COMPLEX SYSTEMS
Current Research - Multisensor Fusion
 Fig. 2: Results: b) Performance of our VQQL learning technique for various state sizes. (Click image for larger view) |
There is currently a wide choice of function estimators, and it is often more effective and practical to fuse them rather than choosing a "best" one. An optimal projective fuser was proposed earlier based on the lower envelope of error regressions of the estimators. In most practical cases, however, the error regressions are not available and only a finite sample is given. Consequently this optimal fuser is hard to implement and furthermore guarantees only the asymptotic consistency.
We are currently developing a projective fuser based on the nearest neighbor concept, which is easy to implement. Under fairly general smoothness and non-smoothness conditions on the individual estimators, we show that this fuser's expected error is close to optimal with a high probability, for a finite sample and irrespective of the underlying distributions. This performance guarantee is stronger than the previous ones for projective fusers and also implies asymptotic consistency. The required smoothness condition, namely Lipschitz continuity, is satisfied by sigmoid neural networks and certain radial-basis functions. The non-smoothness condition requires bounded variation which is satisfied by k-nearest neighbor, regressogram, regression tree, Nadaraya-Watson and feedforward threshold network estimators.
We applied this method to overcome the practical difficulties in training sigmoidal neural networks, namely the solution is very sensitive to the initial conditions and the learning rate of the back propagation algorithm. We trained six neural networks using different starting weights and learning rates. Then we combined the outputs of he neural networks using the nearest neighbor projective fuser. The fused estimate is significantly better than any of the individual estimates, and interestingly the overall worst neural network is used to closely approximate the function in certain localities where it is better than others.
We are currently in the process of applying this fuser for predicting embrittlement prediction and mesoscale grain growth computations.
- N.S.V. Rao, Nearest neighbor projective fuser for function estimation, Proc. Int. Conf. on Information Fusion, 2002.
- N. S. V. Rao, Projective method for generic sensor fusion problem, Proc. Int. Conf. on Multisensor Fusion and Integration for Intelligent Systems, August 15-18, 1999, Taipei, Taiwan.
- N. S. V. Rao, On optimal projective fusers for function estimators, Proc. Int. Conf. on Information Fusion, 1999.
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