Fundamentals of speech recognition
Fundamentals of speech recognition
Machine Learning
SIAM Review
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
On-Line Handwriting Recognition with Support Vector Machines " A Kernel Approach
IWFHR '02 Proceedings of the Eighth International Workshop on Frontiers in Handwriting Recognition (IWFHR'02)
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Learning the Kernel Matrix with Semidefinite Programming
The Journal of Machine Learning Research
Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA
Neural Computation
Embedding time series data for classification
MLDM'05 Proceedings of the 4th international conference on Machine Learning and Data Mining in Pattern Recognition
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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.