A General Exponential Framework for Dimensionality Reduction

By Su-Jing Wang, Shuicheng Yan, Jian Yang, Chun-Guang Zhou, Xiaolan Fu. IEEE Transactions on Image Processing, 2014

321 citations recorded by the source corpus.

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/d264cd1b81c77fca67d4abadb84dd684f928512c

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In Artificial Intelligence

  1. Diego Raphael Amancio
  2. Gustavo R. Ferreira
  3. Filipi Nascimento Silva
  4. Luciano da Fontoura Costa
  5. Henrique Ferraz de Arruda
  6. Cesar Henrique Comin
  7. Felipe L. Gewers

In Computer Vision and Pattern Recognition

  1. Diego Raphael Amancio
  2. Luciano da Fontoura Costa
  3. Cesar Henrique Comin

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