Improving ISOMAP Efficiency with RKS: A Comparative Study with t-Distributed Stochastic Neighbor Embedding on Protein Sequences

Abstract

Data visualization plays a crucial role in gaining insights from high-dimensional datasets. ISOMAP is a popular algorithm that maps high-dimensional data into a lower-dimensional space while preserving the underlying geometric structure. However, ISOMAP can be computationally expensive, especially for large datasets, due to the computation of the pairwise distances between data points. The motivation behind this study is to improve efficiency by leveraging an approximate method, which is based on random kitchen sinks (RKS). This approach provides a faster way to compute the kernel matrix. Using RKS significantly reduces the computational complexity of ISOMAP while still obtaining a meaningful low-dimensional representation of the data. We compare the performance of the approximate ISOMAP approach using RKS with the traditional t-SNE algorithm. The comparison involves computing the distance matrix using the original high-dimensional data and the low-dimensional data computed from both t-SNE and ISOMAP. The quality of the low-dimensional embeddings is measured using several metrics, including mean squared error (MSE), mean absolute error (MAE), and explained variance score (EVS). Additionally, the runtime of each algorithm is recorded to assess its computational efficiency. The comparison is conducted on a set of protein sequences, used in many bioinformatics tasks. We use three different embedding methods based on k-mers, minimizers, and position weight matrix (PWM) to capture various aspects of the underlying structure and the relationships between the protein sequences. By comparing different embeddings and by evaluating the effectiveness of the approximate ISOMAP approach using RKS and comparing it against t-SNE, we provide insights on the efficacy of our proposed approach. Our goal is to retain the quality of the low-dimensional embeddings while improving the computational performance.