图 书 馆
Haussler卷积核映射核的推广A Generalization of Haussler's Convolution Kernel - Mapping Kernel |
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| 课程网址: | http://videolectures.net/icml08_shin_ghsk/ |
| 主讲教师: | Kilho Shin |
| 开课单位: | 卡内基梅隆大学 |
| 开课时间: | 2008-07-28 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Haussler's convolution kernel provides a successful framework for engineering new positive semidefinite kernels, and has been applied to a wide range of data types and applications. In the framework, each data object represents a finite set of finer grained components. Then, Haussler's convolution kernel takes a pair of data objects as input, and returns the sum of the return values of the predetermined primitive kernel calculated for all the possible pairs of the components of the input data objects. Due to the definition, Haussler's convolution kernel is also known as the cross product kernel, and is positive semidefinite, if so is the primitive kernel. On the other hand, the mapping kernel that we introduce in this paper is a natural generalization of Haussler's convolution kernel, in that the input to the primitive kernel moves over a predetermined subset rather than the entire cross product. Although we have plural instances of the mapping kernel in the literature, their positive semidefiniteness was investigated in case-by-case manners, and worse yet, was sometimes incorrectly concluded. In fact, there exists a simple and easily checkable necessary and sufficient condition, which is generic in the sense that it enables us to investigate the positive semidefiniteness of an arbitrary instance of the mapping kernel. This is the first paper that presents and proves the validity of the condition. In addition, we introduce two important instances of the mapping kernel, which we refer to as the size-of-index-structure-distribution kernel and the edit-cost-distribution kernel. Both of them are naturally derived from well known (dis)similarity measurements in the literature (e.g. the maximum agreement tree, the edit distance), and are reasonably expected to improve the performance of the existing measures by evaluating their distributional features rather than their peak (maximum/minimum) features. |
| 关 键 词: | 卷积内核; 半正定内核; 细粒度组件 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-04-21：lxf |
| 阅读次数: | 71 |