# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
###### Abstract  
In many machine learning applications, measurements are sometimes incomplete or noisy resulting in missing features. In other cases, and for different reasons, the datasets are originally small, and therefore, more data samples are required to derive useful supervised or unsupervised classification methods. Correct handling of incomplete, noisy or small datasets in machine learning is a fundamental and classic challenge. In this article, we provide a unified review of recently proposed methods based on signal decomposition for missing features imputation (data completion), classification of noisy samples and artificial generation of new data samples (data augmentation). We illustrate the application of these signal decomposition methods in diverse selected practical machine learning examples including: brain computer interface, epileptic intracranial electroencephalogram signals classification, face recognition/verification and water networks data analysis. We show that a signal decomposition approach can provide valuable tools to improve machine learning performance with low quality datasets.  
empirical mode decomposition; machine learning; sparse representations; tensor decomposition; tensor completion +
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such big deep learning models requires accessing to extremely large datasets, which are not always available or they are too expensive to obtain.  
Standard training algorithms for modern deep learning models assume that datasets are \"infinite\", i.e., they are large enough to allow successful training of very large models. In practice, and particularly when an image dataset is not large enough, it is common practice to artificially generate additional samples by applying a composition of random class-preserving transformations on available data samples such as crops, translations and rotations, which is widely known as \"data augmentation\".  
Moreover, available ML algorithms not only assume \"infinite\" datasets, they were also designed for perfect input data samples. Nevertheless, in practical applications data samples often suffer from imperfections, such as missing or noisy features. For example, when recording electroencephalographic (EEG) signals, corrupted data can be originated from impedance mismatching, electrode disconnection, body movements, etc. [3]. Other practical problems where data samples can be incomplete include: computer vision systems where objects in the view field can be partially occluded [4]; recommendation systems built from the information gathered by different users where not all the users have fully completed their forms [5]; or medical datasets where typically not all tests can be performed on all patients [6].  
In this article, we review recent techniques to alleviate the serious consequences of having different types of low-quality datasets in ML applications. We demonstrate that, by using decomposition methods, we can model one-dimensional and multi-dimensional signals, which allow us to artificially generate class-preserving new signals or make inference on missing/corrupted features.  
This article is organized as follows: in Section 1.1, a review of the state-of-the-art approaches for low-quality datasets in ML is given; in Section 1.2, the mathematical notation used throughout the paper is introduced; in Section 2, a unified view of signal decomposition methods is presented, which includes: subspace approximation, Empirical Mode Decomposition (EMD), sparse representations and tensor decompositions; Section 3 covers practical applications including ML problems in neurosciences, face detection/classification and analysis of water networks data; finally, the main conclusions and discussion are presented in Section 4.