Exploring unsupervised feature extraction algorithms: tackling high dimensionality in small datasets.

Small datasets are common in many fields due to factors such as limited data collection opportunities or privacy concerns. These datasets often contain high-dimensional features, yet present significant challenges of dimensionality, wherein the sparsity of data in high-dimensional spaces makes it difficult to extract meaningful information and less accurate predictive models are produced. In this regard, feature extraction algorithms are important in addressing these challenges by reducing dimensionality while retaining essential information. These algorithms can be classified into supervised, unsupervised, and semi-supervised methods and categorized as linear or nonlinear. To overview this critical issue, this review focuses on unsupervised feature extraction algorithms (UFEAs) due to their ability to handle high-dimensional data without relying on labelled information. From this review, eight representative UFEAs were selected: principal component analysis, classical multidimensional scaling, Kernel PCA, isometric mapping, locally linear embedding, Laplacian Eigenmaps, independent component analysis and Autoencoders. The theoretical background of these algorithms has been presented, discussing their conceptual viewpoints, such as whether they are linear or nonlinear, manifold-based, probabilistic density function-based, or neural network-based. After classifying these algorithms using these taxonomies, we thoroughly and systematically reviewed each algorithm from the perspective of their working mechanisms, providing a detailed algorithmic explanation for each UFEA. We also explored how these mechanisms contribute to an effective reduction in dimensionality, particularly in small datasets with high dimensionality. Furthermore, we compared these algorithms in terms of transformation approach, goals, parameters, and computational complexity. Finally, we evaluated each algorithm against state-of-the-art research using various datasets to assess their accuracy, highlighting which algorithm is most appropriate for specific scenarios. Overall, this review provides insights into the strengths and weaknesses of various UFEAs, offering guidance on selecting appropriate algorithms for small high-dimensional datasets.