Exercise 1
Test the the prediction power of the kernel ridge regression in the presence of noise and outliers. The original data are samples from a music recording of Blade Runner by Vangelis Papathanasiou https://en.wikipedia.org/wiki/Vangelis.
- Read the audio file, BladeRunner.wav, using the Python SoundFile library (https:// org/project/SoundFile/). Then take 100 data samples starting from the 100,000th sample. Add white Gaussian noise at a 15 dB level and randomly “hit” 10% of the data samples with outliers (set the outlier values to 80% of the maximum value of the data samples).
- Find the reconstructed data samples using the unbiased kernel ridge regression method,that is,
yˆ(x) = y>(K + CI)−1κ(x).
Employ the Gaussian kernel with σ = 0.004 and set C = 0.0001. Plot the fitted curve of the reconstructed samples together with the data used for training.
- Repeat step (b) using C = 10−6,10−5,0.0005,0.001,0.01,0.
- Repeat step (b) using σ = 0.001,0.003,0.008,0.01,0.
- Comment on the results.
