# Decomposition Methods for Machine Learning with Small, Incomplete or Noisy Datasets
## 2 Methods
### Comparison of Methods for ML with Low-Quality Datasets  
In Table 1, we summarize all the methods discussed in this paper and compare them in terms of their main characteristics, shortcomings, advantages and main applications. A detailed reference to the sections of this article where each of the methods is presented and discussed is given. Furthermore, main bibliographic references are indicated for each of the approaches.  
\begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & **Characteristics** & **Shortcomings** & **Advantages** & **Application** & **References** \\ \hline
**Class preserving transforms** & \(\text{Ad-hoc}\): mostly images oriented but scene extensions to other types of data were explored & Limited theory available; difficult to apply to arbitrary type datasets & Easy to use; widely available in deep learning platforms & Data augmentation [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17] \\ \hline
**Empirical Decomposition (EMD) based data generation** (Section 2.4, 3.1.2, 3.1.3 and 3.2) & Ad-hoc based on the manipulation and recombination of Intrinsic Mode & Lack of theoretical ground Functions (IMFs); Functions (IMFs); & Easy to use; capture dataset discriminative features & E electroencephalography (EEG) and invasive EEG (EEG) data augmentation and denoising & E electroencephalography (EEG) data [45, 52, 53, 54, 55] \\ \hline
**Transform domain based data generation** & \(\text{Ad-hoc}\): based on the manipulation and recombination components obtained by Discrete Cosine Transform (DCT), Wavelets, etc. & Lack of theoretical ground discriminative features & Easy to use; capture dataset discriminative features & iEEG data augmentation [45, 52, 53, 54, 55] \\ \hline
**Statistical** & **impulation** & Preprocessing step in ML; exploit statistical properties of databases; wide variety of methods, from simple ones (mean) to more sophisticated (regression, k-Nearest Neighbor (kNN), Self Organization & Does not use the class label information of data samples & Computationally efficient & ML with incomplete or corrupted data [18, 19, 20, 21, 22, 23] \\ \hline
**Probabilistic** & **modeling** & \(\text{Gaussian Mixture Model (CMBO)}\) as data model. Bayesian classification; fitting model and classifiers in an Expectation-Maximization (EM) fashion; can be adapted to deep neural networks. & Computationally expensive & Incorporates class label information of data samples; elegant theoretical approach & ML with incomplete or corrupted data [19, 24, 28] \\ \hline
**Low-rank matrix completion** & \(\text{Based on Singular Value Decomposition (SVD)}\) & \(\text{Computiationally very}\) & \(\text{Computiationally very}\) & \(\text{Incorporates class label information of data samples}\) & ML with incomplete or corrupted data [25, 26, 27] \\ \hline
**Tensor decomposition (TD) based imputation** (Sections 2.5, 3.1.1 and 3.3) & \(\text{Proprocessing step in ML; based on N-rank TDs (e.g., Tucker, CAMDCCOMP/FAFAAC (CP), etc.) or sparse TDs & Does not use the label information of data samples in multimodal data & Exploits intricate relationship among modes in multimodal data & ML with incomplete or corrupted data [50, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85