Evaluating the Results of Applying Dimensionality Reduction Algorithms for Predicting the Clustering Performance

Abstract

The possibility of evaluating the effectiveness of different dimensionality reduction methods before the high-dimensional data clustering stage is studied. The main attention is paid to analyzing how well the data passed through different dimensionality reduction algorithms are suitable for subsequent clustering. Different dimensionality reduction algorithms (PCA, Isomap, Locally Linear Embedding, MDS, Spectral Embedding, T-SNE, and UMAP) are applied to four sets of high-dimensional gasoline spectra. The dimensionality reduction results are evaluated using the silhouette coefficient (SC) and the Davies-Bouldin index (DBI). After that, the evaluated data are clustered using different algorithms (DBSCAN, HDB-SCAN, K-Means, Spectral Clustering), and the clustering is estimated using the adjusted Rand index (ARS). Then, the correspondence between the clustering and dimensionality reduction estimates is assessed. Attempts to reliably evaluate most of the dimensionality reduction algorithms using the cluster silhouette coefficient and the Davies-Bouldin index have been met with success. The Chebyshev, Euclidean, Manhattan, and square Euclidean metrics have yielded the most accurate results. Also, the two most effective algorithms T-SNE and UMAP were the only ones that could be evaluated using the DBI assessment. The obtained data can be used to select the optimal dimensionality reduction algorithm prior to perform clustering of multidimensional data, as well as to evaluate the data preprocessing quality. The correlation between the evaluations of dimensionality reduction methods and the efficiency of subsequent clustering has been successfully demonstrated. The T-SNE and UMAP algorithms have shown the best results in evaluation, and the Chebyshev, Euclidean, Manhattan, and square Euclidean metrics have given the most accurate results for these algorithms.