图 书 馆
通过运输多面体的直方图上的内核Kernels on histograms through the transportation polytope |
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| 课程网址: | http://videolectures.net/mlss06tw_cuturi_khttp/ |
| 主讲教师: | Marco Cuturi |
| 开课单位: | 京都大学 |
| 开课时间: | 2007-02-25 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | For two integral histograms and of equal sum, the Monge-Kantorovich distance MK(r,c) between r and c parameterized by a d × d cost matrix T is the minimum of all costs taken over matrices F of the transportation polytope U(r,c). Recent results suggest that this distance is not negative definite, and hence, through Schoenberg's well-known result, may not be a positive definite kernel for all t > 0. Rather than using directly MK to define a similarity between r and c, we present in this talk kernels on r and c based on the whole transportation polytope U(r,c). We prove that when r and c have binary counts, which is equivalent to stating that r and c depict clouds of points of equal size, the permanent of their Gram matrix induced by the cost matrix T is a positive definite kernel under favorable conditions on T. We also show that the volume of the polytope U(r,c), that is the number of integral transportation plans, is a positive definite quantity in r and c through the Robinson-Schensted-Knuth correspondence between transportation matrices and Young Tableaux. |
| 关 键 词: | 积分直方图; 传输多面体; 正定核 |
| 课程来源: | 视频讲座网 |
| 最后编审: | 2019-07-16：cjy |
| 阅读次数: | 72 |