中文摘要：

针对传统模型建模复杂、算法效率较低等缺点,提出了一种学习自然图像拓扑表示的新方法.不同于传统的空域汇集操作,文中利用＂成对累计量＂对初级视皮层复杂细胞之间的二元关系进行建模,并结合向量在高维空间中的分布特点,得到了能够模拟V1区复杂细胞特性的自然图像拓扑表示模型.此外,在模型的估计部分,推导出基于＂不动点迭代＂的快速学习算法.实验表明,该模型能够有效地捕捉复杂细胞中的非线性依赖关系,从自然图像中学习的基向量具有类似于V1区复杂细胞的特性.与传统方法相比,文中算法不仅适用于完备或超完备基的学习问题,而且具有类似于FastICA算法的收敛性能,比同类算法更加快速可靠.

英文摘要：

For overcoming complexities and inefficiencies of traditional models,we propose a simple method for learning the topographic representations of nature image.Basing on high order cumulant,we define the ＂pairwise cumulant＂ to model the binary relations for every pair of two adjacent complex cells in primary visual cortex（V1）.Combining with topography function represented adjacency relations of cells,we construct a model for natural images to learn topographic representations and the properties of complex cells.According to the distribution characteristics of vectors in high-dimensional space,we extend the model to solve overcomplete and topographic representations of nature image.In addition,we provide a fixed point algorithm for fast training our model.Experiments on nature image data show that our method can capture the nonlinear correlations among these neighboring complex cells effectively.The leant complete and overcomplete basis vectors demonstrate a clear topography with local continuity of orientation,frequency,and location,which give the properties similar to those complex cells.Besides,numerical experiments confirm both in complete and overcomplete cases,the convergence of our algorithm is similar with the convergence of FastICA and exceeds the convergence of traditional algorithm.