PWA (Piecewise affine) model is natural and powerful extension of commonly used linear models. But, its identification from noisy data set has been extremely challenging problem so far, and our group have been developing the new method for this problem.
In our method, the model is also represented by a set of data and constructed by compressing the noisy data set obtained from the real world. And, we developed compression strategy which removes undesired noise from the data set while preserving essential property of the target system. The compression is performed via l1 optimization, which can enjoy the benefits of rapidly growing computation technology, and can be performed for the problems with practical size.
Now, our interest is to develop the strategy for more larger scale / higher dimensional problems and to search for stimulating applications.
This movie shows how the obtained PWA map changes according to the power of compression.