Learning a kernel matrix for nonlinear dimensionality reduction
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
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Virtually all methods of learning dynamic systems from data start from the same basic assumption: that the learning algorithm will be provided with a sequence, or trajectory, of data generated from the dynamic system. In this paper we consider the case where the data is not sequenced. The learning algorithm is presented a set of data points from the system's operation but with no temporal ordering. The data are simply drawn as individual disconnected points. While making this assumption may seem absurd at first glance, we observe that many scientific modeling tasks have exactly this property. In this paper we restrict our attention to learning linear, discrete time models. We propose several algorithms for learning these models based on optimizing approximate likelihood functions and test the methods on several synthetic data sets.