同参数对所选算法进行优化。这些参数包括：（a）定义数据集预处理过程的参数；（b）将两个时间序列（视为p维向量，其中p是fMRI数据集中连续图像的数量）之间的距离定义；以及（c）要考虑的聚类数量。基于这样一种假设，即此类聚类算法应根据像素时间序列的相似性而非它们的接近程度（就距离而言）对其进行聚类，定义了基于互相关的距离。提出了该算法的清晰数学描述，并证明了当使用相似性度量而非传统欧几里得距离时它的收敛性。明确揭示了该算法给出的隶属函数与概率之间的差异。该算法在人工数据集以及来自六名接受初级视觉皮层刺激的志愿者的数据集上进行了测试。将模糊逻辑算法提供的fMRI图谱与通过成熟的互相关技术获得的图谱进行了比较。
