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Piecewise Linear Methods

The “piecewise linear methods” group at the Pattern Recognition Lab (LME) is to investigate machine learning methods and apply them in industry. Specifically, we are interested at piecewise linear (PWL) technology, which on one hand is the simplest extension of linear method, and on the other hand is flexible to obtain desired properties. For example, the hinge loss, one of the most commonly used function in classification, is a PWL function. In sparse regression field, the l1 norm is also a PWL function. We can also construct more complicated PWL functions, e.g., pinball loss, ramp loss, and sorted l1 norm, in order to enhance robustness and sparsity, and meanwhile to take the advantage of local linear analysis.

As one group of LME, who covers many aspects of machine learning, we will build a bridge from theoretical analysis, algorithm design, to industrial applications, such as CT image reconstruction and failure behavior analysis. Our major methodology is piecewise linear technique and the current interests include: 

  1. Quantile learning

  2. Sparse and robust learning

  3. Limited Angle Reconstruction

  4. Failure behaviours analysis for sheet metals

  5. Cancer staging based on automatic classification of confocal laser endomicroscopic images

 

          piecewise linear classification         piecewise linear penalty for sparse recovery

 

 

                                   

                                    failure behaviours of sheet metals (approx. pwl)