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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Miyamoto, S. Sawazaki, K. |
| Copyright Year | 2011 |
| Description | Author affiliation: Master's Program in Risk Engineering, University of Tsukuba, Ibaraki 305-8573, Japan (Sawazaki, K.) || Department of Risk Engineering, University of Tsukuba, Ibaraki 305-8573, Japan (Miyamoto, S.) |
| Abstract | The method of kernel data analysis is now a standard tool in modern data mining. An implicit mapping into a high-dimensional feature space is assumed in this method, in other words, an explicit form of the mapping is unknown but their inner product should be known instead. Contrary to this common assumption, we propose a method of explicit mappings. The reason why we use explicit mappings is as follows. (1) The use of these mappings does not lose any fundamental information in kernel data analysis. (2) We have the same formulas in kernel methods with and without the explicit mappings. (2) Usually the derivation becomes simpler by using these mappings. (3) New applications of the kernel methods become possible using these mappings. Two types of the mappings are proposed, one of which uses uses Ф(xk) = ek (k = 1,…, N) while the second type uses Ф (xk) = $K^{1/2}$ ek, where K = (K(xi, xj)) is N × N matrix. As an application we consider L1 space fuzzy c-means clustering and lower dimensional approximation of kernel K. The effectiveness of the proposed method is shown by numerical examples. |
| Starting Page | 381 |
| Ending Page | 385 |
| File Size | 295143 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424473151 |
| ISSN | 10987584 |
| e-ISBN | 9781424473175 |
| e-ISBN | 9781424473168 |
| DOI | 10.1109/FUZZY.2011.6007494 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2011-06-27 |
| Publisher Place | Taiwan |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Kernel Approximation methods Data analysis Principal component analysis Matrix decomposition Presses Clustering algorithms |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Artificial Intelligence Theoretical Computer Science Software |
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