An Advanced Clustering with Toeplitz and Circulant Matrices and a Comparison Against Spectral Clustering, and K-Means

In an effort to increase computing efficiency, this work presents an improved spectral clustering technique that approximates the affinity matrix using Toeplitz and Circulant matrices. To preserve the quality of the clustering, we take advantage of the spectral characteristics of the similarity graph's Laplacian matrix. The Iris flower, Wine Quality, and Mushroom datasets are used to assess the approach. The following six clustering methods are contrasted: PCA combined with either spectral or K-means clustering, K-means clustering (with and without matrix approximation), and spectral clustering (with and without matrix approximation). The Silhouette Score, Fl score, precision, recall, and Adj usted Rand Index (ARI) are used to evaluate performance. The suggested method produces similar results to traditional methods with a significant reduction in computational cost, according to the results. In order to fully investigate the advantages of these matrices, architectures in spectral clustering are explored.