# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
## 4 Conclusions and Discussion  
Machine learning methods were typically designed by assuming that training data is perfect and of infinite size. However, in real life, machine learning practitioners need to deal with imperfect training data or datasets of limited size. To alleviate the problem of incomplete/corrupted datasets or to increase the size of a training dataset, it is necessary to use powerful data models that can capture the essential features of the dataset. In this article, a unifying introduction to signal decomposition methods is presented, which are available in different flavors but sharing a common property: every signal in a dataset (sample) can be written as a linear combination of elementary, simpler components.  
The main idea behind the reviewed decomposition models is that they are able to be learned from a limited or low-quality dataset. Once the right model for the dataset of interest is learned from the available samples, one can use it for different tasks: (1) to complete missing entries in data samples, (2) to compensate distortions or eliminate noise in data samples, and (3) to artificially create class-preserving new data samples.  
We have demonstrated that low-rank, sparse coding and EMD decomposition methods are excellent candidates for models that can capture essential information of a dataset. All these methods can be applied to vector as well as to tensor datasets. However, some issues remain and there is space for improvement in future research. For example:  
* The decomposition methods reviewed in this work for imputation of missing/corrupted values do not exploit the class label information in a supervised learning scenario. A possible further improvement of current methods is to incorporate label information into the decomposition models. We believe that missing data values could be better recovered if the class label of the corresponding data sample is known.
* EMD based data augmentation was developed in an ad-hoc fashion. We believe that more theoretical insights could be explored allowing future improvements, for example, by re-designing the way that IMFs are calculated in order to produce class-preserving artificial samples.  
This review article illustrates the application of a variety decomposition methods to vector and tensor datasets in a wide range of technological areas including: classification of brain signals (EEG and iEEG), identification of face images and analysis of water network data. While this represents a non-exhaustive review of existing methods and applications of machine learning with low-quality datasets, we believe that it can be a useful reference for machine learning practitioners who are normally faced with incomplete, noisy or small datasets, and can inspire new methods to address these fundamental problems.  
Conceptualization, C.F.C., J.S.-C. and S.Z.; investigation C.F.C., J.S.-C., P.M.-P., S.Z. and T.T.; writing--Original draft preparation C.F.C., J.S.-C., P.M.-P. and T.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by JST CREST Grant Number JPMJCR1784 and by the University of Vic--Central University of Catalonia (ref. R0947). J.S.-C. work is also based upon work from COST Action CA18106, supported by COST (European Cooperation in Science and Technology).  
We are grateful to the anonymous reviewers for their valuable comments, which helped us to improve the first version of this manuscript. The authors declare no conflict of interest.