图核及其在模式识别中应用的研究
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摘要
统计模式识别和结构模式识别是模式识别中两种主要方法。在统计模式识别中，研究对象一般用特征向量来表示，因此，可以借用向量空间中的一些成熟算法。统计模式识别的缺点是难以表示复杂物体各部分之间的关系。在结构模式识别中，研究对象一般用图来表示，对象的相似性或匹配问题就变为图的相似性或匹配问题。图匹配的计算复杂度高并且没有系统化的计算方法，因此，自结构模式识别出现之日起，研究人员就试图把统计模式识别和结构模式识别统一起来。
近年来，由于核方法具有坚实的理论基础，以及在许多实际问题中成功的应用，引起了人们越来越大的关注。核方法不仅适用于以特征向量表示的模式，也适用于结构化的数据。因此，把核方法引入图成了新的研究热点。所谓图核，就是把图映射到特征向量空间，使得两个图的相似性就是它们在特征向量空间的点积。因此，向量里的运算都适用于图。
目前提出的图核有：通路核，扩散核，卷积核。但是仍然有许多问题需要进一步研究，本文研究图核及其在模式识别中的应用。
本文主要包括以下创新工作：
（1）构造了生成树核及其派生核，并对这些核进行了比较。本文构造的生成树核是可表示的、正定的、可计算的、适用范围较宽的图核；计算它们的时间复杂度低于随机通路核的时间复杂度；将这些核应用在人脸识别中，它们的人脸识别正确率高于通路核的识别正确率。
（2）用两种方法构造了基于生成树的回路核及其派生核，并对这些核进行了比较。本文构造的基于生成树的回路核的时间复杂度低于现有的回路核的时间复杂度，它们是可计算的；并且克服了随机通路核的不足：通路中的顶点和边可以重复出现。将这些核应用在人脸识别中，它们的人脸识别正确率高于通路核的识别正确率。
（3）构造了强分支核。强分支核不仅适用有向图，也可扩展为适用无向图；既适用连通图，也适用不连通图；既适用平面图也适用非平面图；既适用有标号图，也适用无标号图。将定义的强分支核应用于人脸识别中，人脸识别正确率平均为96%。
（4）提出了一种基于合成核的人脸识别方法，合成核的人脸识别正确率高于单核的识别正确率。本文对人脸图像进行了区域和LBP的特征提取，并改进了直方图交核，提高了人脸识别正确率。在此基础上，把直方图交核和图核结合在一起，进一步提高了人脸识别正确率。
最后，作者介绍了今后的进一步研究方向，并对本文进行了总结。
The discipline of pattern recognition is usually divided into the statistical and thestructural approach. In statistical pattern recognition, the object is generallyrepresented by feature vector, so we can use the mature algorithms in the vector space.The disadvantage of statistical pattern recognition is that it is difficult to representcomplex relationships that might exist among different parts of a pattern. In structuralpattern recognition, object of study is generally represented by graph, and then thesimilarity of objects has been transformed to the similarity of graph. However, thecomputational complexity of graph matching algorithm is high and there is nosystematic computing method. Therefore, researchers have tried to unify statisticalpattern recognition and structural pattern recognition since the birth of structuralpattern recognition.
In recent years, kernel methods have solid theoretical foundation and have beensuccessfully applied to many practical problems. Kernel methods have become aresearch hotspot. Kernel method applies not only to feature vector representation ofthe pattern but also to the structural data. Consequently, graph kernel has become anew research hotspot. Graph kernel can be thought of as a dot product in some featurespace. Consequently, algorithms in vector space are also fit for graph.
Diffusion Kernels, Convolution Kernels and Walk Kernels have been proposed inthe literatures. But there are still many issues that need further research, the paperresearches on graph kernels and their application in pattern recognition.
The following innovative works have been completed:
(1) The spanning tree kernel and its derived kernels have been constructed, andalso a comparison of these kernels has been made. The constructed spanning treekernel is expressive, positive definite, computable graph kernel, and it is applicableto most graphs. Their compution time complexity is lower than the random walkkernel. In the face recognition, the recognition accuracy rate of these kernels ishigher than the walk kernel.
(2)The cycle kernel, based on spanning tree, and its derived kernel have beenconstructed by two methods, and a comprison of these kernels has been made. Thetime complexity of the cycle kernel based on spanning tree is lower than the existingcycle kernel. They are computable and overcome the lack of random walk kernel, inwhich the vertices and edges can be repeated. In the face recognition, the recognition accuracy rate of these kernels is also higher than the walk kernel.
(3)The diconnected components kernel has been constructed. It is applicable todirected graph, undirected graph, connected graph, non-connected graph, plan graph,non-plan graph, labeled graph and non-labeled graph. When the diconnectedcomponents kernel is applied to face recognition, the average recognition accuracyrate reaches to96%.
(4)Finally, the face recognition method based on synthesis kernel has beenproposed, and the face recognition accuracy rate of synthesis kernel is higher than thesingle kernel. Here the paper extractes the region and LBP features of face images,and improves the histogram intersection kernel, and the face recognition accuracy rategets a lot improvement. On this basis, the combination of histogram intersectionkernel and graph kernel furtherly improves the face recognition accuracy rate.
Finally, a summary of this article has been made and the direction of the furtherresearch has been described.
近年来，由于核方法具有坚实的理论基础，以及在许多实际问题中成功的应用，引起了人们越来越大的关注。核方法不仅适用于以特征向量表示的模式，也适用于结构化的数据。因此，把核方法引入图成了新的研究热点。所谓图核，就是把图映射到特征向量空间，使得两个图的相似性就是它们在特征向量空间的点积。因此，向量里的运算都适用于图。
目前提出的图核有：通路核，扩散核，卷积核。但是仍然有许多问题需要进一步研究，本文研究图核及其在模式识别中的应用。
本文主要包括以下创新工作：
（1）构造了生成树核及其派生核，并对这些核进行了比较。本文构造的生成树核是可表示的、正定的、可计算的、适用范围较宽的图核；计算它们的时间复杂度低于随机通路核的时间复杂度；将这些核应用在人脸识别中，它们的人脸识别正确率高于通路核的识别正确率。
（2）用两种方法构造了基于生成树的回路核及其派生核，并对这些核进行了比较。本文构造的基于生成树的回路核的时间复杂度低于现有的回路核的时间复杂度，它们是可计算的；并且克服了随机通路核的不足：通路中的顶点和边可以重复出现。将这些核应用在人脸识别中，它们的人脸识别正确率高于通路核的识别正确率。
（3）构造了强分支核。强分支核不仅适用有向图，也可扩展为适用无向图；既适用连通图，也适用不连通图；既适用平面图也适用非平面图；既适用有标号图，也适用无标号图。将定义的强分支核应用于人脸识别中，人脸识别正确率平均为96%。
（4）提出了一种基于合成核的人脸识别方法，合成核的人脸识别正确率高于单核的识别正确率。本文对人脸图像进行了区域和LBP的特征提取，并改进了直方图交核，提高了人脸识别正确率。在此基础上，把直方图交核和图核结合在一起，进一步提高了人脸识别正确率。
最后，作者介绍了今后的进一步研究方向，并对本文进行了总结。
The discipline of pattern recognition is usually divided into the statistical and thestructural approach. In statistical pattern recognition, the object is generallyrepresented by feature vector, so we can use the mature algorithms in the vector space.The disadvantage of statistical pattern recognition is that it is difficult to representcomplex relationships that might exist among different parts of a pattern. In structuralpattern recognition, object of study is generally represented by graph, and then thesimilarity of objects has been transformed to the similarity of graph. However, thecomputational complexity of graph matching algorithm is high and there is nosystematic computing method. Therefore, researchers have tried to unify statisticalpattern recognition and structural pattern recognition since the birth of structuralpattern recognition.
In recent years, kernel methods have solid theoretical foundation and have beensuccessfully applied to many practical problems. Kernel methods have become aresearch hotspot. Kernel method applies not only to feature vector representation ofthe pattern but also to the structural data. Consequently, graph kernel has become anew research hotspot. Graph kernel can be thought of as a dot product in some featurespace. Consequently, algorithms in vector space are also fit for graph.
Diffusion Kernels, Convolution Kernels and Walk Kernels have been proposed inthe literatures. But there are still many issues that need further research, the paperresearches on graph kernels and their application in pattern recognition.
The following innovative works have been completed:
(1) The spanning tree kernel and its derived kernels have been constructed, andalso a comparison of these kernels has been made. The constructed spanning treekernel is expressive, positive definite, computable graph kernel, and it is applicableto most graphs. Their compution time complexity is lower than the random walkkernel. In the face recognition, the recognition accuracy rate of these kernels ishigher than the walk kernel.
(2)The cycle kernel, based on spanning tree, and its derived kernel have beenconstructed by two methods, and a comprison of these kernels has been made. Thetime complexity of the cycle kernel based on spanning tree is lower than the existingcycle kernel. They are computable and overcome the lack of random walk kernel, inwhich the vertices and edges can be repeated. In the face recognition, the recognition accuracy rate of these kernels is also higher than the walk kernel.
(3)The diconnected components kernel has been constructed. It is applicable todirected graph, undirected graph, connected graph, non-connected graph, plan graph,non-plan graph, labeled graph and non-labeled graph. When the diconnectedcomponents kernel is applied to face recognition, the average recognition accuracyrate reaches to96%.
(4)Finally, the face recognition method based on synthesis kernel has beenproposed, and the face recognition accuracy rate of synthesis kernel is higher than thesingle kernel. Here the paper extractes the region and LBP features of face images,and improves the histogram intersection kernel, and the face recognition accuracy rategets a lot improvement. On this basis, the combination of histogram intersectionkernel and graph kernel furtherly improves the face recognition accuracy rate.
Finally, a summary of this article has been made and the direction of the furtherresearch has been described.
引文
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