2007 Fiscal Year Final Research Report Summary
Embedding time series data in Euclidean space from DTW distances
| Project/Area Number |
18500116
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Intelligent informatics
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| Research Institution | Hiroshima City University |
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Principal Investigator |
HAYASHI Akira Hiroshima City University, Faculty of Information Sciences, Professor (60240909)
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| Co-Investigator(Kenkyū-buntansha) |
SUEMATSU Nobuo Hiroshima City University, Faculty of Information Sciences, Associate Professor (70264942)
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| Project Period (FY) |
2006 – 2007
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| Keywords | time series data / embedding / multi-dimensional scaling / dynamic time warping / kernel method / semidefinite proaramming |
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| Research Abstract |
One of the advantages of the kernel methods is that they can deal with various kinds of objects, not necessarily vectorial data with a fixed number of attributes.
In this paper, we develop kernels for time series data using dynamic time warping (DTW) distances. Since DTW distances are pseudo distances that do not satisfy the triangle inequality, a kernel matrix based on them is not positive semidefinite, in general. We use semidefinite programming (SDP) to guarantee the positive definiteness of a kernel matrix. We present neighborhood preserving embedding (NPE), an SDP formulation to obtain a kernel matrix that best preserves the local geometry of time series data. We also present an out-of-sample extension (OSE) for NPE.
We use two applications, time series classification and time series embedding for similarity search to validate our approach.
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