摘要
模式识别成为国内外人工智能研究的热点问题之一。由于样本的高维数据集呈现低维几何流形分布的特性,使得传统模式识别方法在很多问题上遇到了瓶颈。如何认识和利用高维数据的内部几何分布特性,探索人类对事物认识的方式是解决模式识别问题的新方向。高维仿生信息几何学正是从几何学的角度来认识和分析数据分布,试图通过模拟人类形象思维来解决模式识别中的实际问题。
我们从高维仿生信息几何学在模式识别的应用中发现以下问题：首先,如何对高维数据集进行合理的覆盖,也就是怎样提取高维数据集的“核”来构造覆盖区域;其次,在样本数量比较大的情况下,怎样提高识别效率?怎样构造半监督分类器?等等。
针对以上一些问题,本文试图将高维仿生信息学理论和流形学习、机器学习等方法结合起来找到答案,本文研究工作主要包括以下几方面：
研究了传统仿生模式识别的超香肠神经元模型和网络学习算法,针对其不足提出了多自由度神经元模型和网络学习算法,通过人脸识别实验比较了两种神经元模型的优劣,与SVM算法的比较证明了仿生模式识别的覆盖型神经元识别算法在“小样本”数据库的识别问题上更具优势。
针对邻近样本点误识问题,提出了核邻近点Fisher判别分析,这一算法的目的在于使最近的异类数据点和最远的同类样本点在投影子空间的距离尽量扩大,从而减少误识率,并通过人脸识别实验验证了算法的有效性。
针对传统的仿生模式识别算法的不足之处,结合流形学习的理论提出了基于流形距离的仿生识别算法(主要包括基于局部PCA主流形的求取和切距离的求取两部分),并通过实验证明了基于流形距离的仿生识别算法比传统仿生模式识别算法更适合“大样本”数据库的识别问题。传统仿生模式识别方法是通过单纯形神经元覆盖来逼近样本的分布流形,而基于流形距离的仿生识别算法是通过将数据集投影“主流形”上来寻找样本的分布流形,是解决同一个问题的两种方法。因为都需要预知样本的类别,它们都属于有监督的模式识别方法。
另外我们还研究一种无监督的聚类算法。基于高维仿生信息几何学的“同源连续性原理”改进了谱聚类算法中的相似性量度,提出了基于路径相对相似度的谱聚类算法,改善了谱聚类算法对高斯函数中尺度参数的敏感性。
最后,是对高维仿生信息学方法的应用研究。基于高维仿生信息学形象思维方法提出了适用于图像检索和图像配准的特征提取方法,给出了图像检索和图像配准的原型系统,实验证明了提取特征的有效性。
Pattern recognition becomes to the hot issues of artificial telligence research at home and abroad.The traditional method of pattern recognition encounters a bottleneck when it is used to deal with high-dimensional data set with low-dimensional geometry structure. Recognizing and utilizing the internal geometry distribution characteristics of high dimensional data, simulating the way of human's recognition are the new directions to solve the problem of pattern recognition. The High-dimension biomimetic information geometric recognizes and analyzes the data distribution from the view of geometric, and attempts to solve practical problems in artificial intelligence and pattern recognition by simulating the human thinking in images.
Through the research on High-dimension biomimetic information geometric in the application of pattern recognition, we have found the following problems that have not been solved, such as how to cover the high-dimensional data set and how to extra the'CORE" of the data set? In the case of relatively large number of samples how to improve the recognition efficiency, and how to construct semi-supervised classification?
For solving the above problems, we try to find the answers by combining the High-dimension biomimetic information geometric with the manifold learning and machine learning. Our contribution includes the following works:
We have studied on the Hyper Sausage Neuron model and network learning algorithm of biomimetic patter recognition, and proposed the Multi-degree of Freedom Neurons Model and network learning algorithm. Further more we compared the advantages and disadvantage of the two kinds of neuron model through the face recognition experiments. And comparing with the SVM we improved that the biomimetic pattern recognition algorithm based on the neurons coverage is more suitable for the recognition problems of the'small sample' database.
We have also proposed an algorithm of kernel near point Fisher discriminant analysis combining with the manifold learning and linear dimensionality reduction for reducing the error of the near sample points. The algorithm aims at maximizing the distance of the heterogeneous data points in the projection subspace. And its effectiveness has been improved by the face recognition experiments.
Combining with the theory of manifold learning, we proposed the biomimetic recognition algorithm based on the manifold distance (including two algorithms: principal manifold based on local PCA and tangent distance) for the inadequacies of the traditional biomimetic pattern recognition algorithm. And the manifold distance algorithm is proved more suitable for recognition problem of the'large sample" database than the traditional biomimetic pattern recognition algorithm by experiments. The traditional biomimetic pattern recognition algorithm approximates the sample distribution manifold by the simplex neuron covering while the manifold distance algorithm looks for the sample distribution manifold by dataset projecting to the "principal manifold". They are the two algorithms to solve the same problem. And they both belong to the supervised pattern recognition because the types of the samples are needed to be known.
In further research, we find that the machine learning can get some illumination in High-dimension biomimetic information geometric. We proposed the relative Similarity'Path-based Spectral clustering algorithms. And it improves the sensitivity of the spectral clustering algorithm on the scale parameter in the Gaussian function.
We also studied the application of the High-dimension biomimetic information geometric method, and which has been used in the feature extraction of image retrieval and image registration. The prototype systems for image retrieval and image registration are given in this paper. And the effectiveness of feature extraction methods is verified by the experiments.
引文
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