| Presentation | 2012-11-08 Construction of Node-Permutation-Invariant Matrix Kernels based on a Linear-Algebraic Approach Shunsuke HIROSE, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | This paper addresses the issue of constructing a kernel between matrices which are symmetric, have different dimensions, and have no node identity (namely the kernel is invariant under a permutation of matrix elements' labels). Kernels between matrices are necessary in many analysis including structured data analysis. When constructing such matrix kernels, we face the following difficulties. First, it is not trivial how to compare matrices having different dimensions. Second, node permutation invariance is of required. It is not trivial how to costruct a kernel function which have node permutation invariance. In this paper we construct a matrix kernel by overcoming these difficulties. The key ideas are (1) by introducting projection operator, we project matrices of different dimensions to the same space, (2) by conducting eigen value decomposition, we decompose a input matrices to node permutation invariant part and non-invariant part (we need to project this part to a invariant function), (3) by projecting eigen vectors to probability density functions, we construct a node permutation invariant kernel. We demonstrate effectiveness of the proposed kernel through the experimental results using artificial data consisting of graph adjecency matrices. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | matrix kernel / node permutation invariance / projection operator / eigen value decomposition |
| Paper # | IBISML2012-69 |
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| Committee | IBISML |
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| Conference Date | 2012/10/31(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Information-Based Induction Sciences and Machine Learning (IBISML) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Construction of Node-Permutation-Invariant Matrix Kernels based on a Linear-Algebraic Approach |
| Sub Title (in English) | |
| Keyword(1) | matrix kernel |
| Keyword(2) | node permutation invariance |
| Keyword(3) | projection operator |
| Keyword(4) | eigen value decomposition |
| 1st Author's Name | Shunsuke HIROSE |
| 1st Author's Affiliation | Consulting Services Department, SAS Institute Japan Ltd.() |
| Date | 2012-11-08 |
| Paper # | IBISML2012-69 |
| Volume (vol) | vol.112 |
| Number (no) | 279 |
| Page | pp.pp.- |
| #Pages | 8 |
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