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Optimal Component Analysis

The Florida State Vision Group

By Xiuwen Liu,   Anuj Srivastava,   and Kyle Gallivan

Here the initial representation is computed using an ICA algorithm.  

Linear representations have been widely used in computer vision and many other areas due to their simplicity and efficiency with great success, including principle component analysis, Fisher discriminant analysis, and independent component analysis. All these problems can be viewed as a solution to a particular optimization problem, which is solved using properties of these problems. As such, these techniques can not be generalized easily to situations where these required properties are no longer valid. Optimal Component Analysis poses the problem of finding a linear representation as an optimization problem, which is then solved using an intrinsic stochastic gradient algorithm on the underlying manifolds, such as Grassmann, Stiefel, or any other ones. In particular, we have used it to search optimal linear representations for recognition/classification problems. Extensive experiments show the algorithm is effective for different kinds of data. The following shows a few examples. For more details, see references [1]. We also extend OCA to the kernel space as KOCA ([3] [4]). We have studied a set of efficient algorithms that provide a compromise between computational efficiency during the training phase and accuracy and see reference [5] for details.

References

  1. X. Liu, A. Srivastava, and Kyle Gallivan, ``Optimal linear representations of images for object recognition,'' IEEE Transactions on Pattern Recognition and Machine Intelligence, vol. 26, no. 5, pp. 662--666, 2004.
  2. X. Liu, A. Srivastava, and K. Gallivan, ``Optimal linear representations of images for object recognition,'' In the Proceedings of the International Conference on Computer Vision and Pattern Recognition, vol. I, pp. 229--234, 2003.
  3. Q. Zhang and X. Liu, ``Kernel optimal component analysis,'' In the Proceedings of the IEEE Workshop on Learning in Computer Vision and Pattern Recognition, 2004.
  4. W. Mio, Q. Zhang and X. Liu, ``Nonlinearity and optimal component analysis,'' In the Proceedings of the International Conference on Neural Networks, 2005.
  5. Q. Zhang and X. Liu, ``Hierarchical learning of optimal linear representations,'' In the Proceedings of the International Joint Conference on Neural Networks, 2003.

Acknowledgement

This material is based upon work supported by the National Science Foundation under Grant No. IIS-0307998.

Disclaimer

"Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).


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