# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
## 3 Results
### Classification of Noisy Faces  
Working with noisy data is a challenge and generates many problems when developing classification systems. Denoising algorithms have to be applied before deriving the classifier and /or when using it. This can be the case in image processing, in which noise can corrupt the image. In an image recognition or verification system, noise could make the task difficult inducing more errors. This is why robust to noise systems are needed. To this end, several strategies can be implemented, for example using classical filters such as a Gaussian [67], bilateral [68], arithmetic [69], median [70] or Wiener filters [71]. However, all of these filters are good in some situations or type of noise, but not good enough in others.  
To overcome that issue, a denoising technique based on an empirical mode decomposition with [PERSON]'s functions was proposed in [55]. The system uses the capability of the bi-dimensional EMD decomposition to capture (almost all of) the noise in the first IMFs. Therefore, the noisy images are decomposed using a bi-dimensional EMD algorithm, then the first modes are eliminated and the rest of the modes are summed up together to recover the remaining image, almost without noise. In this specific work, the bi-dimensional EMD algorithm was the [PERSON]'s function in tension BEMD (GiT-BEMD) which uses [PERSON]'s functions to interpolate the surface of the images [72].  
The method used in [55] is depicted in Figure 5, in which we can see that the image is decomposed by means of the GiT-BEMD algorithm, the first IMF is discarded, the image is later reconstructed without the contribution of the noise and used to feed a classifier.  
Experiments were carried out using several type of noise (Gaussian, Uniform, Laplacian and Speckle) and at several levels (SNR from \(20_{dB}\) to \(-6_{dB}\)). The classification accuracy was compared to the ones obtained with classical filters (the ones named before). Classical filters were able to keep good performance when \(SNR>3_{dB}\), but they started to fail in much noisy scenarios, corresponding to \(3_{dB}>SNR>-6_{dB}\). The proposed method was able to maintain the same level of performance in all the ranges, from almost noise-free images (\(SNR=20_{dB}\)) to highly noisy images (\(SNR=-6_{dB}\)). Similar results occurred in the verification case, in which the Equal Error Rate (EER) were reported to  
Figure 5: (**a**) The new proposed approach to eliminate the noise and improve the classification accuracy is based on the GiT-BEMD decomposition. The high frequency IMFs are discarded and the (noiseless) image is reconstructed by summing up the rest of the modes. This is the image that will feed the classifier. (**b**) Comparison of classification results using a Support Vector Machine (SVM) and K-Nearest Neighbor (kNN) classifiers applied to noisy, filtered faces (Gaussian, Mean, Median) and GiT-BEMD processed faces.  
evaluate the results. Independently of the type of classifier used (SVM or k-NN), GiT-BEMD method obtained the lowest EER.  
Finally, it is interesting to note that the method is efficient for any type of noise and under high levels of it, and is transparent to the user, hence simple to apply. There are no parameters to tune because the GiT-BEMD algorithm is data-driven, and the IMFs of the images are obtained automatically. Bidimensional EMD algorithms, and specially GiT-BEMD algorithm, are able to decompose images in several IMFs, capturing the noise in the first IMF, which allows for training a classification system that is robust to noisy scenarios.