Comparativo visual e analítico de algoritmos de redução de dimensionalidade

Abstract

High-dimensional data often pose challenges in terms of visualization and utilization in classification algorithms. Processing such data can be time-consuming and computationally demanding. However, there exist low-dimensional datasets that exhibit structures utilized in the field known as Manifold Learning. To study the structures of the data, as well as reduce the input for classifiers, optimize processing time, and decrease data complexity, dimensionality reduction algorithms are employed. In this work, a selection of algorithms including PCA, MDS, Isomap, LLE, Random Trees, t-SNE, and Autoencoder were used to identify the approach that best represented the information visually, while assessing whether the nature of the data was affected by distortions occurring during the dimensionality reduction process. Synthetic datasets such as Swiss Roll, S Curve, and Hello, as well as real datasets like MNIST and Iris, were utilized to apply these dimensionality reduction algorithms. The results of this study showed that, based on Kruskal Stress metric, the algorithms exhibited distortions, except for PCA on the Hello dataset. In terms of visual comparison, for Swiss Roll, S Curve, Hello, and Iris datasets, PCA and MDS algorithms yielded better interpretability, whereas t-SNE achieved superior results for MNIST, contrasting with other algorithms for both datasets.