| 摘要: |
| 传统的Laplacian 特征映射是基于欧氏距离的近邻数据点的保持,近邻的高维数据点映射到内在低维空间后仍为近邻点,高维数据点的近邻选取最终将影响全局低维坐标.将测地线距离和广义高斯函数融合到传统的Laplacian 特征映射算法中,首先提出了一种基于测地线距离的广义高斯型Laplacian 特征映射算法(geodesicdistance-based generalized Gaussian LE,简称GGLE),该算法在用不同的广义高斯函数度量高维数据点间的相似度时,获得的全局低维坐标呈现出不同的聚类特性;然后,利用这种特性进一步提出了它的集成判别算法,该集成判别算法的主要优点是:近邻参数K 固定,邻接图和测地线距离矩阵都只构造一次.在木纹数据集上的识别实验结果表明,这是一种有效的基于流形的集成判别算法. |
| 关键词: 流形学习 Laplacian 特征映射 广义高斯函数 测地线距离 集成 |
| DOI： |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60773016, 60373029 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2007AA01Z168 (国家高技术研究发展计划(863)); the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No.20050004001 (国家教育部博士点基金); the Scientific Research Foundation of Sichuan Provincial Education Department of China under Grant No.07ZA121 (四川教育厅重点项目) |
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| Geodesic Distance-Based Generalized Gaussian Laplacian Eigenmap |
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ZENG Xian-Hua,LUO Si-Wei,WANG Jiao,ZHAO Jia-Li
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| Abstract: |
| The conventional Laplacian Eigenmap preserves neighborhood relationships based on Euclidean
distance, that is, the neighboring high-dimensional data points are mapped into neighboring points in the low-dimensional space. However, the selections of neighborhood may influence the global low-dimensional coordinates. In this paper, both the geodesic distance and generalized Gaussian function are incorporated into Laplacian eigenmap algorithm. At first, a generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance (GGLE) is proposed. The global low-dimensional coordinates obtained by GGLE have different clustering properties when different generalized Gaussian functions are used to measure the similarity between the high-dimensional data points. Then, this paper utilizes these properties to further propose the ensemble-based discriminant algorithm of the above-motioned GGLE. The main advantages of the ensemble-based algorithm are: The neighborhood parameter K is fixed and to construct the neighborhood graph and geodesic distance matrix needs
one time only. Finally, the recognition experimental results on wood texture dataset show that it is an efficient ensemble discriminant algorithm based on manifold. |
| Key words: manifold learning Laplacian eigenmap generalized Gaussian function geodesic distance ensemble |
