Biological sequence analysis is crucial in understanding the sequence structure, function, and evolutionary relationships. In traditional methods, using Euclidean distance metrics is common in measuring the similarity between sequence embeddings. However, they fail to capture sequence space’s inherent curvature and spherical nature. Therefore, we explore the application of spherical geometry and distance metric, circular arc length (CAL) based distance for comparing biological sequence embeddings. Spherical geometry is a non-Euclidean geometry that models the surface of a sphere, accounting for its curvature. By leveraging CAL, we can more accurately measure the pairwise distances between bio-sequence embeddings. In this study, we propose the utilization of CAL for comparing bio-sequence embeddings. We develop a function to compute the CAL distance between two sequence embeddings, enabling researchers to accurately measure the similarity between sequences while considering the underlying spherical geometry. Incorporating spherical geometry enables a more comprehensive understanding of the relationships and similarities between biological sequences, improving various downstream tasks such as classification, clustering, and evolutionary analysis. Our experimental evaluation demonstrates the advantages of using a spherical distance metric over Euclidean metrics for bio-sequence analysis. Our proposed CAL-based approach outperforms the Euclidean geometry-based baselines by depicting a huge performance improvement for the protein subcellular location classification task. In our experiments, accuracy is improved by 52.5% and 60. 3% compared to the PWM2Vec and Autoencoder methods, respectively, corresponding to the DT classifier.

The t-distributed stochastic neighbor embedding (t-SNE) is a method for interpreting high dimensional (HD) data by mapping each point to a low dimensional (LD) space (usually two-dimensional). It seeks to retain the structure of the data. An important component of the t-SNE algorithm is the initialization procedure, which begins with the random initialization of an LD vector. Points in this initial vector are then updated to minimize the loss function (the KL divergence) iteratively using gradient descent. This leads comparable points to attract one another while pushing dissimilar points apart. We believe that, by default, these algorithms should employ some form of informative initialization. Another essential component of the t-SNE is using a kernel matrix, a similarity matrix comprising the pairwise distances among the sequences. For t-SNE-based visualization, the Gaussian kernel is employed by default in the literature. However, we show that kernel selection can also play a crucial role in the performance of t-SNE.In this work, we assess the performance of t-SNE with various alternative initialization methods and kernels, using four different sets, out of which three are biological sequences (nucleotide, protein, etc.) datasets obtained from various sources, such as the well-known GISAID database for sequences of the SARS-CoV-2 virus. We perform subjective and objective assessments of these alternatives. We use the resulting t-SNE plots and k-ary neighborhood agreement (k-ANA) to evaluate and compare the proposed methods with the baselines. We show that by using different techniques, such as informed initialization and kernel matrix selection, that t-SNE performs significantly better. Moreover, we show that t-SNE also takes fewer iterations to converge faster with more intelligent initialization.