###### Abstract
To make use of machine learning approaches, we need to prepare the appropriate input--numerical (real-valued) vectors--that is compatible with these methods. This would give us the ability to perform meaningful analytics. As a result, these amino acid sequences should be converted into numeric characters in a way that preserves some sequential order information of the amino acids within each sequence. The most prevalent strategy in this area is one-hot encoding due to its simplicity [10]. Since we need to compute \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Pango** & \multirow{2}{*}{**Region**} & \multirow{2}{*}{**Labels**} & **No. Mutations** & **No. Sequences** \\
**Lineage** & & & & **S-Region/Genome** & \\ \hline B.1.1.7 & UK [12] & Alpha & 8/17 & 13,966 \\ B.1.351 & South Africa [12] & Beta & 9/21 & 1727 \\ B.1.617.2 & India [13] & Delta & 8/17 & 7551 \\ P.1 & Brazil [14] & Gamma & 10/21 & 26,629 \\ B.1.427 & California [15] & Epsilon & 3/5 & 12,784 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variants information and distribution in the dataset. The S/Gen. column represents the number of mutations in the S-region/entire genome. The total number of amino acid sequences in our dataset is 62,657. Figure 1: The SARS-CoV-2 genome is roughly 29–30 kb in length, encoding structural and non-structural proteins. Open reading frame (ORF) 1 ab encodes the non-structural proteins, and the four structural proteins: S (spike), E (envelope), M (membrane), and N (nucleocapsid) are encoded by their respective genes. The spike region is composed of 3821 base pairs, hence coding for 1274 amino acids. pairwise distances (e.g., Euclidean distance), one-hot encoding order preservation would not be operational [20]. To preserve order information of each sequence while being amenable to pairwise distance computation, \(k\)-mers (length \(k\) substrings of each sequence) are calculated and input to the downstream classification/clustering tasks [20; 21] (see Figure 2). In this work, we propose a robust feature-vector representation of biological sequences based on \(k\)-mers that, when combined with the appropriate feature selection, allows many different downstream clustering approaches to perform well on a variety different measures. This results in fast and efficient clustering methods to cluster the spike amino acid sequences of SARS-CoV-2. We demonstrate that our method performs considerably better than the baseline approach (called one-hot embedding), and the variants are clustered into unique clusters with high \(F_{1}\) score as a result, among other quality metrics. The following are the contributions of this paper:  
1. For efficient sequence clustering, we propose an embedding based on \(k\)-mers, and show that the downstream clustering methods cluster the variants with a high \(F_{1}\) score, among other quality metrics. 2. We performed experiments using different clustering algorithms and feature selection approaches and show the trade-off between the clustering quality and the runtime for these methods. 3. We use both hard and soft clustering approaches to study the behavior of different coronavirus variants in detail. 4. After comparison of our \(k\)-mers based algorithm with the baseline embedding method called one-hot embedding (OHE), we show that our proposed model is able to cluster the variants with higher clustering quality. The rest of the paper is organized as follows: Section 2 contains related work of our approach. Our proposed approach is detailed in Section 3. A description of the datasets used are given in Section 4. We provide a detailed discussion about the results in Section 5, and then we conclude our paper in Section 6.